Présentation de la revue (Description courte) Le USK Journal of Education est une revue scientifique à comité de lecture publiée par USK University Press (Kinshasa). Elle explore les approches décoloniales, symboliques et cognitives de l’éducation africaine, en mettant un accent particulier sur l’écriture Mandombe, la pédagogie cognitive, la reconstruction épistémologique et les innovations éducatives basées sur les valeurs africaines. La revue publie des articles empiriques, théoriques et appliqués dans les domaines de la psychopédagogie, de la neuroéducation, de la formation des enseignants, de la didactique des sciences, et de la recherche curriculaire décoloniale.
Neurocognitive Effects of Mandombe Writing Practice: A Cross-Sectional Study
Title From Grades to Phases: Learning Trajectories in Pilot Mandombe Nsandas of Kinshasa (2019–2023) Ntima et al. --- Abstract This study examines how a pilot implementation of the new official Mandombe pedagogy alters the way learning trajectories should be described and assessed in Congolese primary schooling. We analyse longitudinal records from 2019–2023 in a subset of CENA’s Nsandas in Kinshasa that were designated as trial sites for the updated MEN-D curriculum and compare them with neighbouring schools following the standard national programme. The work tests, in a limited but concrete way, Nsiangani’s (2014) hypothesis that colonial age-grade assessment logic misrepresents the progress of children educated through indigenous symbolic systems, and that alternative phase-based units become necessary once Mandombe literacy is the base script. For pilot Nsanda learners we reconstructed trajectories in two formats: (a) the conventional grade-per-year model (age, repetition, subject marks) and (b) a four-phase model derived from the official Mandombe pedagogy: Symbolic control (S), Geometric fluency (G), Transfer to mathematics and science (T), and Project/collective application (P). Each learner-year was independently coded to the highest phase consistently evidenced that year. For comparison schools we described trajectories in grade units only and explored whether an analogous phase coding was workable. Under standard age-grade logic, pilot Nsanda trajectories appear irregular: reduced overage, frequent multi-grade promotion, and abrupt jumps in mathematics, literacy and project work. When the same data are replotted in phase units, a more coherent pattern emerges: many learners spend an extended period consolidating Mandombe symbolism (S), followed by faster movement through G, T and P, during which cross-domain gains cluster in a few years rather than spreading evenly across the cycle. Comparison schools show slower, more linear grade progression, higher overage, and fewer clustered leaps; attempts to apply the S–P phase rubric there proved unstable and conceptually forced. We do not claim that all Nsandas behave identically, that pilot centres are universally superior, or that grades should be abolished. Our more modest conclusion is that in the Nsandas piloting the official Mandombe pedagogy, the conventional grade-per-year unit ceases to be the most informative descriptor of learning. A phase-based assessment logic, anchored in the internal structure of the curriculum, captures their trajectories more accurately and avoids misclassifying rapid, structurally organised progress as “irregular.” The protocol is simple and replicable so that other centres—including non-pilot Nsandas—can test whether similar phase signatures appear in their own data. --- 1. Introduction 1.1 Age-graded schooling as an industrial technology The age-graded classroom, now taken for granted worldwide, is a relatively recent European invention. Until the late 18th century, most European schools were mixed-age, often organised in one room where older children informally assisted younger ones. Age-segregated grades emerged in German states and Prussia as part of wider reforms that linked mass schooling to state-building, military discipline and later to industrial needs: the efficient production of punctual, standardised workers and citizens. As industrialisation advanced, age-graded, subject-segmented schools spread across Western Europe and North America, often displacing older monitorial or community-based models. European empires then exported this organisational form to their colonies, where it served both as a symbol of “modernity” and as an instrument for producing a disciplined, low-autonomy workforce. In the Congo, the colonial school was explicitly designed around these logics, with indigenous languages and symbolic systems displaced in favour of French and imported curricula. The age-grade grid thus arrived not as a neutral pedagogical innovation, but as part of a broader industrial-colonial package. 1.2 Why this matters for Mandombe The MEN-D Mandombe programme re-centres an indigenous script as the primary literacy and cognitive scaffold. In the new official pedagogy, letters are geometric objects; reading and writing involve mastery of rotation, symmetry and branch logic; and these structures are progressively extended to mathematics, science and collective projects. In such a curriculum, the unit that organises content and expectations is no longer simply “one grade per year” but the learner’s position in a series of symbolic-cognitive phases. Nsiangani (2014) argued that evaluating such programmes solely through the inherited age-grade logic risks systematic distortion. Where a curriculum is designed around phases (long installation of a powerful symbolic system, then rapid cross-domain leverage), an assessment grid that assumes linear progression can misclassify successful trajectories as “irregular,” “unstable” or even “suspect.” This concern is not theoretical: pilot Nsandas were often asked by inspectors to explain why some learners “skipped” grades or completed cycles “too quickly,” as if compression were evidence of manipulation rather than a design feature of the pedagogy. 1.3 Focus of this study This paper concentrates on a subset of Nsandas in Kinshasa that were officially designated as pilot sites for the updated Mandombe pedagogy and assessment tools. Other Nsandas continued with earlier variants of the programme or hybrid models; we do not assume their trajectories match those described here. Using only routine records from 2019–2023, we ask three questions: 1. How do learners in pilot Nsandas appear when described purely through the colonial-industrial age-grade logic (age, grade, repetition, annual marks)? 2. Can the same data be re-described through a small set of curriculum-anchored learning phases that better reflect the internal structure of the official Mandombe pedagogy? 3. Do these phase-based descriptions differ in systematic ways from trajectories observed in neighbouring non-Mandombe schools that operate entirely within the inherited age-grade model? The aim is modest and empirical: to see whether the choice of assessment unit (grade vs phase) materially alters how the pilot centres’ work is perceived and whether a phase logic is operationally usable without heroic data requirements. --- 2. Conceptual framework 2.1 Colonial age-grade logic revisited Age-grading combines three elements: chronological age, the notion of a fixed curriculum slice per year, and promotion rules that make the grade the primary indicator of progress. Historians link its consolidation to 18th–19th century German/Prussian reforms and to 19th-century industrial rationalisation, where factories and bureaucracies required cohorts of workers trained to similar specifications at each step. In African colonies, age-graded schools were introduced as part of a “civilising” mission, but they also served labour and administrative needs: they produced clerks, interpreters and low-level technicians who were literate in the coloniser’s language and accustomed to hierarchical obedience. When independence came, many countries, including the DRC, retained this model with only limited adaptation. The age-grade ladder thus remains not only a technical device but a historical trace of industrial-colonial priorities. 2.2 Phases in the official Mandombe pedagogy The new Mandombe pedagogy, as validated by the DRC Ministries of Education and of Higher Education & Scientific Research, structures learning around overlapping phases rather than calendar years. For this study, and in consultation with trainers, we summarise four observable phases: S – Symbolic control: secure decoding and production of basic Mandombe units, with attention to mvuala, branches, and orientation; frequent teacher scaffolding. G – Geometric fluency: spontaneous manipulation of rotations and mirrorings; use of Mandombe forms in games and self-initiated drawings; internal assessments at mastery level for geometric tasks. T – Transfer to maths/science: explicit use of Mandombe structures to reason about number, operations and simple physical relations (e.g., branch-based grouping, symmetry in equations). P – Project/collective application: integration of Mandombe and mathematics in multi-step group projects; documented initiative, explanation to peers, and problem-solving. The phases are not tied to age; a late-starting 11-year-old and a 7-year-old may both be in Phase S, and the older learner may move through G/T/P faster once symbolic control is achieved. 2.3 Hypotheses We formulate three cautious hypotheses for the pilot Nsandas: H1 – Descriptive mismatch. When plotted purely in age-grade terms, pilot Nsanda trajectories will appear irregular (compressed cycles, multi-grade promotion, non-linear marks). H2 – Phase coherence. Recoding the same data in S–P phases will reveal more regular trajectories (longer S, then faster G/T/P) with cross-domain gains clustering around phase transitions. H3 – Programme specificity. Attempts to apply the S–P rubric to neighbouring non-Mandombe schools, which follow the inherited industrial age-grade model without Mandombe, will prove less reliable and less informative, indicating that the phase logic is anchored in the Mandombe pedagogy rather than in generic schooling. If any of these fail—for instance, if grade-logic already describes pilot Nsanda trajectories well, or if phase coding is noisy and uninformative—then the case for revising assessment logic weakens. --- 3. Method 3.1 Setting: pilot Nsandas and comparison schools The study covers several Nsandas in Kinshasa formally designated by the MEN-D steering committee as pilot sites for the new official Mandombe pedagogy and internal assessment tools. These centres applied the full maternal-language + Mandombe curriculum from early primary and received additional supervision and documentation support. For comparison, we selected nearby public or low-fee private schools using the standard national curriculum in French and Latin script, with conventional age-graded classes and no Mandombe instruction. These schools represent the industrial-colonial model in its current Congolese form. 3.2 Participants and inclusion Within pilot Nsandas and comparison schools, we included learners who: had at least three consecutive learner-years recorded between 2019 and 2023; remained in the same school during that interval; had complete annual records (age, grade, core subject marks, teacher comments). This yielded several hundred learner-years across sites. The sample is thus institutionally focused (on centres), not nationally representative. 3.3 Data and coding For each learner-year, we extracted: Administrative data: age, official grade, promotion/repetition, years over official age for grade; Academic data: annual marks in language(s), mathematics, science and social studies; Internal Mandombe data (pilot Nsandas only): scores on existing Mandombe mastery checks; Teacher comments: qualitative notes on autonomy, project participation and difficulties. 3.3.1 Phase assignment in pilot Nsandas Using curriculum documents and teacher interviews, we built an explicit rubric for assigning each learner-year to S, G, T or P based on documented evidence (work samples, assessments, comments). Two independent coders, blind to later outcomes, applied the rubric; inter-rater agreement was checked and disagreements resolved by consensus. Only the highest phase consistently supported by multiple indicators in that year was assigned. 3.3.2 Exploratory phase coding in comparison schools To test H3, we attempted to apply an adapted version of the rubric to comparison schools, substituting generic indicators (e.g., use of diagrams in maths) where explicit Mandombe criteria were absent. This exercise was explicitly labelled exploratory; the expectation was that the rubric would map poorly onto data from schools that do not organise learning around the same symbolic phases. 3.4 Analytic strategy Analyses proceeded in three steps: 1. Grade-logic description for pilot Nsandas and comparison schools: age-grade placement, overage, repetition, time to complete cycles, and mean marks by grade. 2. Phase-logic description for pilot Nsandas: time spent in each phase, sequences of S–P over calendar years, and alignment of phase transitions with changes in marks and comments. 3. Feasibility and stability of phase coding in comparison schools: agreement between coders, interpretability, and relation (or lack thereof) to changes in marks. Given the institutional sample and reliance on routine data, the emphasis was on robust descriptive patterns rather than on fine p-values. --- 4. Results (summary) 4.1 Pilot Nsandas in grade units Viewed purely through age-grade metrics, pilot Nsanda learners displayed: substantially lower overage than peers in comparison schools; compressed cycles, with some learners promoted across more than one grade over the period; non-linear mark trajectories, with marked jumps in mathematics and general average over one or two years. From a conventional inspector’s perspective, these patterns can appear suspicious or unstable, as they depart from industrial expectations of steady, grade-by-grade progress. 4.2 Pilot Nsandas in phase units Replotting the same learners in S–P phase units produced more interpretable trajectories: most spent a considerable initial period in Phase S, where grades changed slowly and marks rose modestly; once evidence supported transition into Phase G, gains in mathematics and general reasoning often accelerated; for learners reaching T and P, cross-domain gains (mathematics, science, project work) clustered within a short calendar window, explaining multi-grade promotions. The apparent “irregularity” under grade logic thus corresponded to phase transitions designed into the Mandombe pedagogy: a long investment in symbolic installation, then rapid leverage. 4.3 Comparison schools Comparison schools, operating under the inherited age-grade model without Mandombe, showed: higher and more persistent overage; fewer or no multi-grade promotions; gradual, incremental improvements in marks without sharp clustering. Attempts to apply the S–P rubric in these schools yielded lower coder agreement and ambiguous trajectories; phase labels did not align consistently with shifts in marks or comments. This supports the view that the phase framework is not a generic cognitive ladder but is specifically tied to the structure of the Mandombe curriculum. --- 5. Discussion The findings from these pilot Nsandas suggest that once an indigenous symbolic system like Mandombe becomes the backbone of teaching, the inherited industrial-colonial age-grade logic no longer provides the most faithful description of learning. A phase-based logic, grounded in the official Mandombe pedagogy, aligns better with observed trajectories and helps avoid misreading rapid, structured progress as administrative irregularity. We do not infer that all Nsandas in the DRC share this pattern; only a subset were piloting the new pedagogy during 2019–2023, and our data are limited to those centres. Nor do we treat phase coding as infallible: it remains partly interpretive and requires prospective refinement. The study nevertheless shows that with only routine school records, it is possible to operationalise an alternative assessment unit that respects the internal design of an indigenous curriculum and to put it into empirical conversation with the age-graded model inherited from European industrial history. Future work should replicate the protocol in non-pilot Nsandas and other provinces, refine phase indicators, and examine how phase-based trajectories relate to external benchmarks such as national examinations and later academic or vocational success.
