Different kinds of knowledge have different shapes.
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Built by Gareth Manning, 2026
I’m building an AI tutor and teacher assistant grounded in something most AI in education doesn’t have: a validated map of how knowledge in each domain is actually structured. This site shows that map. It’s the foundation of a layered system:
Knowledge graph — the concepts in a domain and how they relate (what this site shows)
Competencies and Learning Targets — what learners should know, understand, and do, tracked as developmental progressions from early years through graduation
Curriculum plans — year plans, unit plans, lesson plans, built on the layers below
Together those layers become the tutor and teacher assistant. This site shows the foundation only.
The six domains include traditional subjects (Mathematics, History, Literacy) and multidisciplinary fields (Regeneration, Wellbeing, Entrepreneurship). They’re treated as domains rather than subjects because some don’t fit inside a single school subject.
Why this matters
Two problems with AI in education, rarely named together.
The AI itself doesn’t have structural knowledge. LLMs are prediction systems — they guess the next word based on patterns they’ve seen. They don’t know what a student has mastered, what the prerequisites are, or where scholars disagree. They produce fluent output that’s often wrong in ways hard to catch. For a tutor this is a problem. For a teacher assistant — which is the priority in what I’m building — it’s worse, because teachers making decisions based on AI misreads of student understanding is a failure mode nobody is talking about enough.
Existing curricula don’t have structural knowledge either. Most national and state curricula are lists of topics rather than coherent progressions. I built a Curriculum Decomposer — a tool that ingests standard curriculum documents and reorganises their content into Learning Targets in a more coherent developmental order. I ran it on the Ontario curriculum as one example. The source material was largely disconnected topic lists — a pattern I’d expect to see in many jurisdictional curricula, though that’s a hypothesis from this case, not a tested claim across curricula. Large portions of what’s in those documents never gets taught or assessed; teachers fall back on textbooks because the curriculum itself doesn’t describe how the learning actually builds.
So the knowledge graph layer isn’t only for the AI. It’s filling a gap in how curricula themselves are written. A tutor or teacher assistant built on standard curriculum documents inherits their incoherence. Built on validated graphs, it has something to reason over.
How the domains differ
A tutor that treats all domains the same will fail all of them.
Hierarchical. You cannot divide fractions before you can multiply them. You cannot multiply fractions before you understand what a fraction is. Mathematics runs on real prerequisite chains — teach a later concept before the earlier one and the student fails, because the earlier concept is a component of the later one.
Horizontal. Modern history doesn’t require ancient history as a prerequisite. You can enter through the French Revolution, the fall of Rome, or colonial India — each teaches you causation, evidence, continuity and change. The thinking skills develop through exposure to multiple examples; there’s no fixed order.
Dispositional. Curiosity, persistence, self-regulation. These develop through practice and relationship, not through prerequisite chains or examples. They don’t belong in a graph at all — I track them separately in a developmental profile.
What this isn’t
A claim to have mapped these domains definitively. A replacement for teachers or curriculum designers. An argument that AI should sit between student and teacher — it shouldn’t. The teacher assistant is the priority; the tutor supports the student only through and with the teacher.
The layers above this one — the developmental competency and Learning Target system, the Curriculum Decomposer, and the tutor and teacher assistant itself — are separate pieces of work that will be documented elsewhere.
Different domains on this site are organised differently because different fields have different shapes. Mathematics is organised by topic strand because mathematical knowledge is genuinely topical. Regeneration, Wellbeing, Entrepreneurship, and Literacy are organised by scholar-panel-derived traditions because these fields are structured by which scholarly lineage you are reading. History is organised by kinds of historiographical thinking because the History graph maps how historians think rather than what happened.
Why this needed inventing
Two kinds of knowledge, two ways to validate.
Validated knowledge graphs mostly exist for hierarchical domains. ACE/EKG has mapped 756 mathematics concepts. Similar resources exist for parts of some other hierarchical domains. For horizontal and multidisciplinary domains — History, Regeneration, Wellbeing, Entrepreneurship — almost nothing comparable exists. The structure of these domains is debated rather than established, and no external benchmark is available to validate against.
Hierarchical: Karpathy loop against external benchmark
For Mathematics, the ACE/EKG dataset provides 756 expert-mapped concepts. I used a Karpathy-style iterative loop: a generator proposes the graph, an evaluator scores it against the benchmark, revisions run until the stopping criterion is met. The loop halts when precision against ACE/EKG exceeds 0.85 and recall exceeds 0.80, or after 10 iterations, whichever comes first.
The Mathematics run reached the 10-iteration cap with a final graph of 222 concepts at Precision 1.0 and Recall 0.93 — well above the stopping thresholds, but the cap was reached before the stability criterion was evaluated. Those numbers measure agreement with the benchmark, not correctness in an absolute sense.
Horizontal: agent-designed panel and deliberation
For the other domains, the Karpathy loop doesn’t apply — you can’t score against a benchmark that doesn’t exist. So I replaced the benchmark with a panel.
An agent designs a panel of scholar personas spanning the traditions that carry weight in the field. For Regeneration, that means Indigenous knowledge systems (Kimmerer, Yunkaporta), resilience science (Folke, Berkes), political ecology (Shiva, Escobar), regenerative economics (Raworth), and others. I review the panel composition before the harness runs.
