Many cognitive scientists have tried to tackle the question of how the brain represents concepts in a topic and how this representation evolves as we learn more about that topic.

Michelene T.H. Chi, a learning scientist at ASU's school of education, looks at the process as an evolution of a graph-like structure, a person's "ontology". Imagine a student tackling the following stoichiometry problem:

The Novice's Ontology

When a novice approaches this problem, Chi argues that they often categorize concepts incorrectly. They might see "methane" and "oxygen" as static things rather than as participants in a dynamic process.

The novice's mental model might look something like:

Concept	Novice Category	Expert Category
Molecules	Static objects	Dynamic entities
Chemical equation	Recipe/instruction	Constraint system
Mole ratio	Arbitrary numbers	Emergent relationship
Conservation	Optional rule	Fundamental law

Ontological Shift

Learning, in Chi's framework, is not merely adding new facts—it requires ontological recategorization. The student must shift their understanding of what kind of thing a chemical reaction is.

The difficulty in learning science is not that students lack knowledge, but that they possess knowledge organized around fundamentally different ontological categories than experts use.

This explains why stoichiometry is notoriously difficult: students must simultaneously:

1. Track multiple quantities across a transformation
2. Understand ratios as constraints rather than procedures
3. See the equation as expressing conservation rather than instruction

Implications for Instruction

If conceptual change requires ontological shift, then effective teaching must:

• Surface the student's existing ontology explicitly
• Create cognitive conflict that reveals categorical errors
• Scaffold the construction of new ontological categories
• Provide practice that reinforces the new categorization

The stoichiometry problem above is not just about calculating grams—it's a window into how a student understands the nature of matter itself.

The Neuroscience

So perhaps Chi's model is kind of the high level of the relevant cognitive operations. How does it actually work? The concept "Hydrogen" is not in any particular location in your brain when you think about it. Populations of neurons represent the concept. The model of this with the strongest empirical backing is the Lambon Ralph model of conceptual organization, often called the "Hub and Spoke Model". The spokes of this model are modality-specific regions of the brain which use a particular kind of representation to interpret concepts. The visual system, for instance, represents the image of the hydrogen atom, perhaps as a white sphere as it is in a typical molecular representation of H2O as a ball-and-stick figure. The auditory system might represent the sound of the word as it is pronounced in a person's preferred language, and the tactile system might represent the heat of hydrogen gas, etc. The word-association systems, or "verbal spoke" located in the perisylvian language network, might represent the word as its spelled in its symbolic representation in that language, and so on.

The anterior temporal lobe is the central organizing hub of these various modal spokes, which computes similarities between these representations, membership in a category (such as the elements, or the set of chemical materials, or the types of matter in the world). It also computes semantic associations and generalizations.

But what about the actual concept itself? What is it exactly? It is a "population code", a set of activations of particular neurons across these spokes and the central hub in the ATL. It might be represented by a list in a programming language like python:

[.3,.4,.5.,.6...]

Where each item in the list is a number representing that activation, perhaps from 0 to 1, indicating the strength of a particular neuron's firing or "firing rate", the rate it which it sends action potentials (neuron number one here fires at a rate of .3 or 30% of the time being measured).

The expert's ontology in Chi's model is then a matrix or list of lists of these activation patterns, each list in the list representing a concept. The novice's ontology features different concepts and relationships, some of them misconceptions and some of them right on target.

So we now have a matrix transformation problem. How do we get the conceptual change described by Chi through transformations of these population code lists of lists (matrices) in the brain? That is not elucidated by Chi, but a literature has emerged since early work by her and Posner in the 80s and 90s opposing the original hypotheses.

The Contemporary Picture of Conceptual Change in the Brain

Originally, Chi thought that cognitive conflict precedes the expert level conceptual graph, or ontology, until misconceptions are eliminated from the ontology, and those neurons don't get activated anymore, or feature in other lists that code for the new scientific concept.

New work by Patrice Potvin and his colleagues (Steve Masson, Lorie-Marlène Brault Foisy, Martin Riopel) from the Université du Québec à Montréal (UQAM) has shown that misconceived activation structures don't ever get fully eliminated, and scientific concepts are introduced before the real cognitive conflict happens with them. The conflict reaches its peak when the inhibition of older misconceptions is persistent enough that the more activated new expert concepts can now generate new insight on problems.

In Potvin's model, control flows from the anterior cingulate cortex (ACC), which detects cognitive conflict and activates both the older misconceptions and expert concepts, to the inferior frontal gyrus (IFG), which inhibits and supresses misconception population codes in the brain, and then to the middle frontal gyrus which maintains the correct answer and applies the corresponding rules.

So we still have every matrix, no matrix gets eliminated, its activations just get smaller and smaller as your understanding develops more.

Next up, we'll explore these notions more in depth, and actually apply them to classroom learning through systems that utilize these principles!