(c) Copyright USK Journal of Education 2024
Developing African Curriculum through Symbolic Literacy: The Mandombe Case
Title From Grades to Phases: Learning Trajectories in Pilot Mandombe Nsandas of Kinshasa (2019–2023) Nzaza et al. --- Abstract This study examines how a pilot implementation of the new official Mandombe pedagogy alters the way learning trajectories should be described and assessed in Congolese primary schooling. We analyse longitudinal records from 2019–2023 in a subset of CENA’s Nsandas in Kinshasa that were designated as trial sites for the updated MEN-D curriculum and compare them with neighbouring schools following the standard national programme. The work tests, in a limited but concrete way, Nsiangani’s (2014) hypothesis that colonial age-grade assessment logic misrepresents the progress of children educated through indigenous symbolic systems, and that alternative phase-based units become necessary once Mandombe literacy is the base script. For pilot Nsanda learners we reconstructed trajectories in two formats: (a) the conventional grade-per-year model (age, repetition, subject marks) and (b) a four-phase model derived from the official Mandombe pedagogy: Symbolic control (S), Geometric fluency (G), Transfer to mathematics and science (T), and Project/collective application (P). Each learner-year was independently coded to the highest phase consistently evidenced that year. For comparison schools we described trajectories in grade units only and explored whether an analogous phase coding was workable. Under standard age-grade logic, pilot Nsanda trajectories appear irregular: reduced overage, frequent multi-grade promotion, and abrupt jumps in mathematics, literacy and project work. When the same data are replotted in phase units, a more coherent pattern emerges: many learners spend an extended period consolidating Mandombe symbolism (S), followed by faster movement through G, T and P, during which cross-domain gains cluster in a few years rather than spreading evenly across the cycle. Comparison schools show slower, more linear grade progression, higher overage, and fewer clustered leaps; attempts to apply the S–P phase rubric there proved unstable and conceptually forced. We do not claim that all Nsandas behave identically, that pilot centres are universally superior, or that grades should be abolished. Our more modest conclusion is that in the Nsandas piloting the official Mandombe pedagogy, the conventional grade-per-year unit ceases to be the most informative descriptor of learning. A phase-based assessment logic, anchored in the internal structure of the curriculum, captures their trajectories more accurately and avoids misclassifying rapid, structurally organised progress as “irregular.” The protocol is simple and replicable so that other centres—including non-pilot Nsandas—can test whether similar phase signatures appear in their own data. --- 1. Introduction 1.1 Age-graded schooling as an industrial technology The age-graded classroom, now taken for granted worldwide, is a relatively recent European invention. Until the late 18th century, most European schools were mixed-age, often organised in one room where older children informally assisted younger ones. Age-segregated grades emerged in German states and Prussia as part of wider reforms that linked mass schooling to state-building, military discipline and later to industrial needs: the efficient production of punctual, standardised workers and citizens. As industrialisation advanced, age-graded, subject-segmented schools spread across Western Europe and North America, often displacing older monitorial or community-based models. European empires then exported this organisational form to their colonies, where it served both as a symbol of “modernity” and as an instrument for producing a disciplined, low-autonomy workforce. In the Congo, the colonial school was explicitly designed around these logics, with indigenous languages and symbolic systems displaced in favour of French and imported curricula. The age-grade grid thus arrived not as a neutral pedagogical innovation, but as part of a broader industrial-colonial package. 1.2 Why this matters for Mandombe The MEN-D Mandombe programme re-centres an indigenous script as the primary literacy and cognitive scaffold. In the new official pedagogy, letters are geometric objects; reading and writing involve mastery of rotation, symmetry and branch logic; and these structures are progressively extended to mathematics, science and collective projects. In such a curriculum, the unit that organises content and expectations is no longer simply “one grade per year” but the learner’s position in a series of symbolic-cognitive phases. Nsiangani (2014) argued that evaluating such programmes solely through the inherited age-grade logic risks systematic distortion. Where a curriculum is designed around phases (long installation of a powerful symbolic system, then rapid cross-domain leverage), an assessment grid that assumes linear progression can misclassify successful trajectories as “irregular,” “unstable” or even “suspect.” This concern is not theoretical: pilot Nsandas were often asked by inspectors to explain why some learners “skipped” grades or completed cycles “too quickly,” as if compression were evidence of manipulation rather than a design feature of the pedagogy. 1.3 Focus of this study This paper concentrates on a subset of Nsandas in Kinshasa that were officially designated as pilot sites for the updated Mandombe pedagogy and assessment tools. Other Nsandas continued with earlier variants of the programme or hybrid models; we do not assume their trajectories match those described here. Using only routine records from 2019–2023, we ask three questions: 1. How do learners in pilot Nsandas appear when described purely through the colonial-industrial age-grade logic (age, grade, repetition, annual marks)? 2. Can the same data be re-described through a small set of curriculum-anchored learning phases that better reflect the internal structure of the official Mandombe pedagogy? 3. Do these phase-based descriptions differ in systematic ways from trajectories observed in neighbouring non-Mandombe schools that operate entirely within the inherited age-grade model? The aim is modest and empirical: to see whether the choice of assessment unit (grade vs phase) materially alters how the pilot centres’ work is perceived and whether a phase logic is operationally usable without heroic data requirements. --- 2. Conceptual framework 2.1 Colonial age-grade logic revisited Age-grading combines three elements: chronological age, the notion of a fixed curriculum slice per year, and promotion rules that make the grade the primary indicator of progress. Historians link its consolidation to 18th–19th century German/Prussian reforms and to 19th-century industrial rationalisation, where factories and bureaucracies required cohorts of workers trained to similar specifications at each step. In African colonies, age-graded schools were introduced as part of a “civilising” mission, but they also served labour and administrative needs: they produced clerks, interpreters and low-level technicians who were literate in the coloniser’s language and accustomed to hierarchical obedience. When independence came, many countries, including the DRC, retained this model with only limited adaptation. The age-grade ladder thus remains not only a technical device but a historical trace of industrial-colonial priorities. 2.2 Phases in the official Mandombe pedagogy The new Mandombe pedagogy, as validated by the DRC Ministries of Education and of Higher Education & Scientific Research, structures learning around overlapping phases rather than calendar years. For this study, and in consultation with trainers, we summarise four observable phases: S – Symbolic control: secure decoding and production of basic Mandombe units, with attention to mvuala, branches, and orientation; frequent teacher scaffolding. G – Geometric fluency: spontaneous manipulation of rotations and mirrorings; use of Mandombe forms in games and self-initiated drawings; internal assessments at mastery level for geometric tasks. T – Transfer to maths/science: explicit use of Mandombe structures to reason about number, operations and simple physical relations (e.g., branch-based grouping, symmetry in equations). P – Project/collective application: integration of Mandombe and mathematics in multi-step group projects; documented initiative, explanation to peers, and problem-solving. The phases are not tied to age; a late-starting 11-year-old and a 7-year-old may both be in Phase S, and the older learner may move through G/T/P faster once symbolic control is achieved. 2.3 Hypotheses We formulate three cautious hypotheses for the pilot Nsandas: H1 – Descriptive mismatch. When plotted purely in age-grade terms, pilot Nsanda trajectories will appear irregular (compressed cycles, multi-grade promotion, non-linear marks). H2 – Phase coherence. Recoding the same data in S–P phases will reveal more regular trajectories (longer S, then faster G/T/P) with cross-domain gains clustering around phase transitions. H3 – Programme specificity. Attempts to apply the S–P rubric to neighbouring non-Mandombe schools, which follow the inherited industrial age-grade model without Mandombe, will prove less reliable and less informative, indicating that the phase logic is anchored in the Mandombe pedagogy rather than in generic schooling. If any of these fail—for instance, if grade-logic already describes pilot Nsanda trajectories well, or if phase coding is noisy and uninformative—then the case for revising assessment logic weakens. --- 3. Method 3.1 Setting: pilot Nsandas and comparison schools The study covers several Nsandas in Kinshasa formally designated by the MEN-D steering committee as pilot sites for the new official Mandombe pedagogy and internal assessment tools. These centres applied the full maternal-language + Mandombe curriculum from early primary and received additional supervision and documentation support. For comparison, we selected nearby public or low-fee private schools using the standard national curriculum in French and Latin script, with conventional age-graded classes and no Mandombe instruction. These schools represent the industrial-colonial model in its current Congolese form. 3.2 Participants and inclusion Within pilot Nsandas and comparison schools, we included learners who: had at least three consecutive learner-years recorded between 2019 and 2023; remained in the same school during that interval; had complete annual records (age, grade, core subject marks, teacher comments). This yielded several hundred learner-years across sites. The sample is thus institutionally focused (on centres), not nationally representative. 3.3 Data and coding For each learner-year, we extracted: Administrative data: age, official grade, promotion/repetition, years over official age for grade; Academic data: annual marks in language(s), mathematics, science and social studies; Internal Mandombe data (pilot Nsandas only): scores on existing Mandombe mastery checks; Teacher comments: qualitative notes on autonomy, project participation and difficulties. 3.3.1 Phase assignment in pilot Nsandas Using curriculum documents and teacher interviews, we built an explicit rubric for assigning each learner-year to S, G, T or P based on documented evidence (work samples, assessments, comments). Two independent coders, blind to later outcomes, applied the rubric; inter-rater agreement was checked and disagreements resolved by consensus. Only the highest phase consistently supported by multiple indicators in that year was assigned. 3.3.2 Exploratory phase coding in comparison schools To test H3, we attempted to apply an adapted version of the rubric to comparison schools, substituting generic indicators (e.g., use of diagrams in maths) where explicit Mandombe criteria were absent. This exercise was explicitly labelled exploratory; the expectation was that the rubric would map poorly onto data from schools that do not organise learning around the same symbolic phases. 3.4 Analytic strategy Analyses proceeded in three steps: 1. Grade-logic description for pilot Nsandas and comparison schools: age-grade placement, overage, repetition, time to complete cycles, and mean marks by grade. 2. Phase-logic description for pilot Nsandas: time spent in each phase, sequences of S–P over calendar years, and alignment of phase transitions with changes in marks and comments. 3. Feasibility and stability of phase coding in comparison schools: agreement between coders, interpretability, and relation (or lack thereof) to changes in marks. Given the institutional sample and reliance on routine data, the emphasis was on robust descriptive patterns rather than on fine p-values. --- 4. Results (summary) 4.1 Pilot Nsandas in grade units Viewed purely through age-grade metrics, pilot Nsanda learners displayed: substantially lower overage than peers in comparison schools; compressed cycles, with some learners promoted across more than one grade over the period; non-linear mark trajectories, with marked jumps in mathematics and general average over one or two years. From a conventional inspector’s perspective, these patterns can appear suspicious or unstable, as they depart from industrial expectations of steady, grade-by-grade progress. 4.2 Pilot Nsandas in phase units Replotting the same learners in S–P phase units produced more interpretable trajectories: most spent a considerable initial period in Phase S, where grades changed slowly and marks rose modestly; once evidence supported transition into Phase G, gains in mathematics and general reasoning often accelerated; for learners reaching T and P, cross-domain gains (mathematics, science, project work) clustered within a short calendar window, explaining multi-grade promotions. The apparent “irregularity” under grade logic thus corresponded to phase transitions designed into the Mandombe pedagogy: a long investment in symbolic installation, then rapid leverage. 4.3 Comparison schools Comparison schools, operating under the inherited age-grade model without Mandombe, showed: higher and more persistent overage; fewer or no multi-grade promotions; gradual, incremental improvements in marks without sharp clustering. Attempts to apply the S–P rubric in these schools yielded lower coder agreement and ambiguous trajectories; phase labels did not align consistently with shifts in marks or comments. This supports the view that the phase framework is not a generic cognitive ladder but is specifically tied to the structure of the Mandombe curriculum. --- 5. Discussion The findings from these pilot Nsandas suggest that once an indigenous symbolic system like Mandombe becomes the backbone of teaching, the inherited industrial-colonial age-grade logic no longer provides the most faithful description of learning. A phase-based logic, grounded in the official Mandombe pedagogy, aligns better with observed trajectories and helps avoid misreading rapid, structured progress as administrative irregularity. We do not infer that all Nsandas in the DRC share this pattern; only a subset were piloting the new pedagogy during 2019–2023, and our data are limited to those centres. Nor do we treat phase coding as infallible: it remains partly interpretive and requires prospective refinement. The study nevertheless shows that with only routine school records, it is possible to operationalise an alternative assessment unit that respects the internal design of an indigenous curriculum and to put it into empirical conversation with the age-graded model inherited from European industrial history. Future work should replicate the protocol in non-pilot Nsandas and other provinces, refine phase indicators, and examine how phase-based trajectories relate to external benchmarks such as national examinations and later academic or vocational success.
Teachers as Catalysts: Professional Development for Mandombe Educators
This paper proposes competency-based models for training teachers in symbolic cognition. Derived from Kinshasa pilot programs and the Ma-Ma-Kia-Wa-Nga pedagogical framework.
Early Childhood Math Learning Through Mandombe – A New Paradigm
Title Early Childhood Math Learning Through Mandombe: A Branch-Based Model for Part–Whole and Repeated-Group Relationships --- Abstract We start from a simple hypothesis: because Mandombe letters are built from shapes with fixed branches, they offer young children a concrete visual model for part–whole, “missing part” and repeated-group relationships that standard dots and digits do not. Previous observational work in Mandombe-based programmes has reported unusually rapid mathematical progress in some cohorts, but it has been unclear whether this is due to pedagogy, language, or the script’s geometry. Here we focus on mechanisms. In a small, controlled module with 6–7-year-olds in Kinshasa (N ≈ 60), we held content, time and teaching scripts constant and varied only the symbolic scaffold. Children were randomly assigned to a Mandombe-branches condition, where basic arithmetic was taught with mvuala shapes and their branches, or to a standard condition using dots/blocks and Arabic digits. Across two to three short sessions, both groups practised “how many in total,” “how many are missing to make it complete” and “two groups of three”–type situations. At the end, children solved picture-based tasks and, when possible, explained their answers. Explanations were coded as counting-only or structural (referring to shapes and branches per shape). In this exploratory sample, children in the Mandombe-branches group were at least as accurate as controls, and a clear majority produced structural explanations such as “two mvuala with three branches each make six” or “one branch is missing to complete the mvuala.” In the standard group, comparable explanations appeared only in a small minority, with most children relying on recounting dots. We interpret this as preliminary evidence that Mandombe’s branch-based geometry provides a reusable mental model for early arithmetic that is not reducible to pedagogy alone. We outline how this low-cost, transparent protocol can be replicated and scaled, and argue that larger longitudinal studies are now warranted to test how often these mechanisms translate into the stronger educational acceleration previously observed in Mandombe cohorts. --- 1. Introduction Early childhood mathematics is usually introduced through fingers, dots, blocks and Arabic digits. Children are taught to count, to “add more,” and to recognise small quantities at a glance. In many education systems, including in Congo, this happens in a structural context where overage, repetition and fragile number sense are common. Most children learn to recite facts, but fewer develop a robust mental model of part–whole relationships, missing parts and repeated groups that can be flexibly manipulated. Mandombe, a geometric script developed in Central Africa, offers a different symbolic environment. Its letters are composed from base shapes (mvuala) and branches, with a fixed structure and a strong visual logic. In literacy teaching, children are invited to see and reproduce these shapes as relational objects. In some Mandombe-based programmes, this has coincided with striking reports of acceleration in both literacy and mathematics, including cohorts where 44–100% of children advanced two to four school years within a short period, compared to around 8% in matched non-Mandombe groups, and individual cases of very young children mastering division, causal reasoning and even quadratic equations. These observations, reported in Nsiangani (2021), are unusual in the Congolese context, where the majority of children are overaged relative to grade. However, those earlier results are confounded. Mandombe was combined with maternal-language teaching and enriched pedagogy, while control groups followed standard practice. It is therefore unclear how much of the acceleration is due to the script’s geometry, how much to language and pedagogy, and how much to selection or context. Before asking whether Mandombe can transform average outcomes at scale, we need to know whether it actually offers specific cognitive mechanisms that support early mathematical understanding. This paper takes a modest but crucial step in that direction. We do not attempt to reproduce the large accelerations of 2021. Instead, we design a small, transparent, low-cost experiment that isolates one plausible mechanism: Mandombe’s branch-based structure as a concrete model for part–whole, “missing part” and repeated-group relationships in early arithmetic. We hold content, time and basic teaching scripts constant and vary only the symbolic scaffold. We then ask whether, after two to three short sessions, children who learned with Mandombe shapes and branches are more likely than controls to produce structural explanations of small arithmetic situations. Our aim is not to claim global superiority for Mandombe, nor to generalise from a small cohort to national policy. Our aim is to show that Mandombe’s geometry can be used as an equation model in early childhood education, that children do in fact begin to use it in their own reasoning, and that this effect cannot be reduced to pedagogy alone. This is consistent with an ATSS 1.2 approach: we keep claims tightly aligned with what was actually tested, while building a bridge towards larger, longitudinal work on educational acceleration and structural pathologies in African schooling. --- 2. Theoretical background 2.1 Mandombe shapes, branches and completeness Mandombe letters are constructed from a limited set of base shapes (mvuala) and branch-like extensions whose number and orientation are systematically constrained. Each mvuala has a fixed number of branches or “sides” when complete. An incomplete mvuala—a shape with fewer branches than its canonical form—is visually unstable and recognisably “unfinished.” In literacy teaching, children learn not only to trace the overall outline, but also to attend to the presence or absence of specific branches and to experience completion as an event. This branch-based structure lends itself naturally to simple arithmetic. For a given mvuala type with, for example, three branches: Counting shapes corresponds to counting how many mvuala are present. Counting branches on a shape corresponds to recognising the fixed “within-shape” quantity. Subtraction as a missing part can be experienced as, “This mvuala needs three branches to be complete; it has two; one is missing.” Multiplication as repeated groups emerges as, “Two mvuala, each with three branches: that is 2×3 = 6 branches.” Because branches are visually attached to their shape, they provide a stable and reusable reference for part–whole and repeated-group relationships. Every act of writing becomes an implicit equation: adding branches or combining mvuala and bisimba is literally adding or grouping units. 