The harness runs for hours. Personas propose concepts, critique each other, argue for inclusion. Contested concepts stay contested — disagreement is not averaged away, and the orange edges on each graph show where the field itself is divided. Multiple independent runs are compared; concepts that recur across runs are higher-confidence. Each graph reports how many runs, how many personas, how many traditions.
What threshold concepts are
A threshold concept (Meyer and Land, 2003) is one that transforms how you see a field. Understanding it changes everything above it, can’t easily be un-learned, and reveals connections that were previously invisible.
Classic example from maths: once you understand that = means equivalence — the expressions on either side refer to the same thing — rather than “now compute this”, algebra becomes possible. Before that, it’s arithmetic with letters in it.
A concept is marked threshold on these graphs when a majority of the panel flags it as transformative. I report this as counted agreement (“14 of 14 panellists across 7 traditions flagged this as central”) rather than “universal.”
The History graph
What this graph is. The History graph maps 269 historiographical concepts — the ways historians have developed for thinking about the past — rather than historical content. If you’re looking for material on specific events, periods, or regions, this isn’t that site.
How it was produced. A panel of 12 historians deliberated to produce the concept set and relationships. The panel was deliberately decolonial-leaning: Indigenous, postcolonial, and African historiography are over-represented relative to Western historiography. Scholars dominant in the panel’s contributions include Silvia Rivera Cusicanqui (Andean decolonial), Achille Mbembe (postcolonial/African), Gayatri Spivak (postcolonial/subalternity), Linda Tuhiwai Smith (Kaupapa Māori), Dipesh Chakrabarty (provincialising historiography), Toyin Falola (African historiography). Western historiographical traditions (Annales, Marxist, Rankean, microhistory) are under-represented as panel voices.
The five axes. The graph is organised by five axes of historiographical thinking: Evidence, Temporality, Causation, Agency, Silence. These emerged as the recurring moves made across the panel’s traditions. Other historiographical frameworks — for example Seixas’s six second-order concepts (significance, evidence, continuity/change, cause, perspective, ethical dimension) — would organise the same graph differently. The five axes are a position, not a neutral taxonomy.
Who this is for. Primary audience: teachers designing historical-thinking tasks. If you’re building a unit and want to know which kinds of historical reasoning students could practice within it, this graph helps you see the options. The graph is not a curriculum and does not tell you what students should study.
The Literacy graph
What this graph is. 254 concepts, 686 relationships, 13 confirmed threshold concepts, 18 structurally contested concept pairs. The graph covers reading, writing, and oral language development from ages 5–18, and is organised into five super-categories derived by a tradition-clustering meta-panel: Discourse & Genre, Multilingual & Translingual, Critical & Ideological, Cognitive Reading Science, and Indigenous & Sovereign.
How the panel was composed. The 12-persona scholar panel was deliberately composed for integrative pluralism across eight strands of literacy scholarship: cognitive science of reading (Ehri, Leong), cognitive neuroscience of reading (Hoeft), vocabulary and comprehension research (Cain, Grøver), bilingual and translingual literacy (García), critical literacy (Luke), New Literacy Studies (Gee, Prinsloo), Indigenous literacy and language revitalisation (McCarty), and writing development research (Bazerman, Kynard). Six of the twelve were calibrated as sceptics of the dominant tradition; three were practitioner-educators; three were structural representatives of Global South or non-Western positions. Previous Literacy runs over-weighted cognitive science of reading and missed several strands entirely; this composition was designed to prevent that.
Per-concept sequential / horizontal / dispositional argumentation. This is the first domain on the site to ask scholars to argue, per concept, whether it is a sequential prerequisite (some concepts really do need to come before others, even in a horizontal domain), a horizontal association (related to other concepts but without a clean ordering), or a dispositional stance (something the learner takes up as an identity or orientation, not a skill mastered in sequence). The argumentation lives in each concept’s free-text justification rather than as a structured field — a schema-level version is planned as a cross-domain backfill pass that will reach back to Regeneration, Wellbeing, Entrepreneurship, and History. Literacy is where the per-concept S/H/D deliberation starts.
The Indigenous cluster. Panellists preserved Indigenous literacy and language revitalisation as a distinct cluster on explicitly ontological grounds — language-land-kinship, sovereignty, and ceremony are incommensurable commitments that cannot be absorbed into critical literacy or multilingual repertoire traditions without epistemic violence. An earlier clustering run held this cluster as category-resistant (the same pattern the Regeneration panel produced for Kimmerer and Yunkaporta); the final run reached consensus on preserving it as a standalone super-category. Either shape is defensible; the underlying argument is the same.
Who this is for. Primary audience: teachers and curriculum designers who need to hold reading science and multilingual/critical/Indigenous literacy together without collapsing any of them. The graph is not a curriculum, does not prescribe a sequence, and deliberately does not resolve the phonics-vs-translanguaging debate — both positions remain visible.
Limits
A different panel would produce a different graph. I think the panels are defensible, the disagreements are real, and the process is honest — but these are claims, not facts. The Karpathy loop for Mathematics gives that graph more external validation than the others have; the panel-validated domains are more exploratory. These graphs are defensible starting points for curriculum designers, AI developers, and researchers interested in knowledge structure — not prescriptive standards, and not suitable for high-stakes assessment decisions.