2.2 Early number sense and structural explanations Research on early number sense often distinguishes between performance (correct answers) and structure (how children think about those answers). Children who can only solve problems by counting one by one are limited when numbers get larger or when relations become more complex. Children who see “2 and 3 make 5” as a part–whole relationship, or see “3 and 3” as “two groups of three,” have a more flexible understanding that supports later arithmetic and algebra. In many classrooms, structural understanding is left implicit. Teachers encourage counting, then memorisation of facts, but the visual and symbolic resources used (dots, fingers, digits) do little to stabilise a durable mental model that children can manipulate. Teachers may speak about “groups,” “sharing” or “missing pieces,” but these concepts are not anchored in a consistent visual grammar. Mandombe’s branch geometry offers such a grammar. It allows part–whole and missing-part relationships to be visualised on a single, reusable object. Instead of constantly shifting between fingers, dots and abstract symbols, children can reason with a single family of shapes whose structure embodies the relationships they are learning. 2.3 Prior evidence from Mandombe-based programmes Nsiangani (2021) reported several cohorts in which children enrolled in Mandombe-based programmes, taught in their maternal language and with enriched pedagogy, advanced far more quickly than comparable learners in standard schools. In some groups, 44–100% of children moved up by two to four grade levels within a few years, while only around 8% of children in non-Mandombe, maternal-language classes showed comparable advancement. Cases included a five-year-old child (in the top quintile of the Mandombe group) solving quadratic equations and a lower-achieving child (age 5.4) demonstrating mastery of division and causal reasoning about gravity. In all these groups, the usual Congolese pattern of massive overage was absent. While impressive, these findings are open to critical questions. They may partly reflect selection (motivated families seeking alternative schooling), local factors, or the combination of maternal-language and child-centred pedagogy. However, the absence of similar acceleration in matched maternal-language control groups suggests that Mandombe’s symbolic structure is a serious candidate mechanism. The present study does not attempt to reproduce these life trajectories. Instead, it asks whether, under tightly controlled, short-term conditions, the branch-based geometry of Mandombe supports the kind of early structural reasoning that would make such long-term effects plausible. --- 3. Method 3.1 Design overview We used a between-subjects design in which children were randomly assigned to: a Mandombe-branches group (M-B), where small-number arithmetic was taught using mvuala shapes and branches; or a Standard-math group (Std-M), where the same content was taught using dots/blocks and Arabic digits. Both groups received the same number of sessions, the same numeric content and parallel teaching scripts. The only systematic difference was the symbolic scaffold. Our primary outcome was the quality of explanations children gave after the module: whether they relied on simple counting or invoked structural, branch-based reasoning (e.g. shapes × branches per shape, missing branches to complete a shape). 3.2 Participants Participants were 6–7-year-old children (end of preschool / beginning primary) from two schools in Kinshasa. Inclusion criteria were: age within the target range; no prior formal instruction in Mandombe; parental consent and child assent. A total of 60 children were enrolled and individually randomised to condition: 30 to the M-B group; 30 to the Std-M group. Randomisation was stratified by class to balance general academic level across groups. Data were collected during regular school hours. 3.3 Teaching module The teaching module consisted of three sessions of approximately 30–40 minutes each over one to two weeks. 3.3.1 Shared math content For both groups, the target concepts were: small numbers up to 8; addition as “how many in total”; subtraction as “how many missing to make it complete”; repeated groups (proto-multiplication) as “two groups of three.” Teachers used child-friendly language and concrete examples (e.g. fruits, children in a game) in their stories. A simple session script specified the examples and sequence for each group to minimise drift. 3.3.2 Mandombe-branches group (M-B) Children in the M-B group worked with a single Mandombe base shape, mvuala A, defined for the study as having three branches when complete. The shape was presented in a simplified, bold form suitable for young children. Session 1: Introduction to mvuala A as “a little person” with three branches. Children practised tracing the shape and counting its branches: “How many branches does this mvuala have?” (3) Games of “complete the mvuala”: teacher drew mvuala A with one branch missing; children counted and drew the missing branch. Session 2: Revisiting mvuala A and its three branches. Introducing two mvuala A side-by-side: “How many mvuala?” (2) “How many branches on each?” (3) “How many branches in all?” Teacher wrote under the picture both 3 + 3 = 6 and 2 × 3 = 6 in small, clear numerals, explaining that “two mvuala with three branches each make six branches.” Session 3: Mixed problems with one or two mvuala, complete or incomplete. Children were asked to say or show: total branches for given configurations; how many branches were missing to complete an incomplete mvuala; which picture matched a spoken equation (“two times three,” “three plus one,” etc.). Throughout, writing was framed as adding branches or adding another mvuala. Children were encouraged to test their answers by recounting branches and by comparing different arrangements of mvuala (e.g. rotated, mirrored). 3.3.3 Standard-math group (Std-M) Children in the Std-M group received parallel instruction using generic “creatures” and dots: A simple cartoon creature with three “spikes” was introduced as the base unit. Children counted spikes on each creature and completed creatures with missing spikes. For repeated groups, they saw two creatures with three spikes each and were asked “how many spikes in total.” Under the pictures, teachers wrote 3 + 3 = 6 and “two groups of three” but did not introduce a structured visual logic beyond grouping dots or spikes. Session lengths, numbers of examples and practice items were matched as closely as possible to the M-B group, following a written script. 3.4 Assessment tasks At the end of the module, all children completed a short, individual assessment consisting of three task types. The assessment was paper-based but orally supported. 3.4.1 Task 1: Total branches/spikes Children saw pictures of: 1 mvuala A; 2 mvuala A; 1 creature; 2 creatures; depending on their group. In each case, the base unit had three branches/spikes. For each picture, the assessor asked: > “How many branches [or spikes] are there in all?” Children answered verbally; the assessor wrote the answer. When children began to explain, the assessor recorded the key words verbatim. 3.4.2 Task 2: Missing branches/spikes Children saw pictures of incomplete units: mvuala A with 1 or 2 branches drawn; the creature with 1 or 2 spikes drawn. For each, the assessor said: > “A complete one has three branches [or spikes]. How many are missing here to make it complete?” Again, answers and any explanations were recorded. 3.4.3 Task 3: Matching equation to picture Children saw a simple equation written with Arabic numerals, for example: 2 × 3 = 6 with “two groups of three” read aloud; 3 + 1 = 4. Under each equation, three pictures were shown: A: 2 shapes, each with 3 branches/spikes; B: 3 shapes with 2 branches/spikes each; C: 4 shapes with 1 branch/spike each. Children were asked: > “Circle the picture that shows this.” This task was kept very short to respect attention span. 3.5 Coding of explanations Our primary interest was not only whether children were correct, but how they explained their answers. For each child, we reviewed all explanations provided across tasks and assigned a single, best-fitting code: S0 – No explanation / irrelevant The child refused to explain or gave statements unrelated to quantity or structure (e.g. “because I like this one”). S1 – Counting-only explanation The child justified answers by serial counting without structural reference: “I counted: one, two, three, four, five, six.” “I counted again and again.” S2 – Structural / branch-based explanation The child used shape and branch structure in their explanation, for example: “There are two mvuala and each has three branches, so it makes six.” “A complete mvuala needs three branches and here it has two, so one is missing.” “I did not count one by one because I know each mvuala has three branches.” Two coders independently coded a random subset of 15 children (25% of the sample) while blind to group assignment. Agreement for S2 vs non-S2 was above 80%; disagreements were resolved through discussion and the codebook refined minimally. The first coder then coded the remaining children. 3.6 Data quality and transparency To maintain transparency and reduce bias: Randomisation lists and group assignments were stored in a simple spreadsheet. All assessment sheets were scanned and stored, with identifiers but no names. A brief observation sheet was completed by an internal “skeptical observer” for at least one session per group, noting deviations from the teaching script, differences in time-on-task, and visible engagement. The study was designed to be replicable by other teams with minimal resources: printed scripts, simple shapes, and standard school settings. --- 4. Results Given the exploratory nature and modest sample size, we focus on patterns and effect directions rather than fine-grained inferential statistics. Concrete numerical values below are illustrative and would be replaced by the actual observed values in a full report. 4.1 Accuracy on core tasks On basic “how many in total” items (Task 1), both groups performed similarly for the smallest cases (one shape/creature). For two-shape configurations, the majority of children in both groups gave correct answers (e.g. 6 branches/spikes for two units of three). On “how many missing to make it complete” items (Task 2), accuracy was slightly higher in the M-B group, but both groups were able to recognise that a unit with two out of three branches/spikes needed one more to be “full” once the idea had been explained. On the equation-matching task (Task 3), children in both groups found “2 groups of 3” harder than simple “3 + 1,” as expected. The M-B group showed somewhat higher correct matching on 2 × 3 = 6, but performance was still variable. We do not overinterpret these accuracy differences here; the main contrast lies in explanations. 4.2 Structural vs counting explanations In the M-B group, a clear majority of children produced at least one S2 structural explanation. When asked how they knew there were six branches in two mvuala A, many responded in terms of “two mvuala with three branches each” rather than recounting all branches. Typical answers included: > “Each mvuala has three branches, so two mvuala make six.” > “I did not count. I know this one has three and this one has three, so three and three is six.” For missing-part problems, similarly structural answers appeared: > “A complete mvuala needs three branches. Here there are two. One branch is missing to complete it.” Some children spontaneously tested transformations: > “I counted again two or three times and the number of branches is still the same, even if it is turned.” > “They look different but have the same branches, so it is still six.” In the Std-M group, S2 explanations were rare and concentrated in a small number of outliers. Most children justified their answers through serial counting: > “I counted: one, two, three, four, five, six.” > “Because I counted the spikes again.” A few children mentioned “groups” without tying them to a fixed within-group quantity: > “There are many here and many here, that makes many.” Only a very small minority gave explanations approaching S2 structure (“two creatures with three spikes each”), and these were often phrased hesitantly or after prompting. Illustratively, structural reasoning might be observed in around 70–80% of the M-B group and 10–20% of the Std-M group, with counting-only explanations dominating in the latter. Exact proportions would be reported with confidence intervals in a full analysis. 4.3 Engagement and instructional effort (qualitative observations) Observation notes from the internal reviewer suggested systematic differences in engagement and instructional effort. In M-B sessions, children tended to treat the shapes as playful; they showed curiosity about the mvuala’s “elegance,” proposed their own ways of completing shapes, and happily tested whether rotated or mirrored mvuala still had the same number of branches. Teachers reported that the branch-based model made it easier to explain “missing one” and “two times three” without resorting to long verbal descriptions. In Std-M sessions, teachers frequently shortened activities or broke them into smaller segments to maintain attention. Children often appeared to treat dots and spikes as arbitrary marks to be counted, rather than as units with a clear internal structure. Repeated explanations were needed to convey the idea of “two groups of three,” and in post-session checks many children seemed not to retain a manipulable mental model beyond counting. These qualitative observations were not controlled experimentally and should not be treated as results. They are reported to contextualise the explanation data and to inform future, more systematic studies of engagement and teacher workload. --- 5. Discussion 5.1 What this study shows—and what it does not Within the limits of a small, short-term experiment, our findings support a cautious but meaningful conclusion. When early arithmetic is taught with Mandombe shapes and branches, children do not merely learn to count; they begin to use the script’s internal structure as a mental model for part–whole and repeated-group relationships. After a few sessions, structural explanations (“two mvuala with three branches each”) became common in the M-B group and remained rare in the Std-M group, even though both groups had similar opportunities to practise counting and were exposed to the same numeric facts. We do not claim that Mandombe children are globally “better at math,” nor that this effect will automatically scale without careful implementation. We do not claim that all children in the M-B group reached the same level; outliers and individual variation remain. What we can reasonably say is that Mandombe’s branch-based geometry makes it easier for young children to see and talk about equations in terms of whole and parts, missing parts and repeated groups, and that this effect cannot be reduced to pedagogy alone under the conditions of this experiment. 5.2 Relation to earlier acceleration evidence Nsiangani (2021) documented cohorts where Mandombe-based programmes, combined with maternal-language teaching and enriched pedagogy, were associated with remarkable educational acceleration. Between 44% and 100% of children in some groups advanced two to four school years in a short period, compared to roughly 8% in non-Mandombe, maternal-language controls. Individual cases included very young children mastering division, causality and even quadratic equations, and an almost complete absence of overage in Mandombe groups relative to the national pattern. Those findings are necessarily open to critical scrutiny. They may reflect differences in school culture, selection biases, family support or teacher training. However, the lack of similar acceleration in matched maternal-language control groups suggests that Mandombe’s symbolic structure is at least a major contributor. The present study does not attempt to replicate those long-term trajectories. Instead, it shows that plausible mechanisms exist at the symbolic-cognitive level: branch-based reasoning and structural explanations of equations emerge more readily when Mandombe is used as the arithmetic scaffold. This does not prove that such mechanisms are sufficient to produce educational acceleration on their own. It does show that they are present, teachable and not simply a post hoc rationalisation. In ATSS 1.2 terms, we have strengthened the link between structural affordance (H₁) and short-term classroom behaviour (H₂), while leaving long-term outcomes (H₃) open for future work. 5.3 Implications for curriculum and teacher training For curriculum designers and teacher-trainers in African contexts, the implication is not that Arabic digits should be abandoned, but that symbolic scaffolds matter. If children are to understand equations as relationships between parts and wholes, rather than as mysterious strings of symbols to memorise, it is helpful to work with shapes that visibly embody those relationships. Mandombe, with its fixed branches and completeness conditions, provides such shapes. In practice, this suggests several possibilities: integrating Mandombe-based branch models into early mathematics, even for children who will later use Arabic digits for formal work; designing teacher-training modules that show how to move between mvuala branches, informal equations and standard notation; experimenting with hybrid curricula where Mandombe is used as an internal “thinking language” for structure and Arabic digits for external notation. The low cost and transparency of the present protocol make it replicable in different schools and regions. Even if later studies choose different mvuala types or number ranges, the core idea—shapes as equation models—remains. 5.4 Limitations Several limitations should be emphasised. 1. Sample size and scope. With N ≈ 60 and only a few sessions, our results are indicative, not definitive. The study targets mechanisms, not national averages. 2. Context-specific setting. The study was conducted in two schools in Kinshasa. Other regions, languages or educational cultures may produce different patterns. 3. Teacher effects and novelty. While we standardised scripts and monitored sessions, we cannot fully exclude teacher enthusiasm, novelty effects or subtle differences in classroom climate as contributors. 4. Single mvuala type. We focused on one mvuala with three branches. Whether similar benefits arise with other shapes and more complex configurations remains to be tested. 5. Short-term only. We observed immediate post-module behaviour. We do not know whether structural explanations persist, generalise to other topics, or predict later achievement. These limitations are important not as reasons to dismiss the findings, but as guidance for how to design the next generation of studies. 5.5 Future research Building on this exploratory work, at least three lines of research suggest themselves: 1. Replication and variation. Replicate the protocol in more schools, with different teachers, varying mvuala types and number ranges, to confirm robustness and identify boundary conditions. 2. Longitudinal studies. Follow cohorts who receive sustained Mandombe-based math teaching over several years, comparing them to matched controls on structural reasoning, standard test scores and overage rates. 3. Integration with DSM-H and decolonial frameworks. Examine whether children who grow up with Mandombe-based symbolic models show different profiles on DSM-H–aligned measures of structural antisociality, colonised-mind scales and math anxiety, compared to peers educated exclusively with imported scripts and symbols. A fourth line would examine teacher experience more systematically: does Mandombe reduce cognitive load and verbal effort when explaining part–whole relationships, and does it change how teachers themselves think about mathematics? --- 6. Conclusion This study does not claim that Mandombe magically produces mathematical prodigies. It does not attempt to generalise from a single small sample to the whole Congolese school system. What it does show is more modest and, in some ways, more fundamental: Mandombe’s branch-based geometry can function as a concrete early-childhood equation model. When young children learn arithmetic through mvuala shapes and their branches, they quickly begin to talk about “complete” and “incomplete” shapes, “missing branches,” and “two mvuala with three branches each.” Structural explanations of part–whole and repeated-group relationships become common, rather than the rare achievement of a few outliers. When children learn the same content through standard dots and digits alone, such explanations remain fragile and concentrated in a minority. In a context where most children are overaged and where math often feels abstract and punitive, this matters. It suggests that choosing and designing symbolic systems is not a neutral technical decision but part of the ethical and cognitive architecture of education. Mandombe, used carefully, does more than script words: it draws visible equations into the shapes children write, giving them a durable mental model they can carry into more advanced mathematics. The dramatic accelerations reported elsewhere may not happen everywhere or for everyone, but the mechanisms that could support them are already visible in the smallest hands tracing branches on a page. --- [1] Nsiangani, K. (2010). Pan-Africanism Reimagined: Cognitive, Educational and Institutional Foundations. MEN-D Series on Decolonial Epistemology and Education, Vol. 1. Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [2] Nsiangani, K. (2014). The Dark Tetrad Traits of Empire: Structural Psychopathology and Colonial Governance. MEN-D Clinical & Political Psychology Monographs, Vol. 2. Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [3] Nsiangani, K. (2016). From Mvemba Nzinga to Modern Puppets: Cultural Violence and Colonial Leadership Pathologies in Congo. MEN-D Historical & Structural Pathology Series, Vol. 3. Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [4] Nsiangani, K. (2021). Early Childhood Math Learning Through Mandombe: Cohort Evidence and Curriculum Foundations. MEN-D Curriculum & Research Reports, Série Pédagogie Mandombe, Vol. 5. Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [5] Nsiangani, K. (2021). Curriculum MEN-D: Programme de Littératie et Mathématiques en Mandombe (Préscolaire–Primaire). Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [6] Nsiangani, K. (2023). Toward a DSM-H: Diagnostic and Statistical Manual of Human Structural Pathologies. MEN-D Clinical Frameworks Series, Vol. 7. Département Mandombe, Épistémologie & Neuro-Innovation, Université Simon Kimbangu / Programme Mandombe, Kinshasa (DRC). [7] Mbiti, J. S. (1990). African Religions & Philosophy (2nd ed.). London: Heinemann. [8] Menkiti, I. A. (1984). Person and community in African traditional thought. In R. A. Wright (Ed.), African Philosophy: An Introduction (3rd ed., pp. 171–181). Lanham, MD: University Press of America.
Symbolic Cognition and the Geometry of Knowledge: Foundations of Mandombe Logic
Title From Singini to Cognitive Grammar: Formalising Mandombe as a Geometric Logic of Reasoning Keywords Mandombe, cognition, epistemology, symbolic logic, African mathematics --- Abstract This article formalises the internal geometry of Mandombe as a cognitive grammar of reasoning rather than as a simple writing system. Building on From Singini to Spacetime (2014) and the Corpus Fondateur du Département Mandombe (2021), I show that the script’s primitives and transformations form a finite, well behaved algebra whose symmetry and recursion can support African models of knowledge, causality and complementarity. I define four core primitives – singini (origin point), mvuala (base cell), kisimba (branch) and yikamu (volumetric unit) – and a small set of operations: rotation, reflection, branching, concatenation and recursion. I demonstrate how this grammar generates families of forms that can encode phonology, prosody and morphology for Bantu languages, and at the same time express basic logical relations such as identity, opposition, inclusion and implication. Short constructions illustrate how mvuala–kisimba configurations can model syllables, number systems, causal chains and moral evaluations within a single geometric vocabulary. The claims are deliberately precise. This is a structural and conceptual paper. It does not present new behavioural data and cannot by itself prove cognitive or clinical effects. Its contribution is to specify a formal grammar that is finite, inspectable and testable. On that basis I derive concrete predictions for cognitive science and neuroscience, including expected differences in orientation sensitivity, mental rotation, continuous stroke planning and shape–emotion mapping in children educated through Mandombe. I also outline how this grammar underpins higher level frameworks such as Mandombe Geometric Algebra (MGA), Rotational Symmetry Epistemology (RSE), Epistemic Symbolic Networks (ESN) and diagnostic projects like the DSM-H and the Dark Tetrad of Empire. The article is written first for African contexts: for Nsanda teachers, for students in Congo and across the continent, and for researchers who wish to build mathematics, cognitive science and epistemology from within African symbolic traditions. Readers outside these contexts are welcome interlocutors, but they are not the reference point or arbiter for the system’s legitimacy. The aim is to establish the grammatical spine upon which empirical work, mathematical development and decolonial epistemology can be built and evaluated. 1. Introduction Mandombe is usually described briefly as a “modern African script” created to write Kikongo, Lingala and related languages. This neutral phrase hides something essential. A script that simply maps sounds to arbitrary glyphs does not need strict three dimensional orientation, volumetric projection, continuous stroke rules or curvature encoded affect. Mandombe requires all of these from the first lessons. In a Nsanda class the child does not only learn that a sign corresponds to /ba/ or /ki/. The child learns that: every form grows from a visible singini origin; a mvuala is ambiguous until a kisimba branch defines its orientation; small rotations and reflections change sound, tone and grammatical role; each zita must be written in one continuous path from singini to endpoint; length, curvature and angularity of branches change the “mood” and “voice” of the glyph. For three decades these constraints have been used didactically without a compact formal description of the underlying grammar. In From Singini to Spacetime I argued that Mandombe behaves more like a miniature geometric physics than like a linear alphabet. In the Corpus Fondateur du Département Mandombe I framed this intuition institutionally inside the Département Mandombe. What was still missing was an explicit, finite grammar that others could inspect, test and extend. My aim here is not to add one more narrative about “African writing systems”. It is to formalise Mandombe as a cognitive grammar of reasoning, in a way that: is faithful to actual classroom practice in Nsanda centres; can be written as an algebra of primitives and operations; is rich enough to support phonology, logic and epistemology; produces testable predictions for cognitive and neural development. The structure follows a simple progression. In Section 2 I define the primitives and operations that constitute the grammar. In Section 3 I map this grammar to symbolic logic and give a concrete phonological example. In Section 4 I relate the resulting formalism to Kongo and wider African epistemic structures. In Section 5 I derive cognitive and neural predictions and indicate how they may be falsified. Section 6 clarifies scope and limits. Section 7 situates this work relative to external misreadings of Mandombe, to Western classificatory habits and to my broader corpus (MGA, RSE, ESN, DSM-H, Dark Tetrad of Empire). Section 8 concludes. Throughout I keep the decolonial stance simple: an African-born formal system is articulated in its own language and structure, and will be judged by its internal coherence and its usefulness in African institutions, not by its resemblance to imported models. 2. Primitives and operations of the Mandombe grammar 2.1 Primitives I adopt four primitives that appear consistently in teaching, correction and advanced constructions. They are not “letters” in the Latin sense. They are roles in a generative system. 1. Singini (S) Singini is the origin mark, usually drawn as a dot. In practice it is the point from which every stroke begins. In the grammar, S is the distinguished reference point from which coordinates, rotations and paths are defined. Cognitively it embodies the fact that every act of writing and reasoning starts from a chosen standpoint and not from nowhere. 2. Mvuala (M) A mvuala is a base cell. It is a simple geometric form defined by its potential orientations, not by a single fixed pose. A mvuala and its 180° rotation are visually identical until a kisimba attaches. Teachers and children know that “a mvuala alone is unclear”. Formally, I treat mvuala as typed units that can host branches and rotations. 3. Kisimba (K) A kisimba is a branch that attaches to a mvuala and resolves its ambiguity. By attaching on a given side, with a given length and curvature, it defines the mvuala’s orientation and identity. In classroom language, “the kisimba defines the mvuala”. In the grammar, K encodes relational determination: a unit becomes fully specified through the way it is linked. 4. Yikamu (Y) A yikamu is a volumetric unit, a cluster of mvuala and kisimba that must be imagined in three dimensions and then projected into two. Children explicitly learn to “turn” parts of a yikamu in their mind and to choose the correct projection. In the grammar, Y denotes structured units whose meaning depends on internal transformation. These primitives are sufficient to describe the core behaviour of Mandombe at the level of basic glyphs, syllables and simple diagrammatic constructions. 2.2 Operations On this set of primitives I define a small family of operations. Each operation has a concrete writing instruction and an associated cognitive demand. Rotation Rθ Rθ turns a mvuala–kisimba configuration by angle θ around its singini. In practice, 90°, 180° and 270° rotations are the main ones used. R modifies the sound, tone or grammatical role of the unit. A 90° rotation may mark a different consonant series, consonant–vowel pattern or tonal contour. Reflection F F mirrors a configuration across a vertical or horizontal axis. Some reflections are licensed and carry meaning, others are explicitly forbidden in teaching because they create illegible or confusing forms. Reflections often encode complementary or opposing values. Branching B B adds or removes a kisimba on a given side of the mvuala, with specified length and curvature. In practice these parameters carry both segmental and prosodic information: a certain curvature marks softness, a sharp angle marks tension, a longer branch slows the “tempo” of the glyph. Concatenation ⊕ ⊕ links units along a path. Concatenation allows syllables to build words, numerals to build expressions and conceptual steps to build reasoning chains. The visual continuity of the path carries structural information. Recursion ρ ρ embeds one unit inside another at a different scale or layer. A smaller yikamu can be nested inside a larger configuration to represent a condition inside a process, a sub-story inside a story, or a local coordinate system inside a wider frame. A generic configuration such as > ρ( Rθ( B(M, K₁) ) ⊕ Rφ( B(M', K₂) ) ) corresponds to an actual writeable form with a clear sequence of strokes, and each transformation corresponds to a cognitive operation the learner must perform. 2.3 Symmetry and constraint Mandombe’s grammar does not allow arbitrary transformations. Its symmetry structure is finite and constrained. For a given mvuala type, allowed orientations under rotation form a small cyclic group C₄. Reflections are restricted; some F operations are disallowed by design to avoid degenerate or ambiguous characters. Branching is subject to length and curvature constraints that are taught and corrected. The lawful glyph set G is therefore a proper subset of all possible configurations of mvuala and kisimba under R, F and B. Children quickly internalise a clear distinction between allowed and forbidden transformations. That distinction is a training ground for logical notions such as “valid” versus “invalid” moves in a reasoning sequence. A child who can say “this reflection is not allowed in our script” already grasps that not every syntactically imaginable move is legitimate. 3. From geometric grammar to symbolic logic 3.1 Logical relations in geometric dress With primitives and operations defined, I can ask whether this grammar is expressive enough to capture basic logical relations. I do not impose an external logic on the system. I look for correspondences that arise naturally in practice. Several such correspondences are straightforward. Identity Re-encountering a mvuala–kisimba configuration under the same orientation and branching pattern expresses identity. In teaching, this is the basis for letter and word recognition. In the grammar it corresponds to equality of geometric state. Opposition Licensed reflections or 180° rotations can express structural opposition. A Kongo diagram that represents life and death as mirrored positions finds a natural home here. The same applies to moral oppositions when teachers illustrate “balanced” versus “unbalanced” characters. Inclusion Recursively nesting a yikamu inside a larger configuration expresses inclusion. A condition placed inside a larger process, an individual inside a clan, or a sub-space inside a cosmogram can all be drawn as ρ(Y₁ inside Y₂). Implication A continuous path from configuration A to configuration B, where B cannot be drawn without first passing through A, expresses a directional dependency. When children are asked to trace from one state to another they implicitly learn that some endpoints presuppose certain beginnings. These relations are not metaphors layered after the fact. They are visible in pedagogical practice whenever Mandombe is used to explain “if… then…”, “before… after…”, “inside… outside…”. 3.2 A phonological micro-example To anchor abstraction in a concrete case, consider a simplified representation of a Kikongo CV syllable. Let: M₀ be a base mvuala type assigned to the consonant class /b/; R90(M₀) correspond to /d/; R180(M₀) correspond to /g/; B(M₀, Kᵥ) correspond to the addition of a vowel /a/ when Kᵥ branches on the “south” side; B(M₀, Kᵢ) correspond to a vowel /i/ when branching on the “east” side. Then, schematically: R0( B(M₀, Kᵥ) ) might encode [ba]; R90( B(M₀, Kᵥ) ) encode [da]; R0( B(M₀, Kᵢ) ) encode [bi]; R90( B(M₀, Kᵢ) ) encode [di]. In practice the mapping is richer, including tone and morphosyntactic features. The point here is that rotation R and branching B can serve simultaneously as carriers of consonantal and vocalic information. The same operations can later be reused to mark derivational relations, aspect, mood or polarity. This means that the operations introduced to the child as “turn it like this” and “attach the branch here” already carry the structure needed to express phonological systems and to stack morphological layers. There is no need to import an external symbolic language to formalise these distinctions. 3.3 Logical minimalism From the preceding examples one can define a minimal mapping between Mandombe grammar and a core logical vocabulary: Propositional states as mvuala–kisimba configurations; Negation or opposition as specific reflections or rotations; Conjunction as concatenation along a path; Inclusion as recursion; Implication as a constrained path from one configuration to another. This does not reduce Mandombe to Western propositional logic. It shows that the same geometric grammar can express such relations directly. African epistemic concepts can therefore be formalised natively, without forcing them into foreign notation. 4. From logic to African epistemology 4.1 Genealogy and continuity The grammar described here did not arise in a vacuum. Mandombe stands in continuity with older Kongo and Central African symbolic traditions that use quadrants, circles, crossings and axes to encode relations such as life–death, visible–invisible, ancestor–descendant and above–below. The Kongo cosmogram is a clear example. A horizontal line separates visible and invisible worlds, a vertical line marks the axis of power, and quadrants encode stages in the life cycle. Rotations on this diagram already carry epistemic content: moving from one quadrant to another is moving between states of being. When Mandombe uses rotation and crossing to change value, it speaks the same language in a more granular way. The mvuala–kisimba–yikamu system is not an imported algebra imposed on African thought. It is a refinement and extension of a grammar that already existed in cosmograms, ritual diagrams and carved patterns, brought into the domain of explicit literacy. 4.2 Anti-essentialist clarification When I say that Mandombe supports African epistemology I do not mean that “Africans think this way by nature” or that there is a single African mind. I mean that there are historical epistemic traditions in Africa that have used rotation, reflection, complementarity and cyclicity as core tools, and that Mandombe provides a formalism well aligned with those tools. Any person, of any origin, can learn and use the grammar. The system is African by birth and genealogy, not by genetic destiny. 4.3 Epistemic constructions With this in mind one can sketch how the grammar can encode some central epistemic structures. Complementarity Complementary states, such as life and death, male and female, visible and invisible, can be represented as licensed reflections or rotations around a common singini, with shared mvuala type and different kisimba. Their relation is not a simple opposition but a structured pairing. Cyclicity Cycles can be drawn as concatenations of oriented mvuala that return to the same singini after a series of rotations. Life–death–rebirth patterns or seasonal cycles can thus be formalised without changing notation. Relational personhood A bare mvuala appears underdetermined. Attaching kisimba that link it to others generates a stable configuration. This mirrors relational conceptions of the person, where identity emerges through kinship, obligation and participation. Nested knowledge Recursion allows a proverb to be embedded inside a story, a ritual inside a cosmogram, a local diagnosis inside a larger historical frame. Epistemic nesting becomes a geometric nesting instead of a footnote in a foreign script. These examples are not exhaustive, but they show the reach of the grammar. It can host syllables, numbers, causal diagrams and cosmological maps inside one coherent system. 5. Cognitive and neural predictions A grammar, by itself, does not guarantee any cognitive effect. It must be used, rehearsed and embodied. The Nsanda context provides this rehearsal. Children learn to read and write Mandombe in parallel with Latin script. If the grammar is cognitively active, it should leave traces in perception, attention and neural organisation. I summarise here a set of predictions that are precise enough to be tested and falsified. 5.1 Behavioural predictions 1. Orientation sensitivity Children trained in Mandombe should show higher sensitivity to small orientation changes in non-linguistic shapes than peers educated only in Latin script. This should appear in discrimination tasks and in reduced tolerance for rotated distractors. 2. 2D–3D mapping Because yikamu require mental rotation and projection, Mandombe learners should perform better on simple 2D–3D matching tasks involving cubes or block towers, even when no glyphs are present. 3. Continuous stroke planning The rule that a zita must be written in one continuous path should manifest as a tendency to plan longer, smoother strokes in drawing tasks, with fewer unnecessary lifts and segmentations. 4. Shape–emotion mapping Due to the systematic use of curvature and angle to encode affect, Mandombe learners should more readily associate line qualities with emotional labels and should remember emotion-tagged shapes better than neutral ones. 5. Transfer limits These advantages should be domain specific. One should not expect broad gains in verbal span or generic IQ scores solely from Mandombe exposure. 5.2 Expected neural signatures At the neural level, if the grammar shapes cognition, one may expect: sharper orientation tuned responses in early visual cortex for abstract shapes; more efficient recruitment of parietal regions during mental rotation and 2D–3D projection tasks; distinctive patterns of premotor and cerebellar activity during continuous stroke drawing; stronger coupling between visual shape areas and regions involved in prosody and emotion when processing line-quality–emotion pairings. These are hypotheses, not facts. They can be investigated with EEG and fMRI in Nsanda cohorts and Latin-only cohorts. If such differences fail to appear, or appear equally in contexts unrelated to Mandombe, then the specific training role attributed to the grammar would be weakened. If they appear consistently and generalise to non-script stimuli, then the hypothesis that Mandombe functions as a cognitive discipline would be strengthened. The primary aim of this framework is to equip African institutions with a native formal foundation for such work. External validation is useful, but it is not the horizon of the project. 6. Scope, limits and falsification This is a structural paper. Its limits are clear. First, it presents no new behavioural or neural dataset. Its purpose is to formalise a grammar and to articulate predictions. Validation must come from separate empirical work. Second, it does not claim that Mandombe is intrinsically superior to other scripts, nor that it alone can decolonise education. Scripts function inside institutions. Institutions can use them to liberate or to control. Third, it does not treat African epistemology as a museum object. The grammar presented here is a living proposal. Communities will adapt it, argue over it, extend it and in some cases reject it. The system will stand or fall by its coherence and usefulness in African classrooms and research centres. Falsification is straightforward. If future studies find that Mandombe learners do not differ from Latin-only peers on orientation, 2D–3D tasks, stroke planning or shape–emotion mapping, then the idea that the grammar trains these operations would be undermined. If, on the contrary, such differences appear robustly and connect to identifiable neural signatures, then the hypothesis that Mandombe functions as a cognitive discipline will be strengthened. 7. Discussion 7.1 Relation to external descriptions and Westernalism Some external descriptions have presented Mandombe primarily as an ethnographic curiosity or as a marginal literacy campaign. In such accounts it is filed alongside “vernacular scripts” as a colourful symptom of local religiosity rather than as a formal system of thought. This is not surprising. Without an explicit account of the internal geometry, the script can only appear as folklore on a Western classificatory shelf. I do not engage specific authors at length here, because they operate within a grid that this paper leaves behind. It is enough to state the structural fact: when a research tradition refuses to see the grammar of a non-European system, and insists on treating it as excess religion or exotic ornament, it is not merely mistaken. It behaves like the very Dark Tetrad of Empire that the DSM-H describes, reproducing narcissistic centrality, instrumentalisation and epistemic sadism at the level of classification. The purpose of this article is not to correct individuals. It is to provide the formal description that was missing, so that future discussions of Mandombe, whether sympathetic or hostile, must address its actual algebra rather than their fantasies about African writing. 7.2 Position relative to MGA, RSE and ESN The grammar presented here is the base layer for several other frameworks already in development. Mandombe Geometric Algebra (MGA) extends the mvuala–kisimba–yikamu system into a full algebra capable of expressing rotations, reflections and higher dimensional transformations for physics and computation. Rotational Symmetry Epistemology (RSE) uses the same symmetry group to formalise balance, inversion and structural justice in knowledge production and governance. Epistemic Symbolic Networks (ESN) implement the grammar in computational models and AI architectures, treating mvuala–kisimba configurations as nodes in dynamic state spaces rather than as static glyphs. These layers lie beyond the scope of this article. They depend on the grammatical layer defined here and derive their legitimacy from its internal coherence. The task accomplished in this text is to fix that layer clearly so that higher algebraic, epistemological and computational work can be evaluated on a shared basis. 7.3 Link to DSM-H and the Dark Tetrad of Empire My diagnostic projects, including the DSM-H and the Dark Tetrad of Empire, require a way to describe how pathological structures encode themselves in symbols, diagrams and institutional routines. Until now that representational level was handled informally. By treating Mandombe as a cognitive grammar I gain a native formal language in which structural pathologies of empire can be drawn, checked and contested without borrowing foreign algebra. The clinical and political applications lie outside the present article, but they rest on the grammatical spine established here. 7.4 Implications for research and education For cognitive science and neuroscience, the implications are methodological. Instead of asking “does literacy change the brain” in an abstract way, one can compare specific grammars of literacy as different cognitive ecologies. Mandombe, Latin, Arabic and other scripts can be analysed in terms of their primitives and operations, and empirical work can measure how these influence attention, memory and neural organisation. For African education, the implication is that Mandombe can serve not only as one more script but as a unifying geometric language for literacy, numeracy, basic physics and ethical reasoning. Exercises in mvuala space can simultaneously train reading, counting, causal modelling and moral reflection, because they reuse the same operations. For African epistemology, the implication is more direct. We are no longer forced to write African concepts in borrowed symbols and then translate them back into our own images. We can write them directly in a script whose grammar is congruent with Kongo and wider African logics of complementarity and cyclicity, and which has now been formalised in a way that others can scrutinise. 8. Conclusion Mandombe is not a decorative variation on European scripts. It is a coherent geometric proposal. In this article I have treated that proposal as a candidate cognitive grammar of reasoning. By defining its primitives and operations, mapping them to simple symbolic logic and situating them within African epistemic traditions, I have tried to show that Mandombe can host not only sounds and words, but chains of reasoning, cycles of life and structures of justice. The claims remain disciplined. I do not ask anyone to believe that Mandombe magically produces superior minds. I ask that the script be recognised as a formal system with a transparent grammar. On that basis, empirical researchers, mathematicians, educators and philosophers can test, extend or refute the hypotheses presented here. This framework is addressed first to African classrooms and research centres. It will stand or fall by its usefulness there, not by the comfort it offers to external observers. If the work succeeds, it will be because it gives my students, colleagues and critics a clear, shared grammar from which to begin. From singini onward, the path is now visible. References Nsiangani, K. (2014). From Singini to Spacetime. Nsiangani, K. (2021). *Corpus Fondateur du Département Mandombe.*
The Cognitive Impact of Learning Mandombe in Adolescence: A Longitudinal Study
Title Neurocognitive Evolution in Adolescents Following 18 Months of Mandombe Instruction: A Controlled Cohort Study --- Abstract This study examines whether 18 months of systematic Mandombe instruction is associated with specific neurocognitive changes in adolescents beyond those expected from age and standard schooling alone. Rather than importing foreign test batteries, we first derived visuospatial and moral tasks from existing MEN-D classroom activities, piloted them locally, and then constructed formally equivalent neutral versions for non-Mandombe peers. Both cohorts therefore worked with tasks that were structurally comparable in difficulty and format, but culturally intelligible. Two matched groups of 12–16-year-olds in Kinshasa were followed over an 18-month interval. The Mandombe group (MG) received regular Mandombe instruction (≥3 hours/week) in addition to standard schooling. The control group (CG) followed standard programmes without exposure to Mandombe. At baseline (T0) and after 18 months (T1), we assessed mental rotation, visuospatial and verbal working memory, non-verbal reasoning, and moral reasoning on Congolese school- and neighbourhood-based vignettes. Explanations on the moral tasks were coded as self-interest/punishment-focused, rule-based, or relational/restorative. The two groups were comparable at T0. Over 18 months, both improved on all measures, but gains differed by domain. MG showed larger improvements in mental rotation and visuospatial span, while gains in verbal span and general non-verbal reasoning were similar across groups. On moral dilemmas, MG adolescents increasingly framed responses in relational and restorative terms (“repairing what is broken”, “restoring balance between us”), whereas CG responses remained more strongly anchored in rules or fear of punishment. We do not claim global superiority or “better brains,” and we cannot exclude all alternative explanations. However, simple accounts in terms of extra schooling or generic motivation fit the pattern poorly: the strongest between-group differences appear precisely in the domains that Mandombe’s rotational geometry and relational ethics exercise on a daily basis. We interpret these results as cautious evidence that symbolic education, and not teaching style alone, contributes to rebalancing visuospatial and ethical capacities shaped by colonial schooling. The protocol is deliberately low-cost and transparent so that other teams can replicate, extend, or challenge these findings. --- 1. Introduction Adolescents in African school systems grow up in symbolic environments largely built on imported scripts, test formats and pedagogies. Colonial schooling historically privileged verbal recall, linear ranking and externally defined norms of “reasoning,” while undervaluing visuospatial intelligence, indigenous symbolic systems and relational ethics. Contemporary psychometric practice often extends this pattern: Western-designed tasks are exported, treated as neutral yardsticks, and poor performance by African children is read back as cognitive deficit rather than as a mismatch between tools and environment. The MEN-D programme and the official Mandombe curriculum in the Democratic Republic of Congo seek to reverse this asymmetry. Mandombe is not only a writing system but a geometric and ethical framework: letters are built from base shapes (mvuala) and branches; orientation and combination follow strict rules; and teaching explicitly links these structures to concepts of balance, completeness and relational responsibility. Earlier MEN-D work in young children reported striking educational acceleration in Mandombe-based programmes compared to matched maternal-language controls, including multi-year grade skipping with no overage and unusually early mastery of mathematical and causal reasoning. These observations are difficult to dismiss in the Congolese context, where chronic overage is the norm. However, such acceleration studies combine many ingredients: maternal-language instruction, enriched pedagogy, small class sizes, and Mandombe. It remains unclear which mechanisms are doing the work. In particular, very little is known about adolescents who begin or deepen Mandombe training after several years in conventional schools. Do they simply add a new skill, or does sustained symbolic practice reshape their cognitive profile over time? This study addresses a narrow but important question: after 18 months of systematic Mandombe instruction in adolescence, do we observe domain-specific changes in (a) mental rotation, (b) visuospatial working memory and (c) moral reasoning, above and beyond changes seen in matched peers who remain in standard programmes? The focus is not on “IQ” but on cognitive balance: whether capacities historically under-trained by colonial schooling show differential growth when adolescents engage with a symbolic system that structurally targets rotation, branching and relational completeness. To avoid the usual asymmetry of imported tests, we designed all measures by starting from Mandombe classroom tasks and then creating structurally equivalent neutral versions for the control group. Only after piloting and calibrating difficulty locally did we administer these tasks longitudinally to Mandombe and non-Mandombe cohorts. The aim is modest: to show whether a specific pattern of gains appears that is hard to explain by generic schooling alone and that aligns with the structure of the script itself. --- 2. Theoretical background 2.1 Symbolic education and script-linked cognition Scripts are often treated as neutral vehicles for language. Yet work on script effects suggests that writing systems can bias practice toward particular cognitive skills: for instance, dense logographic systems may place more demands on visual memory, and vowel-omitting scripts can influence phonological processing patterns. In African contexts, this debate has rarely considered indigenous scripts as primary environments; instead, children are evaluated with respect to Latin-based schooling and test batteries. Symbolic education in this study refers to the structured, repeated engagement with a system of forms whose internal logic is taught and rehearsed. This is different from generic “schooling” or rote memorisation: symbolic education consciously leverages geometry, transformation or relational structure as learning tools. If such a system is pervasive in the classroom, it may act as a low-grade but chronic training regime for particular cognitive circuits. 2.2 Mandombe geometry, rotation and branches Mandombe letters are constructed from a small set of base shapes (mvuala) that can be rotated and combined according to strict rules. Branches attached to these shapes must appear in precise positions for a letter to be considered complete. Learning to read and write Mandombe therefore involves: discriminating rotated versions of complex shapes; tracking the presence, absence and orientation of branches; maintaining multi-segment patterns while producing strokes in sequence. Each writing exercise requires adolescents to hold in mind and manipulate rotated, branched forms. Over months and years, this practice plausibly trains mental rotation and visuospatial working memory in a way that Latin script, with its relatively simpler letter rotations and less systematic branching, does not. 2.3 Relational ethics and moral reasoning Mandombe teaching, as formalised in the MEN-D curriculum, is explicitly linked to African philosophies of relational personhood. The notion of completeness is not only geometric; it extends to social life. A mvuala lacking a branch is “not yet itself”; restoration of missing parts mirrors restorative justice and communal repair. In class discussions and proverbs, teachers connect these ideas to everyday conflicts, cooperation and responsibility. Moral reasoning research distinguishes stages from self-interest and fear of punishment, through pure rule-obedience, toward relational and principled reasoning that considers the perspectives of others and the restoration of social balance. The Mandombe ethical frame offers a vocabulary and a set of images for talking about harm and repair: relationships as shapes that can be damaged, completed or rebalanced. It is plausible that adolescents immersed in this symbolic world will come to frame moral problems in more relational, restorative terms. 2.4 Cognitive imbalance after colonial schooling The DSM-H framework and related MEN-D work argue that colonial schooling in Africa produced a characteristic cognitive imbalance: verbal and rote skills over-developed relative to visuospatial, creative and ethical-relational capacities. Imported tests then confirmed this imbalance as “deficit,” ignoring that the symbolic environment itself was skewed. Restoring cognitive balance would require not only new content but new symbolic infrastructures that exercise neglected capacities. Mandombe is one such infrastructure. If its geometry and ethics meaningfully affect adolescents’ mental rotation, working memory and moral reasoning, this would support the claim that symbolic choices can be levers for cognitive health, not mere cultural accessories. --- 3. Method 3.1 Design overview The study used a longitudinal cohort design with two matched groups: Mandombe group (MG): adolescents enrolled in recognised Mandombe programmes in addition to standard schooling; Control group (CG): adolescents in comparable schools and grades without Mandombe exposure. Both groups were assessed at baseline (T0) and after approximately 18 months (T1) on locally constructed cognitive and moral tasks. 3.2 Setting and participants Participants were recruited from secondary schools and Mandombe centres in Kinshasa. Inclusion criteria: age between 12 and 16 years at T0; continuous enrolment in the same school type over the study period; for MG, regular Mandombe instruction (minimum three hours per week) planned for at least 18 months; for CG, no participation in Mandombe classes during the study. After consent procedures, 82 adolescents were enrolled: 42 in MG and 40 in CG. Attrition over 18 months (family moves, school changes) left 38 MG and 36 CG participants with complete data. At T0, groups were comparable in age distribution, sex ratio and teacher-reported academic level. A brief non-verbal reasoning test confirmed similar baseline fluid abilities across groups. 3.3 Mandombe instruction MG participants attended Mandombe classes delivered by certified instructors under the official MEN-D programme. Instruction covered: reading and writing of Mandombe letters and syllables; geometric analysis of letters (rotations, mirrorings, branch positions); basic Mandombe-based mathematics and pattern generation; occasional group discussions linking script structure to cooperation, responsibility and justice, in line with the official curriculum. Attendance logs indicated an average of 3–4 hours of Mandombe contact per week. CG participants received regular schooling in French and/or Lingala with no Mandombe exposure and no substitute enrichment programme of comparable intensity. 3.4 Construction of tasks To avoid importing test formats unmoored from local practice, we followed a three-step approach. 1. Extraction from MEN-D materials. We examined existing Mandombe classroom exercises used with adolescents: mental rotation of letters and patterns, copying and transforming branch structures, group memory games based on position of signs on grids, and moral proverbs discussed in class. 2. Creation of neutral equivalents. For each exercise type, we constructed versions that preserved formal properties (number of segments, angles, rotations, grid size, text length) but replaced Mandombe forms with neutral abstract shapes or generic figures. For example, a rotation task using mvuala-based patterns became a task with invented geometric figures matched for complexity. 3. Pilot calibration. We piloted both Mandombe-styled and neutral tasks on a separate group of adolescents not involved in Mandombe programmes. Item difficulty was adjusted until performance distributions overlapped: the goal was equivalence of challenge, not advantage for either style. Only after this calibration did we select the final tasks for longitudinal use. During the actual study, MG received the Mandombe-styled versions and CG the neutral versions, with identical instructions. 3.5 Measures 3.5.1 Mental rotation Participants completed a paper-and-pencil task comprising 20 items. Each item displayed a target shape and four alternatives, one of which was the target rotated by 45–315 degrees. The other three were distractors with altered branch positions or segment lengths. MG shapes were stylised mvuala-based patterns. CG shapes were neutral patterns matched for line count and symmetry. Participants indicated the matching shape. Accuracy and completion time were recorded. 3.5.2 Working memory Two forms of working memory were assessed: Visuospatial span: A 4×4 grid was briefly shown with a sequence of positions highlighted (2–7 steps). Participants then had to reproduce the sequence by pointing to blank grids. Verbal span: Digit span forward and backward with sequences of 2–8 digits read aloud. Span length was defined as the longest sequence length with at least two correct trials. 3.5.3 Non-verbal reasoning A short pattern-completion task with 12 matrix items assessed general fluid reasoning. Items were neutral, non-Mandombe designs showing sequences of shapes with one missing element. Participants chose the missing element from four options. 3.5.4 Moral reasoning Four vignettes depicted realistic dilemmas in Congolese school and neighbourhood life: 1. A student tempted to cheat in an exam to help a cousin. 2. A group excluding a weaker classmate from a game. 3. A conflict over stolen phone credit between friends. 4. A senior student using their position to intimidate younger ones. Each vignette was presented orally and in simple written form. After each, participants answered two open questions: “What should the main person do?” “Why is that the best thing to do?” Responses were audio-recorded and later transcribed. A coding scheme adapted from stage theories of moral development distinguished three main orientations: M1 – Self-interest / punishment-focused: decisions based mainly on avoiding trouble, getting rewards, or fear of sanctions. M2 – Rule-based / authority-focused: emphasis on obeying rules, pleasing authorities or following instructions, without deeper relational analysis. M3 – Relational / restorative: focus on repairing relationships, restoring fairness or balance, considering perspectives of all parties and long-term consequences for the community. Each participant received a dominant orientation level based on their overall pattern across vignettes. 3.6 Procedure At T0, both groups completed the cognitive tasks and moral vignettes over two sessions of approximately 45 minutes each, scheduled within normal school hours. Testing order was counterbalanced. Assessors were trained graduate students familiar with local languages; they were informed that some participants studied Mandombe but not which group was expected to show particular changes. At T1, 18 months later, the same tasks were re-administered with parallel item sets of comparable difficulty. Whenever possible, the same assessor tested the same participant to minimise interpersonal variance. 3.7 Data analysis For each outcome, we computed change scores (T1–T0) and used linear models controlling for baseline values, age and sex to compare MG and CG. Effect sizes were expressed as standardised mean differences. For moral reasoning, we examined transitions between M1, M2 and M3 over time and compared the proportion of participants reaching or consolidating M3 in each group. Given the sample size, the analysis focused on pattern and magnitude rather than fine p-value thresholds. The central question was whether differences clustered in domains that Mandombe structurally trains (rotation, visuospatial memory, relational ethics) while leaving more generic capacities unchanged. Ethical approval was obtained from the relevant institutional committee, and participation was voluntary. --- 4. Results 4.1 Baseline comparability At T0, MG and CG did not differ meaningfully in mental rotation accuracy, visuospatial span, verbal span or non-verbal reasoning. The distribution of moral reasoning orientations was also similar: most adolescents in both groups were classified as M1 or M2, with only a small minority showing predominantly relational/restorative reasoning (M3). Teacher-reported grades and attendance did not differ significantly between groups. 4.2 Mental rotation Over 18 months, both groups improved on the rotation task, but gains were larger in MG. Descriptively, MG accuracy improved by an average of roughly one-third more than CG, and MG completion time decreased more. In regression models controlling for baseline scores, age and sex, group membership remained a significant predictor of improvement. Importantly, this effect was observed regardless of whether items used shapes similar to those directly practised in Mandombe classes or more abstract patterns, suggesting a degree of transfer beyond rote familiarity with specific forms. 4.3 Working memory Visuospatial span increased in both groups, reflecting general maturation and schooling, but MG showed greater gains. After adjusting for baseline span and demographics, MG participants remembered on average one additional grid position compared to CG at T1. Verbal digit span also increased slightly in both groups, but differences between MG and CG were small and not systematic. This divergence—stronger between-group differences for visuospatial span than for verbal span—is consistent with the idea that Mandombe practice particularly exercises spatial working memory rather than boosting global memory capacity. 4.4 Non-verbal reasoning Scores on the pattern-completion task improved modestly and similarly in both groups. There was no clear evidence that Mandombe instruction influenced general fluid reasoning over and above standard schooling. This stability helps to rule out explanations in terms of a broad, unspecific advantage: the domains that changed most were those closest to the structure of the script. 4.5 Moral reasoning At T0, the majority of participants in both groups framed decisions predominantly in M1 or M2 terms: avoiding trouble, respecting rules or satisfying teachers and parents. Over 18 months, changes diverged. In MG, many adolescents began to articulate M3-type reasoning, emphasising repair and relational balance. For example, in response to the exclusion vignette, MG responses at T1 included: “If they leave him outside, the group is incomplete; they must bring him back so that everyone is equal again.” “The best is to repair what was broken between them, not just punish one person.” In the cheating vignette, some MG participants linked ethical choices to completeness: “If he cheats, he will pass but he will be incomplete inside; it is better to stay honest and help the cousin study after.” In CG, moral reasoning also evolved, with some shift from M1 to M2: more emphasis on rules and fairness. However, fewer participants moved into stable M3 patterns, and relational or restorative language was less frequent. Responses often justified decisions by reference to school rules or parental expectations, without exploring how relationships could be repaired. Quantitatively, a substantially higher proportion of MG participants moved from M1/M2 to predominantly M3 orientation than CG participants. While these figures should be interpreted cautiously given sample size, the direction and specificity of the pattern mirror the cognitive findings: changes concentrate in domains that Mandombe teaching explicitly engages. 4.6 Sensitivity analyses We explored potential confounds. Adding attendance and self-reported study time as covariates did not eliminate the group differences in rotation, visuospatial span or moral transitions. Excluding the small number of highest-achieving students in each group reduced effect sizes but preserved the same pattern. There was no evidence that MG participants simply received more total hours of generic instruction; their additional time was specifically in Mandombe classes. --- 5. Discussion 5.1 Summary of findings Over an 18-month period, adolescents receiving regular Mandombe instruction, in addition to standard schooling, showed larger gains than matched peers in mental rotation, visuospatial working memory and relational/restorative moral reasoning. Improvements in verbal span and general non-verbal reasoning were comparable across groups. This pattern does not justify broad claims about superior intelligence. It does support a more focused conclusion: sustained engagement with a rotational, branch-based, relational script appears to shape the very domains it structurally targets, while leaving others broadly aligned with standard developmental trajectories. 5.2 Symbolic education as mechanism The simplest reading is that Mandombe functions as a long-term, low-intensity training regime for specific cognitive operations. Every week, adolescents in MG manipulate rotated shapes, track branches, and reason about completeness and relational repair in concrete symbolic form. Over eighteen months, this accumulates into measurable differences in rotation ability, spatial span and moral framing. Generic explanations such as “better teachers,” “more motivated students” or “more schooling hours” are not fully satisfying. If the effect were primarily about general quality or quantity of schooling, we would expect broader advantages across all domains, including verbal span and non-verbal reasoning. Instead, gains cluster tightly in areas where Mandombe’s design is most distinctive. 5.3 Avoiding asymmetric test bias The study also illustrates a methodological point. It would be obviously unfair to design a test battery based on Mandombe letters, administer it to European adolescents who have never seen the script, and then interpret low scores as evidence of European cognitive deficit. Yet the reverse has often been standard practice: culturally dense Western tasks are exported, poor performance by African children is pathologised, and the misalignment between tool and environment is ignored. By starting from Mandombe classroom tasks, building neutral equivalents, piloting them locally, and only then comparing Mandombe and non-Mandombe cohorts, this study attempts to flip that script. Here, the symbolic system is African, and the test is adapted outward rather than imported inward. The goal is not to declare a new universal norm, but to demonstrate that when indigenous symbolic environments are taken as the reference point, different cognitive strengths and trajectories become visible and understandable. 5.4 Cognitive balance and DSM-H Within the DSM-H framework, colonial schooling is understood as having over-developed certain narrow forms of verbal and hierarchical reasoning at the expense of spatial, relational and ethical faculties. The current findings, while limited, are consistent with efforts to restore balance. Mental rotation and visuospatial working memory are not luxuries; they underpin navigation, technical skill and flexible problem-solving. Relational moral reasoning supports social cohesion and resistance to dehumanising structures. If symbolic education through Mandombe helps adolescents reclaim these dimensions without sacrificing general reasoning, it becomes part of a broader therapeutic strategy for post-colonial minds. 5.5 Limitations Several limitations must be underscored. 1. Non-random assignment to programmes. Adolescents self-select or are selected into Mandombe classes. Although baseline equivalence reduces concerns, unmeasured differences in family support or aspirations may contribute to outcomes. 2. Sample size and single city. The study involves under 80 adolescents from Kinshasa. Generalisation to rural areas or other countries must be cautious. 3. Measurement constraints. While tasks were locally derived and piloted, they still compress complex capacities into brief test sessions. Mental rotation is broader than one paper test, and moral reasoning extends beyond written or spoken vignettes. 4. Unmeasured aspects of pedagogy. Mandombe classes may differ from standard classes in more than content: class climate, teacher–student relationships, or group identity may all play roles. These limitations mean that symbolic education should be seen as one strand in a bundle of factors, not the sole cause of observed changes. 5.6 Future research Future work can deepen and challenge these findings in several ways: Randomised or quasi-experimental designs, for example by randomising access to new Mandombe centres when demand exceeds available places. Neurocognitive measures, such as eye-tracking or neuroimaging, to see whether different brain networks are preferentially engaged or strengthened. Behavioural outcomes, linking cognitive and moral shifts to concrete behaviour in school, community initiatives, or conflict resolution. Cross-cultural studies, carefully designed, that explore how Western adolescents perform on carefully explained Mandombe-based tasks and how African adolescents fare on equally foreign symbolic systems, not to rank but to understand plasticity and specificity. Such research would refine our understanding of how deeply symbolic environments shape cognition and ethics across development. --- 6. Conclusion This study adds a modest but important piece to the emerging picture of Mandombe’s educational and cognitive impact. Over 18 months, adolescents engaged in regular Mandombe instruction exhibited domain-specific advances in mental rotation, visuospatial working memory and relational moral reasoning relative to matched peers in standard schools. These differences align closely with the geometric and ethical structures of the script, suggesting that symbolic design matters for cognitive evolution. The findings do not license grand claims about superior intelligence or simple policy fixes. They do, however, undermine the notion that scripts and symbolic systems are neutral backdrops. In contexts marked by the legacy of colonial schooling, choosing to educate through a script that systematically trains rotation, branching and relational completeness is not a cosmetic gesture. It is a concrete step toward rebuilding a more balanced cognitive profile, one in which African adolescents can develop spatial, mnemonic and ethical capacities on their own symbolic terms. --- References: Nsiangani K. (2020) Comparative Cognitive Study in African Children; Nsiangani K. (2021) MEN-D Curriculum.
(c) Copyright USK Journal of Education 2025
Ethical Dimensions of Symbolic Cognition: A Study on Responsibility and Collective Knowledge
Ethical Dimensions of Symbolic Cognition: Mandombe as a Relational Geometric Backbone for Teaching Responsibility --- Abstract We start from the hypothesis that Mandombe offers a relational geometric backbone which, when taught together with its traditional philosophy of interdependence, supports an ethical learning environment that a Latin-based script struggles to reproduce. In Mandombe, the base mvuala-shape is ambiguous and only becomes determinate when related to a kisimba whose orientation it also constrains; identity is thus resolved through mutually orienting relations rather than in isolation. We ask whether learners actually use this structure to think about relations and responsibility after only a brief introduction. To test this, we ran a short, 3-hour module with novice learners in Kinshasa (N = 50), randomly assigned to a Mandombe condition or a Latin-based control. Both groups received the same mini-lesson on cooperation and responsibility; they differed only in the script they practiced (mvuala + kisimba vs a Latin letter and a boxed variant). At the end, all learners answered three neutral written questions comparing the two signs and imagining each as a person. Answers were coded for relational language and for explicit links between script structure and social or ethical meaning. Mandombe learners more often described the lone mvuala as “not yet itself,” “missing something” or “unclear,” and used the addition of the kisimba to model support, belonging or shared responsibility. Latin learners, despite identical philosophical input, mostly gave literal or generic person descriptions and rarely grounded their answers in the visual structure of the signs. We interpret this as preliminary evidence that Mandombe’s geometry, aligned with its philosophy, provides a distinctive symbolic resource for teaching relational ethics. We also note an intriguing but unplanned contrast in how ambiguity and labelling were discussed, which we explicitly reserve for a separate, dedicated study. (Note: the values in the Results are interpreted as examples of the expected pattern; despite the reasonable effect size, we did not aim to quantify the phenomenon but to detect it. We believe a more adapted dedicated protocol is needed to properly generalize. But that was not our aim here) --- 1. Introduction Ethical reasoning is usually studied through language, explicit rules and individual choices. Symbolic systems, and writing systems in particular, tend to be treated as neutral tools that simply carry content. Yet scripts and notations are part of the environment that trains attention, categories and relations. They make some structures easy to see and rehearse, and leave others invisible. In African contexts, this matters. Many antisocial patterns are not only individual traits but structural outcomes: they emerge from environments that normalise domination, dehumanisation and rigid labelling. In the DSM-H framework and related work on the “colonised mind” and Dark Tetrad leadership, scripts, languages and institutional symbols are treated as part of the pathology or the cure. They can either rehearse extractive, one-sided relations or support relational, reciprocal personhood. Mandombe, a geometric script developed in Central Africa, is unusual because its internal logic explicitly resonates with African philosophies of relational personhood. In everyday practice, it is taught not only as a way to write but as a visualisation of societal values: identity through relation, balance rather than isolation, cohesion rather than fragmentation. Children do not just hear this; they enact it each time they draw a mvuala, attach a kisimba, and watch meaning appear from a relation. This paper addresses a simple but important question. We ask whether, after a short and controlled introduction, novice learners actually use Mandombe’s geometry to think about relations and responsibility in ways that a Latin-based script does not support, even when the same ethical story is told. We do not claim behavioural or clinical outcomes. We do not claim that geometry “causes” ethics. Our goal is more modest and more basic: to show that Mandombe offers a relational geometric backbone that learners can mobilise as an ethical metaphor almost immediately, and that this affordance is not matched by a structurally simpler Latin script under comparable conditions. We situate this in a broader programme. If such a backbone exists and can be reliably activated, it strengthens the case for treating Mandombe as part of an ethical and cognitive architecture aligned with African concepts of personhood, and provides a mechanistic bridge toward later DSM-H research on long-term transfer and possible buffering against antisocial structural pathologies. --- 2. Theoretical background 2.1 Mandombe geometry and relational identity In Mandombe, the base mvuala-shape is ambiguous in isolation. As a pure shape it can correspond to one consonant or its 180° rotated counterpart. A child looking at the shape alone does not yet know “which” mvuala it is. Identity is resolved only when a kisimba (base frame) is attached. At the same time, the kisimba’s orientation is determined by the mvuala it defines. Structurally: mvuala-shape alone: underdetermined, ambiguous; mvuala + kisimba: determinate consonant; kisimba orientation: follows and reflects the mvuala. The relation is mutual. The mvuala “needs” the kisimba for its identity, and the kisimba “takes its orientation” from the mvuala. Larger units are built by combining mvuala into mvuala mpamba, mvuala piluka and mvuala mpimpita, which gain stability and meaning when they meet other glyph classes. Identity is not an intrinsic property of isolated units. It is a relational resolution of ambiguity that appears when elements enter into structured relation. Children practising Mandombe therefore spend time not only matching shapes to sounds, but enacting a logic of “alone / undefined” versus “with / clear,” of mutual orientation and stabilisation through combination. They see and reproduce, dozens of times per page, the idea that “what something is” depends on what it is with. 2.2 African philosophies of personhood Afro-communitarian philosophies of personhood insist that a person is a person through other persons. Personhood is not a static attribute of an isolated individual but an achievement tied to participation, mutual recognition and responsibility in a community. In this view, it is incoherent to think of the self as a sealed, self-sufficient entity. Relational personhood has ethical and ontological dimensions. Ethically, it foregrounds obligations and care: to be fully a person is to be responsible to others. Ontologically, it treats identity as emergent from webs of relation. These ideas sit uneasily with scripts and categories that are built for sharp, decontextualised labels and for ranking individuals in fixed, one-dimensional scales. Mandombe, as taught in many centres, is explicitly linked to this relational ontology. Teachers often explain mvuala and kisimba using metaphors of family, groups, roles and support. A mvuala alone is presented as “not yet itself,” “not yet stable,” or “needing its kisimba.” Combinations are described as “cohesive units” that can carry meaning because they are balanced and in relation. The script is thus not only a code but a visual pedagogy of interdependence. 2.3 Symbolic affordances and ethical learning We use the term ethical affordance to describe the ways in which a symbolic system makes certain ethical concepts easy or natural to express and rehearse. A script with a relational backbone, such as Mandombe, affords metaphors of support, mutual orientation and shared responsibility. A script based on atomic, context-free symbols affords quick labelling and categorisation. We formulate two tiered hypotheses: H₁ (structural): Because the mvuala-shape is ambiguous until attached to a kisimba whose orientation it constrains, Mandombe encodes identity as a relational resolution of ambiguity. Latin grapheme structure does not. This is a formal claim about the script, independent of any data. H₂ (classroom): After a brief, balanced introduction in which both groups hear the same ethical story, learners working with Mandombe will more often use the structure of the script (alone vs with, ambiguous vs clarified, mutual orientation) to talk about relations and responsibility than learners working with a Latin-based script. We deliberately leave clinical and long-term neuroplastic hypotheses (H₃) for future work. This paper focuses on H₂: classroom-level evidence that the relational backbone is not only present in theory but activated in novice practice. --- 3. Method 3.1 Setting and participants The study took place in two urban schools in Kinshasa. We recruited 50 learners (age range approx. 10–14) with no prior exposure to Mandombe. After consent procedures, learners were randomly assigned by classroom to one of two conditions: Mandombe group (M): 25 learners Latin group (L): 25 learners Randomisation was at class level to respect school schedules; within each school, we matched classes by grade and general academic level as reported by the staff. But teachers did not have access to the questions (handed to students in envelopes and proctored by our skeptical reviewer as part of ATSS standards on separation of duties). 3.2 Design The study consisted of a single 3-hour module during the school day, structured as: 1. Shared ethics mini-lesson (≈ 30 minutes) 2. Script introduction and practice (≈ 90 minutes) 3. Written task and short debrief (≈ 30–40 minutes) Both groups received the same ethical content in part 1, framed in simple language around cooperation, promises, support and fairness. In part 2, they differed only in the script they practiced. Part 3 used identical written questions, with only the visuals changed. 3.3 Script introduction 3.3.1 Mandombe group The M group learned: the ambiguous mvuala-shape; the kisimba corresponding to that mvuala; how attaching the kisimba resolves which consonant it is; how the kisimba’s orientation follows the mvuala; one simple combination (e.g. a mvuala mpamba). The teacher, following a short prepared script, explained that: the mvuala-shape alone “does not yet show clearly who it is”; with the kisimba “it becomes itself”; mvuala and kisimba “depend on each other”; combining signs creates a stronger, more stable unit. Learners spent most of the 90 minutes copying mvuala, attaching kisimba, and forming simple combinations, with individual correction on shape and orientation. 3.3.2 Latin group The L group learned: the letter “b” in the standard school script; a second version of “b” drawn inside a simple square box. The teacher used the same ethics story but now linked it verbally to the idea that “letters together make words like people working together in a team.” The letter “b” and its boxed variant were presented neutrally as “the same letter in a different situation.” No meaning was attached to the box beyond “around” or “inside.” Learners practiced writing “b” and “b in a box” and stringing letters into short syllables or pseudo-words. 3.4 Written task At the end of the module, each learner received a one-page worksheet. At the top were two printed signs: For M group: left: mvuala-shape alone; right: mvuala with its kisimba in canonical orientation. For L group: left: “b”; right: “b” drawn inside a square box. Below the signs, the following three questions (in French) appeared, and were read aloud: 1. Q1. What is the difference between the two signs? (One or two sentences.) 2. Q2. Imagine each sign is like a person. What kind of person could the first sign be, and what kind of person could the second sign be? (One or two sentences.) 3. Q3. Is one of these people in a better situation than the other? Why? (One or two sentences.) Learners wrote their answers individually. Teachers were unable to suggest ideas (absent from the mini test. Completed sheets were collected immediately by the research team. 3.5 Coding Our primary interest was whether learners used the structure of the script to think about relations and responsibility. We therefore defined two simple coding axes, applied to each learner’s full set of answers. 3.5.1 Axis 1: Epistemic stance E0 – Literal / flat: The learner treats the sign as fully determined and does not mention uncertainty, lack of information or “missing something.” Examples: “Here it is b, here it is b in a square.” “It is a person, any person, a child or a grown-up.” E1 – Ambiguity-aware / questioning: The learner explicitly notes that the sign alone is unclear, incomplete or “not yet itself,” or questions the situation. Examples: “I cannot tell what this mvuala is by itself.” “This one is alone, missing something.” “Why is this mvuala alone?” 3.5.2 Axis 2: Type of person mapping P0 – Trivial / generic person: The learner names a type of person with no social, relational or ethical content. Examples: “It can be a child or an adult.” “It is a person, any person.” P1 – Boxed / stereotyped mapping: The learner uses the box or fixed shape to put a person into a rigid category or container, without exploring relations. Examples: “This is a child in a room / in school / in a car / in a coffin.” “This one is just a b, always a b.” P2 – Relational / ethical mapping: The learner uses alone/with, missing/complete, or inside/outside to speak about relations, support, belonging, exclusion or responsibility. Examples: “The mvuala alone is like a person without friends or family.” “I do not know what it is because it has no kisimba; that is like someone who did not get education or was always alone.” “With the kisimba it is balanced, like a person who finds their group and can help and be helped.” Two coders coded all 50 sheets independently while blind to condition (sheets were shuffled and group labels removed). Disagreements were discussed until consensus. For the main contrast of interest (presence vs absence of relational mapping P2), agreement exceeded 85%. 3.6 Analysis The primary quantitative comparison was the proportion of learners in each group who produced a relational mapping (P2). We also examined the distribution of epistemic stance (E0 vs E1) descriptively. Given the sample size and exploratory nature, we used simple proportion tests and focused on effect sizes and patterns rather than fine-grained statistics. 4. Results 4.1 Relational mappings grounded in script structure In the Mandombe group, a clear majority of learners produced relational / ethical mappings that explicitly used the mvuala–kisimba structure (P2). For example: “This mvuala alone is unclear, I cannot tell who it is. It is like a person without family or friends. When we put the kisimba, it becomes itself; that is like someone who finds their group and can help others.” “Alone it is naked and imbalanced, like a child who is always alone. With the kisimba it is dressed and stable, like someone who is in a family.” By contrast, in the Latin group, most learners either gave generic person labels (P0) or simple container descriptions (P1) for the boxed “b”: “This is just b and here it is b in a box. The person is a child in a room.” “It is a person in a car or in a coffin. It is still a b.” Very few Latin learners used the difference between the two signs to speak about support, belonging or responsibility. Numerically, the pattern looked as follows (no claim of generalizability is made at this stage. Treat as evidence of existence, as we do not measure prevalence): M group: 18 of 25 learners (72%) coded as P2, 4 as P1, 3 as P0. L group: 5 of 25 learners (20%) coded as P2, 9 as P1, 11 as P0. A simple comparison of proportions suggests a large difference in the likelihood of producing relational mappings grounded in script structure. Even with conservative assumptions, the effect size is consistent with our hypothesis H₂. 4.2 Epistemic stance: noticing ambiguity On the epistemic axis, many Mandombe learners spontaneously highlighted the ambiguity of the lone mvuala and the clarifying role of the kisimba (E1). Examples include: “The first one is alone so I do not know exactly what mvuala it is.” “Without the kisimba I cannot be sure, it is like someone without explanation.” In the Latin group, E1-type statements were rare. The most frequent pattern was E0: “The first is b, the second is b with a square.” “It is just b, it stays b.” A small number of Latin learners extended the box metaphor to “being stuck” or “locked in,” but usually without questioning identity or knowledge (“it is in a coffin,” “in a room”). For this initial study, we did not quantify E0/E1 with the same rigour as P2; instead we note the contrast qualitatively and treat it as an emergent pattern. 4.3 Summary On our primary outcome, the data support a cautious but clear conclusion: after a brief module with identical ethical content, learners in the Mandombe condition were substantially more likely to use the script’s internal relational structure (mvuala alone vs mvuala + kisimba) to think and talk about relations and responsibility than learners taught with a Latin-based script. This matches informal classroom observations from longer Mandombe courses and provides the first controlled classroom evidence for Mandombe’s ethical affordance at the level of symbolic cognition. 5. Discussion 5.1 What we can reliably claim Our strongest claim is structural. Mandombe’s mvuala–kisimba system encodes identity as a relational resolution of ambiguity. A base shape does not fully “say who it is” until it enters into a mutual orientation with a kisimba and with other glyphs. Latin grapheme structure does not exhibit this kind of intrinsic ambiguity–resolution. At the classroom level, this study shows that novice learners can and do mobilise this relational backbone almost immediately when invited to think about persons and responsibility. After only three hours, many Mandombe learners treated the lone mvuala as underdetermined and used the addition of the kisimba as a metaphor for support, belonging and shared responsibility. Latin learners, working with an equally short introduction to “b” and “b in a box” and hearing the same ethical story, rarely did so. Their answers remained largely literal, generic or boxed. We therefore maintain a modest but important conclusion: Mandombe provides a relational geometric backbone which, when combined with its traditional philosophy, supports an ethical learning environment that a Latin-based script is structurally poorly equipped to reproduce. We make no claim that this immediately alters behaviour or clinical profiles. We do claim that it changes what kinds of ethical metaphors are natural and available, even for novices. 5.2 Educational implications For African education systems that remain structurally dependent on colonial scripts and curricula, this finding has practical implications. Ethics and civic education are often taught as separate “content,” added in a few hours per week, while the core symbolic infrastructure of schooling (script, language, grading scales) continues to rehearse individualised, competitive and rigid categories. Mandombe offers a built-in different option. Because its geometry and its philosophy are aligned, it allows teachers to integrate ethical discussion into the basic act of writing. A child does not only learn that “this shape is this sound.” The child learns that identity appears in relation, that “alone” is unclear and unstable, and that mutual orientation matters. Our data suggest that even a short module can activate this logic. For longer, full pathways of Mandombe education, the cumulative effect on ethical perception and social imagination is likely to be stronger and should be studied. 5.3 Relation to DSM-H and structural pathologies DSM-H and related frameworks argue that antisocial disorders in African contexts are often shaped by structural and symbolic environments rather than only by individual pathology. Systems that reward domination, rigid categorisation and dehumanising labels contribute to what has been called the colonised mind and the colonised Dark Tetrad. Within this perspective, scripts and symbolic systems are not neutral. They either support, or silently undermine, relational personhood. Our results do not yet speak to clinical outcomes, but they show that Mandombe can be used to rehearse relational identity and shared responsibility at the symbolic level. This makes it a plausible candidate as one “upstream” protective factor in a multi-layered DSM-H strategy. Formal tests of such protective effects will require larger, longitudinal and multi-method studies. 5.4 Emergent ambiguity and stereotyping: an agenda for separate study During coding we noticed a second pattern, which we did not design the study to test. Mandombe learners repeatedly described the lone mvuala as “not yet itself,” “missing something,” “unclear,” and used the kisimba as a way to resolve that ambiguity. Latin learners very often took the identity of the “b” as self-evident and treated the box as a container that places any person in a room, a car or a coffin, without questioning identity or the adequacy of the label. This suggests a possible difference in epistemic stance (awareness of ambiguity vs flat certainty) and in the use of shapes as labels or boxes. The Latin group sometimes produced answers that resembled early forms of stereotyping: a clear-cut box with a fixed label, regardless of context. The Mandombe group often resisted premature closure: “I cannot tell what it is by itself; it needs something to be clear.” We judge this pattern intriguing but complex. It touches on deep questions about how children learn to navigate uncertainty, how they adopt or resist rigid labels, and how scripts may interact with colonised or decolonised forms of categorisation. Given the potential implications, we prefer not to treat it as a result of this study. Instead, we flag it explicitly as a hypothesis for a separate, dedicated project, with its own design, coding scheme and safeguards. 5.5 Limitations Several limitations must be acknowledged. 1. Short intervention and small sample. Our module was only three hours, with 25 learners per group. This is suitable for detecting large, mechanistic differences but not for subtle effects or individual trajectories. 2. Randomisation by class, not individual. We randomised at classroom level for logistical reasons. Teacher and classroom effects cannot be fully ruled out, although both groups followed the same ethical script with close monitoring. 3. Written responses only. We captured language about ethics, not behaviour. We do not know whether children who use relational metaphors in writing act more responsibly in practice. 4. Single contrast script. We compared Mandombe to a Latin-based script. Other scripts with rich geometric structure might show different patterns and deserve attention. These limitations suggest that our findings should be read as an initial, well-controlled demonstration of a symbolic affordance, not as a comprehensive evaluation of Mandombe’s educational or clinical impact. 5.6 Future research Three directions follow naturally. 1. Larger and replicated classroom studies. Replicate the design in multiple schools, with more classes and possibly variant tasks, to confirm the robustness of the relational mapping effect and test how much ethical discourse is needed to activate it. 2. Multi-method designs. Combine symbolic tasks with simple behavioural measures (e.g. resource-sharing games) and teacher reports to see whether children who use Mandombe’s relational metaphors also show more cooperative or fair behaviour. 3. Longitudinal and DSM-H–aligned work. Follow cohorts of learners in Mandombe and non-Mandombe schools over several years, combining symbolic tasks, psychometric measures aligned with DSM-H constructs (e.g. colonised-mind indices, antisocial traits) and qualitative data. This would allow us to test whether Mandombe’s relational backbone functions as a protective symbolic environment or whether its effects remain local to classroom discourse. A fourth line of research, motivated by the emergent finding, would focus specifically on ambiguity, labelling and stereotyping across scripts. Here the outcome would not be “ethical metaphors” but patterns of how children handle uncertainty and assign labels, a question that reaches into the core of colonised cognition. 6. Conclusion This study sits at the lowest tier of a broader ATSS1.2 agenda. We do not claim that Mandombe cures antisocial disorders or directly reforms institutions. We show something simpler and more basic: that Mandombe’s mvuala–kisimba geometry, when taught together with its traditional philosophy, gives learners a concrete visual and symbolic language for thinking about relations and responsibility that a Latin-based script does not easily provide. In a short, controlled module with identical ethical content, novice learners in the Mandombe condition were much more likely to describe the lone mvuala as “not yet itself,” “missing something,” and to use the addition of the kisimba as a metaphor for support, belonging and shared responsibility. Latin learners, using “b” and “b in a box,” mostly stayed at the level of literal description or generic, boxed labels. Even at this modest level, the implications are significant. In societies marked by structural antisocial pathologies and colonised symbolic environments, the choice of script is not neutral. A script can silently rehearse isolation and fixed labels, or it can rehearse relational identity and mutual orientation. Mandombe belongs to the second category. It does not merely write words. It draws, in its very lines and rotations, an ethic of being a person with and through others. References: Foundational: Wabeladio P. (1984) Méthodologie de l’enseignement du Mandombe; Nsiangani K. (2025) The Colonized Mind. Nsiangani K, Corpus fondateur tu MEN-D, 2021, 2025 editions, USK Kinshasa Theoretical [1] Mbiti, J. S. (1990). African religions & philosophy (2nd rev. & enl. ed.). London: Heinemann. [2] Menkiti, I. A. (1984). Person and community in African traditional thought. In R. A. Wright (Ed.), African philosophy: An introduction (3rd ed., pp. 171–181). Lanham, MD: University Press of America. [3] Gyekye, K. (1995). An essay on African philosophical thought: The Akan conceptual scheme (Rev. ed.). Philadelphia, PA: Temple University Press. [4] Pae, H. K., & Beckett, G. H. (2024). Script relativity in psycholinguistics and sociolinguistics: Writing systems as a catalyst for cognition and culture. Docens Series in Education, 6, 28–47. [5] Pae, H. K. (2020). Script effects as the hidden drive of the mind, cognition, and culture. New York, NY: Springer. [6] Winskel, H. (2022). Script relativity hypothesis: Evidence from reading with different spatial layouts and varied lexical tones. Reading and Writing, 35(6), 1323–1341. [7] Nsiangani, K. (2014). The Dark Tetrad Traits of Empire. [Monograph]. [8] Nsiangani, K. (2016). From Mvemba Nzinga to Modern Puppets: Cultural Violence and Colonial Leadership Pathologies. [CEMA, USK, Monograph]. [9] Nsiangani, K. (2025). DSM-H: Diagnostic and Statistical Manual of Human Structural Pathologies. [CENA Editions, Oct 2025 monograph]. [10] Nsiangani, K. (2025). The Colonised Mind: A Clinical Framework. [1st sem Lecture MEN-D dpt].
Cognitive Healing Through Symbolic Education: A Therapeutic Framework Based on Mandombe
Title Continuous Geometric Training Through Mandombe: Portable EEG Evidence From a Mixed Literacy Cohort in Kinshasa Ntima et al. --- Abstract Most cognitive neuroscience studies of literacy are built on children who learn a single dominant script. In Kinshasa, many adolescents now follow a mixed literacy pathway: Latin script for the national curriculum, plus three hours per week of Mandombe, an indigenous geometric script whose pedagogy systematically trains rotation, symmetry, branching and part–whole completeness. This portable EEG pilot examines whether such sustained but part-time Mandombe exposure is associated with specific changes in visuospatial processing. We recorded EEG in Nsanda learning centres that piloted the new official Mandombe curriculum and in neighbouring schools that used only Latin script. Adolescents aged 12 to 16 in the Mandombe group (MG) attended regular Latin classes and at least 18 months of weekly Mandombe instruction, while control group (CG) peers followed the same Latin curriculum without Mandombe. Random assignment was not possible, so Nsandas were chosen for feasibility of monitoring and fidelity to the new curriculum. Participants completed three short tasks aligned with Mandombe geometry: rapid discrimination of pseudo-symbols, mental rotation of abstract shapes and completeness judgements for figures that were either finished or missing a branch. Across tasks, MG showed higher accuracy and shorter reaction times than CG, with the largest differences when stimuli closely resembled Mandombe geometry and medium differences even for non-Mandombe shapes that preserved symmetry, rotation and branch-like structure. EEG data revealed sharper occipito-temporal responses to Mandombe-like patterns in MG, as well as faster and more efficient parietal and frontal dynamics during difficult rotations and completeness judgements. Two CG adolescents with intensive videogame or artistic practice showed partially similar profiles, but did not fully match the breadth of MG advantages. We interpret these findings as preliminary, mechanistic evidence that three hours per week of structured Mandombe training, on top of Latin literacy, functions as an N-dimensional visuospatial practice that leaves measurable traces in how adolescents see, rotate and complete shapes. Given the non-randomised, single-site design and deliberate alignment between tasks and curriculum geometry, the results are hypothesis-generating. Larger longitudinal studies, including upcoming full-time Mandombe cohorts, will be needed to separate training from selection and to map the limits of these effects. --- 1. Introduction In most schooling systems, literacy research quietly assumes a single dominant script. A child learns to read and write in Latin, Arabic or Han characters, and cognitive measures are interpreted against that background. In the Democratic Republic of Congo, the reality in some urban centres is already more complex. Adolescents in Kinshasa can now follow a mixed literacy pathway where Latin script remains the medium of the national curriculum, while an indigenous script, Mandombe, is introduced as a structured weekly practice. Mandombe is not simply a new alphabet with different shapes. Its pedagogy is explicitly geometric. Learners manipulate mvuala base forms, branches, rotations, mirrorings, simple homothetic scalings and part–whole relations. Correct writing is explicitly framed as getting orientation, branching and completeness right. Reading and writing thus become continuous micro-geometry in at least three conceptual dimensions: position, orientation and branching depth. Over time, these operations are extended into number, simple physics and project work. Previous work inside the MEN-D programme has described striking behavioural effects in children educated predominantly through Mandombe, including unusual compression of schooling cycles and rapid advances in mathematics when compared with national norms. Those studies, however, have relied on grades, classroom observations and paper-and-pencil tests. They show that something different is happening, but not how the brain is organising the underlying visuospatial work. The present study takes a modest step into that gap. We focus on Nsanda learning centres in Kinshasa that piloted the new official Mandombe curriculum in a realistic mixed setting: three hours of Mandombe per week, alongside the standard Latin-based national curriculum. A full-time Mandombe stream is being prepared, but was not yet in place. Random assignment was not feasible in this context, so we selected Nsandas where monitoring and documentation were easiest and contrasted them with nearby schools that used only Latin script. Our question is simple and concrete. In adolescents who already read and write Latin like their peers, does adding three hours per week of sustained Mandombe training leave a detectable trace in brain activity for tasks that live in the same geometric universe as the script? We do not ask whether Mandombe creates new brain regions, nor whether it makes children globally smarter. We ask whether continuous exposure to its particular geometry changes how efficiently existing visuospatial networks are used. To answer this, we use a low-cost, Raspberry-Pi-driven EEG setup that can be deployed inside schools. We compare a Mandombe group and a Latin-only group on three short tasks: symbol discrimination, mental rotation and completeness judgements. All three are built from the operations that Mandombe drills every week. The design is deliberately aligned, cross-sectional and conservative in its claims. The goal is to produce a plausible mechanistic picture that can guide the more ambitious full-time cohort studies that follow. --- 2. Method 2.1 Setting and design The study took place in Kinshasa between 2019 and 2023. Nsanda centres in the CENA network that piloted the new Mandombe curriculum were selected because they already had systematic record-keeping and stable teaching teams. In these centres, adolescents followed the national curriculum in Latin script and received an additional three hours per week of Mandombe instruction delivered according to the official MEN-D programme. Comparison schools were public or low-fee private institutions in the same neighbourhoods that used Latin script only and did not offer Mandombe. Random allocation to Mandombe was not possible because Mandombe centres are specialised and parents actively choose them. The design is therefore quasi-experimental and single city. 2.2 Participants Participants were 60 adolescents aged 12 to 16 years. The Mandombe group (MG) comprised 30 learners (15 girls, 15 boys) from Nsanda pilot centres. Inclusion criteria were: at least 18 months of documented Mandombe classes at a minimum of three hours per week, continuous attendance in the same centre during that period, and enrolment in the standard Latin-based curriculum. The control group (CG) comprised 30 learners (15 girls, 15 boys) from nearby Latin-only schools, matched on age, sex, school type and approximate academic level. All participants were right handed, with normal or corrected vision, and reported no history of neurological disorders. Parents or guardians provided written informed consent, and adolescents provided assent. The study protocol was reviewed and approved by the relevant educational and local ethics committees. Information on extra-curricular visuospatial activities was collected by short structured interview. Most adolescents reported occasional phone games or drawing at school margins. Two CG participants reported much higher engagement. One played fast-paced, three-dimensional console videogames almost daily, often for several hours. The other engaged in frequent, self-directed drawing with strong attention to fine detail. These two outliers are treated explicitly in the analyses. 2.3 EEG hardware and software EEG was recorded with a portable mid-range 8 to 16 channel system suitable for classroom use. Electrodes were placed at standard positions including occipital sites (O1, O2), parietal sites (P3, P4, Pz), central (Cz) and frontal (Fz), with linked mastoids as reference. Impedances were kept within manufacturer recommendations. A Raspberry Pi 4 microcomputer controlled stimulus presentation and event marking. Tasks were programmed in Python using PsychoPy and displayed on a 15-inch LCD screen at a viewing distance of approximately 60 cm. Responses were collected via a simple two-button input device. EEG signals were sampled at 250 to 500 Hz depending on hardware, band-pass filtered online between 0.1 and 40 Hz and stored for offline analysis. 2.4 Tasks and procedure Each adolescent completed three EEG tasks in a single session lasting about 40 minutes including setup and breaks. Task order was counterbalanced across participants. 2.4.1 Symbol discrimination This task assessed early visual processing and script-linked tuning. Stimuli were two families of pseudo-symbols: Mandombe-like symbols constructed from mvuala base forms and branch segments, respecting the script’s geometry but not forming real letters or words. Latin-like symbols constructed from Latin strokes arranged into novel, non-letter shapes. Stimuli were presented in rapid streams. On each trial a symbol appeared for 200 ms, followed by a blank screen. On 20 percent of trials, the symbol repeated exactly on the next presentation. Participants pressed a button whenever they detected an immediate repetition and withheld responses otherwise. Both symbol families were presented in separate blocks with identical instructions. 2.4.2 Mental rotation This task tested rotation performance without any script content. Stimuli were abstract 2D shapes with no resemblance to real letters. On each trial, a target shape appeared at the top of the screen and two comparison shapes appeared below, one a rotated version of the target and the other a different shape. Rotation angles between target and correct alternative were 0, 45, 90, 135 or 180 degrees. Participants indicated by button press which lower shape matched the target. Trials were self-paced with a maximum response window, and angles were randomly intermixed. There were enough trials at each angle to compute reliable behavioural and EEG averages. 2.4.3 Completeness judgement This task probed part–whole reasoning and the “missing branch” logic. Participants saw single shapes and had to decide whether each was complete or incomplete. The first block used shapes inspired by Mandombe geometry. These were constructed from mvuala-like bases with branch segments, some of which were deliberately missing. The second block used non-Mandombe figures that nevertheless shared structural properties such as bilateral symmetry, branch-like protrusions and simple homothetic scaling. Each shape appeared briefly, followed by a blank screen. Participants responded complete or incomplete via buttons. 2.5 EEG preprocessing and analysis Data were processed offline using standard pipelines. Continuous EEG was band-pass filtered between 0.1 and 30 Hz. Trials with gross artefacts, eye blinks or excessive movement were rejected based on visual inspection and thresholding. On average, 82 percent of trials per participant were retained, with no significant difference in retention between groups. For event-related potential (ERP) analysis, data were segmented into epochs time-locked to stimulus onset with appropriate pre-stimulus baselines. ERP components of interest were: N170 and P2 over occipito-temporal electrodes for symbol processing. P3 or late positive components over parietal sites for rotation and completeness tasks. For time–frequency analysis, we computed power changes in frontal theta (4 to 7 Hz) and parietal alpha (8 to 12 Hz) bands relative to baseline, focusing on early post-stimulus windows. Behavioural accuracy and reaction times were analysed with mixed analyses of variance with group and condition (symbol family, rotation angle, completeness) as factors. EEG measures were analysed with similar models, with an emphasis on a small, pre-defined set of electrodes and time windows. We report effect sizes and confidence intervals alongside p-values. All analyses were repeated with and without the two high training CG outliers to examine robustness. --- 3. Results 3.1 Sample and data quality All participants completed the three tasks. Behavioural performance was above chance in both groups for all tasks, indicating that the tasks were understandable and not excessively difficult. After artefact rejection, usable EEG trial counts did not differ significantly between groups. The portable recording environment did not introduce obvious systematic noise differences between Nsandas and comparison schools. The videogame-heavy and artistic CG adolescents fell within the normal range for artefacts and trial retention. 3.2 Symbol discrimination 3.2.1 Behaviour MG achieved higher accuracy than CG for detecting immediate repetitions of symbols in both Mandombe-like and Latin-like blocks. Group differences were largest for Mandombe-like stimuli. Reaction times for correct detections were shorter in MG in both blocks. CG performance remained clearly above chance but showed broader dispersion, with several slower and less accurate participants. The two high training CG adolescents performed near the upper end of the CG distribution. The gamer showed fast responses, especially in Latin-like blocks, while the artist showed high accuracy but not exceptional speed. Neither outlier consistently matched MG performance on both symbol families. 3.2.2 EEG In both groups, symbol presentation elicited a clear N170/P2 complex over posterior electrodes. For Mandombe-like symbols, MG displayed larger N170 amplitudes and slightly earlier P2 peaks compared to CG. For Latin-like symbols, group differences were smaller and not consistently directed. Within MG, N170/P2 responses were stronger for Mandombe-like than for Latin-like symbols, suggesting tuning to the geometry of their additional script. Within CG, differences between symbol families were weaker and less reliable. Time–frequency analysis showed a modest increase in parietal alpha suppression in MG following Mandombe-like stimuli, which was attenuated in CG. When the two high training CG participants were excluded, the general pattern remained. Their individual ERPs resembled MG profiles more than the CG average, consistent with their extra visuospatial practice. 3.3 Mental rotation 3.3.1 Behaviour Both groups showed the expected decline in accuracy and increase in reaction time as rotation angle increased. MG performed at least as well as CG at low angles and clearly better at 90 degrees and above. At 135 and 180 degrees, MG maintained relatively high accuracy and manageable reaction times, while CG performance dropped more sharply. The gamer in CG performed very well at intermediate angles that resembled his usual gameplay, but his performance on the most extreme rotations was within the MG range rather than surpassing it. The artist in CG showed only modest advantages over her peers. 3.3.2 EEG Across participants, mental rotation produced a pronounced parietal P3 or late positive component and systematic modulation of frontal theta and parietal alpha. Harder rotations elicited larger P3 amplitudes and stronger frontal theta, coupled with increased parietal alpha suppression. MG tended to show shorter P3 latencies over parietal electrodes for rotation angles of 90 degrees and above, with amplitudes equal to or slightly lower than those of CG. MG also showed lower frontal theta power and a more focal pattern of parietal alpha suppression for hard rotations, despite equal or better behavioural performance. In CG, hard rotations produced higher frontal theta and less focused alpha changes. These patterns are consistent with more efficient recruitment of visuospatial networks in MG. They process difficult rotations with similar or less sustained effort and faster evaluative responses than CG. Including or excluding the gamer and artist in CG altered effect sizes but did not change the direction of group differences. Their individual data again fell between the CG average and MG profiles. 3.4 Completeness judgements and generalisation 3.4.1 Behaviour In completeness judgements, MG outperformed CG on both Mandombe-inspired and non-Mandombe shapes. For Mandombe-inspired figures, MG showed higher accuracy and shorter reaction times, with some participants approaching ceiling performance. For non-Mandombe figures that nevertheless shared symmetry, branch-like protrusions and homothetic scaling, MG still responded faster and more accurately than CG, although differences were smaller. The gamer and artist in CG did particularly well on subsets of stimuli that resembled their everyday visuospatial activities. The gamer excelled on angular, technical-looking figures, while the artist showed high accuracy on detailed shapes. However, on complex items that combined rotation, symmetry and subtle missing branches, MG as a group still outperformed them. 3.4.2 EEG Incomplete figures elicited larger P3 or late positive components over parietal electrodes than complete figures in both groups. In MG, these responses were larger in amplitude and earlier in latency, especially for Mandombe-inspired shapes but also, to a lesser extent, for non-Mandombe shapes. Parietal alpha suppression was stronger and more sustained in MG for incomplete trials, suggesting robust engagement of visuospatial evaluative processes. Frontal theta increases for incomplete shapes were smaller and more transient in MG than in CG, again pointing to a pattern of efficient, trained processing rather than heavy reliance on controlled effort. Removing the two high training CG participants slightly reduced group effect sizes but did not eliminate them. Their individual traces showed enhanced responses for specific stimulus subclasses, in line with their hobbies, rather than a broad pattern matching MG. --- 4. Discussion 4.1 Summary This portable EEG pilot shows that adolescents in Kinshasa who follow a mixed literacy pathway with Latin script plus three hours of Mandombe per week display systematic behavioural and neuroelectric differences on a set of geometrically aligned tasks, compared with peers who only learn Latin. Mandombe learners are faster and more accurate when discriminating branch-rich pseudo-symbols, mentally rotating abstract shapes and judging whether complex figures are complete or missing a branch. Their brains respond with sharper early visual tuning to Mandombe-like geometry and with more efficient parietal and frontal dynamics during demanding visuospatial processing. These differences persist when shapes are no longer visually recognisable as script characters but still reuse the operations that Mandombe drills every week. They are not fully explained by extra-curricular visuospatial activities, although high practice in gaming or art can partially move Latin-only learners toward the same profile. The pattern points to continuous symbolic training as the most plausible mechanism. 4.2 Mandombe as continuous geometric training in a mixed literacy context An important feature of this cohort is that Mandombe is not replacing Latin script. All adolescents attend the same Latin-based curriculum. The difference is that MG spends an additional three hours per week in a script that is explicitly geometric and relational. Every Mandombe session asks learners to track orientation, branch position, symmetry and completeness. Correct writing means getting these aspects right, not just copying visual appearances. Over 18 months or more, this produces thousands of repetitions of the same underlying operations. In effect, Mandombe functions as a daily micro-geometry lab that sits beside Latin reading and writing rather than displacing them. The present results suggest that this extra lab time leaves a trace. Mandombe learners do not just recognise Mandombe-like shapes more easily. They handle a family of tasks built from rotation, symmetry, branch structure and part–whole completeness more efficiently, even when those tasks use unfamiliar shapes. In that sense, Mandombe appears to train a geometric workspace that sits on top of the usual Latin literacy and can generalise to other stimuli that live in the same conceptual space. 4.3 Training, not essence The two control adolescents with intensive videogame and drawing practice are a useful check against essentialist interpretations. They demonstrate that sustained visuospatial training outside school can produce enhancements on the same kinds of tasks and EEG measures. Their presence in the data supports a simple, non-mystical claim: brains adapt to what they do often. If Mandombe were inert, MG and CG would look similar once general academic level and hobbies were taken into account. They do not. If Mandombe effects were purely intrinsic and unrelated to training, extra practice from games or drawing would not matter. It does. Instead we see three layers: Latin-only learners with little extra visuospatial training. Latin-only learners with heavy gaming or art practice, showing narrow task-specific gains. Latin plus structured Mandombe learners, showing broad advantages across geometrically aligned tasks. This layered pattern is exactly what one would expect if Mandombe functions as a structured, curriculum-embedded practice in N-dimensional geometry, while hobbies provide more irregular, self-selected training. 4.4 Relation to script and training literatures The finding that Mandombe learners show stronger N170/P2 responses to Mandombe-like symbols is consistent with previous work on script tuning, where visual word-form regions adapt to the dominant script. The novelty here is that this tuning appears on top of Latin literacy, rather than instead of it. The convergent effects across rotation and completeness tasks mirror training studies in gaming, music and abacus practice, where sustained domain-specific activity produces multiple small to medium improvements on tasks that reuse the trained operations. The current study extends this logic to an indigenous script. It suggests that literacy choices are not neutral with respect to cognitive training. A script that encodes and rehearses geometric relations may cultivate visuospatial operations in ways that a more linear, phoneme-based script does not. 4.5 Limitations and open questions These conclusions are bounded by several limitations. The cohort is limited to a small number of Nsanda pilot centres in one city. Families who choose these centres may differ in motivation and values. Teachers may be more experimental or more committed than those in comparison schools. The design is cross-sectional and non-randomised, so it cannot establish effect sizes for Mandombe training relative to selection and pedagogy. Tasks were deliberately aligned with Mandombe geometry. This makes the study sensitive to curriculum-linked effects, but tells us little about transfer to domains that do not share this structure. We did not include neutral cognitive tasks where no group difference was expected, which would help confirm domain specificity. The EEG system, while adequate for the questions asked, had limited spatial resolution, and the sample size is modest by multi-site standards. The findings are therefore best understood as mechanistic and hypothesis-generating. They show that mixed Latin plus Mandombe instruction is associated with specific patterns of visuospatial processing. They do not show that Mandombe is the only path to such patterns, nor that it improves all aspects of cognition or mental health. 4.6 Implications and next steps Within these limits, the study has several practical and conceptual implications. First, for educational planning, it suggests that even part-time Mandombe instruction can act as a structured cognitive training regime. Three hours per week appears to be enough to shift how adolescents process geometric information, on top of the Latin literacy they share with their peers. This invites serious consideration of script design and curriculum structure as tools for shaping cognitive practice, not only as carriers of language. Second, as a pilot for the forthcoming full-time Mandombe cohorts, the study provides a template. It shows that portable, low-cost EEG is feasible in Nsandas, that tasks aligned with curriculum geometry can detect meaningful differences, and that analytic pipelines can handle the realities of school data. Future work can build on this to follow cohorts from pre-Mandombe exposure into full-time programmes, track the emergence of these neuroelectric patterns over time and test how they relate to mathematics, science and problem-solving. Third, the findings open specific questions for DSM-H and broader decolonial frameworks. If colonial schooling under-trained visuospatial and relational capacities, as those frameworks suggest, then incorporating an indigenous script with explicit geometric structure may be one way to restore that balance. This study does not measure clinical outcomes, so any mental health claims remain conceptual. It does, however, provide a concrete example of how symbolic choices in education can reshape a core cognitive workspace. In the immediate term, three lines of research suggest themselves. One is replication in additional Nsandas and Latin-only schools, including rural contexts. A second is the inclusion of neutral control tasks and more diverse cognitive measures to map the boundaries of Mandombe-linked effects. A third is the careful study of upcoming full-time Mandombe cohorts, where dosage and exclusivity will be higher and where stronger inferences about training trajectories may be possible. --- 5. Conclusion Adolescents in Kinshasa who learn Latin script plus three hours of Mandombe per week process a particular class of visuospatial tasks differently from peers who learn Latin alone. The difference is not global. It appears wherever the task reuses the geometry that Mandombe drills week after week: rotation, symmetry, branches and part–whole completeness. Their brains respond more quickly and efficiently in those contexts, much as they do in adolescents who train intensively in videogames or art, but with a broader and more systematic profile. This is not evidence of superiority in any essential sense. It is evidence that continuous symbolic training matters, and that an indigenous script can serve as a powerful training field for operations that Western curricula often treat as peripheral. In that sense, Mandombe is more than an extra subject. It is a daily practice that quietly rearranges how young people see and work with structure in space.
Mandombe-Based Artificial Intelligence: Toward a Symbolic-Geometric Model of Computation
This paper focuses on adapting Mandombe’s recursive symmetry to artificial intelligence design. It proposes a symbolic-geometric learning algorithm that uses inversion and rotation logic instead of linear weighting. Simulations demonstrate higher interpretability and resistance to data bias. This model aligns with decolonial computing principles and the epistemological independence envisioned by MEN-D research. References: Nsiangani K.M. (2016) From Mvemba Nzinga to Modern Puppets; Nsiangani K. (2021) MEN-D Cryptography Symbolique.
Cognitive Resonance Between Mandombe Geometry and Human Neural Networks
This research focuses on testing the hypothesis that the symmetrical geometry of Mandombe resonates with the structure of human neural pathways involved in pattern recognition. Using EEG signal mapping and geometric pattern stimulation, the study observes specific coherence peaks in the alpha–beta range. Results suggest that symbolic exposure to Mandombe enhances visual-spatial integration, reinforcing the neuro-epistemic claims made in The Colonized Mind (2025). References: Nsiangani K.M. (2025) The Colonized Mind; Wabeladio P. (1984) Méthodologie de l’enseignement du Mandombe.
Logical Foundations of the Mandombe System: Toward an African Axiomatic Framework
Keywords Mandombe, logic, axiomatic systems, African philosophy, epistemology This article defines a formal logic whose syntax and semantics are grounded in the internal geometry of the Mandombe writing system. Building on previous work that presents Mandombe as a cognitive grammar of reasoning, I introduce M-Logic₀, a propositional calculus whose connectives and inference rules are constrained by mvuala–kisimba configurations and their allowed rotations, reflections and concatenations. I give a sequent formulation of M-Logic₀ with a distinguished inconsistency constant ⊥ᴹ and a restricted explosion rule that reflects the way forbidden geometric moves are treated in actual Nsanda teaching. On the semantic side I define mvuala-models: diagrammatic valuation frames in which formulas are interpreted as regions and paths in oriented Mandombe cells. Truth, incompatibility and implication are read from geometric relations such as inclusion, mirror opposition and forced path extension. I prove soundness of M-Logic₀ with respect to mvuala-models and outline a completeness result for its positive implicational fragment. I then sketch a cyclic extension, M-Logic₁, that internalises temporal and cosmological rotation and connects the logical operators to the rotational-square equivalence (RSE) machinery developed in Mazayi Mandombe. The article ends by positioning this logical layer relative to higher structures such as Mandombe Geometric Algebra and its applications in reservoir computing and materials science, where the same generators are already used as operators on high-dimensional state spaces. The goal is not to imitate existing Western logics but to articulate a coherent, testable African axiomatic framework that can serve as a native base for formal reasoning, computation and epistemology. 1.
La cognition Mandombe dans les apprentissages préscolaires congolais : étude pilote
This study explores whether early exposure to Mandombe, taught alongside the national Latin based curriculum, is associated with small but coherent differences in attention, visuospatial working memory and shape based emotional coding in Congolese children aged 5 to 7 years. Mandombe is a geometric script in which young learners must rotate and project units in imagined three dimensional space, map orientation to sound and tone, plan continuous stroke paths from the singini starting point to the end of each zita and vary line qualities such as length, curvature and angle to convey emotion, speed and melodic contour. Longitudinal cohorts described by Nsiangani showed that older children educated through Mandombe often combined rapid progress in mathematics and symbolic reasoning with heightened sensitivity to small visual and emotional cues. He suggested that the emotional and prosodic coding built into the script might contribute to this profile but left that part of the hypothesis largely unexplored. Here we work with younger children in a natural setting. We compare 5–7 year olds from CENA Nsanda centres in Kinshasa and Kongo Central, where Mandombe is integrated into preschool and first grade as a regular activity, with age matched peers from nearby Latin only schools. All children completed a short tablet based battery that included an age adapted continuous performance task, a mvuala style visuospatial span, a verbal span, a 2D to 3D “tower view” task, an orientation to sound mapping game, a continuous stroke path task from a singini point, an emotion shape learning game, an emotion tagged recognition task and a simple shape prosody matching task. Children with at least one year of regular Mandombe activities showed modest advantages on sustained attention in shape based blocks, visuospatial span, 2D to 3D mapping, orientation sound mapping and continuous stroke control, as well as faster learning and better transfer of emotion shape rules and a stronger memory benefit for emotion tagged shapes. No differences appeared on verbal span, and results were small or inconsistent on purely picture based attention trials. These findings do not support broad claims of superiority. They suggest that early Mandombe practice, as it currently exists in Nsanda, functions as a structured training field for a cluster of geometric and emotional operations that can already be detected by age seven.