“Well-Organised Misunderstanding": The Fine Art of Being Wrong

What Michelene Chi Taught Me About Misconceptions

This week I'm writing about Michelene Chi's landmark 2008 chapter "Three Types of Conceptual Change: Belief Revision, Mental Model Transformation, and Categorical Shift" from the Handbook of Research on Conceptual Change. It's something that fundamentally changed how I think about student misconceptions and why some errors are so remarkably persistent.

Michelene Chi

"Coherent but incorrect"

When I first started teaching almost 20 years ago, I used to think that when students gave wrong answers, they simply lacked the correct knowledge, that misconceptions were just gaps to be filled. But then I encountered Michelene Chi's work, and I realised I was wrong about being wrong. Her research revealed something profound: misconceptions aren't always minor misunderstandings or missing facts. They’re often coherent, well-structured, (but fundamentally flawed) mental models. As Chi puts it, students can be reasoning perfectly logically but from incorrect assumptions. In other words, the engine is working perfectly, but it’s driving in the wrong direction.

Consider this example: a child says "the Earth is round," but when asked to elaborate, they describe a flat disc with an edge people could fall off. This is what Vosniadou and Brewer found in their research on child misconceptions; many young children don't picture the Earth as a sphere, but as a flattened disc or a hollow sphere. Their model is wrong but internally consistent.

This tells us something crucial: student errors aren't random, they don’t come from a void, but from somewhere that makes sense to them. They emerge from prior knowledge, everyday experience, and the intuitive frameworks they use to make sense of the world.

Chi emphasises that flawed mental models are "coherent but incorrect," meaning students can use them to generate explanations and predictions that are consistent within that framework, even if they are scientifically wrong. In practice, this means a student can answer several related questions in ways that “fit” together logically, yet still be operating from a fundamentally mistaken premise. Furthermore, they "can use the mental model to offer similar and consistently incorrect explanations and predictions in response to a variety of questions." Again, the logic isn't broken; the assumptions are.

You can even find scientifically accurate statements like "heat flows" embedded in incorrect frameworks. If the student thinks of heat as a substance rather than a process, they've made what Chi calls an ‘ontological category mistake’: assigning a concept to the wrong fundamental category. As she explains, "some false beliefs and flawed mental models are robustly resistant to change because they have been mistakenly assigned to an inappropriate lateral category." These are the most stubborn misconceptions of all.

When Facts Aren't Enough

This is why simply giving students the right answer doesn't always fix a misconception. It often gets absorbed into the wrong model. As Chi observes, "when a learner's flawed mental model is confronted with a description of the correct model presented one sentence at a time, each sentence can either refute (explicitly or implicitly) an existing belief or not." The problem is what happens when information doesn't directly contradict existing beliefs: "the learner can assimilate by embedding or adding the new information from the sentences into her existing flawed model, so that her mental model is enriched, but continues to be flawed."

In other words, you can't overwrite a misconception with a fact; you have to confront and replace the flawed model itself. Contradiction is key. For change to happen, students must recognise that what they believed is incompatible with the correct view. If there's no conflict, they may just absorb the new fact into the wrong framework.

This will be familiar to anyone who has tried to reason with a conspiracy theorist. As Chi puts it, conceptual change is hard because people who are wrong don't think they're wrong. Their model explains the world until it doesn't.

Chi identifies three types of conceptual errors, each requiring different instructional approaches:

1. False beliefs are isolated and often easily corrected. For instance, "The heart oxygenates blood." Simply tell them it's the lungs and you're done. Mostly. Chi found that such false beliefs "can be corrected when learners are explicitly confronted with the correct information by contradiction and refutation." In her studies, "71% of the 31 prior false beliefs were correctly revised if the text students subsequently read included sentences that directly refuted the false beliefs."

2. Flawed conceptual models are more insidious. They're coherent but wrong. Like the "single-loop" model of the circulatory system that Chi studied extensively. In her research, about half the students had this flawed model where "blood goes to the heart to be oxygenated, then it is pumped to the rest of the body, then back to the heart." The model is internally consistent, predictively powerful, and completely incorrect. Chi notes that "five of eight students (62.5%) with prior flawed 'single-loop' model, transformed their flawed models to the correct model" through reading and self-explanation.

3. Ontological category mistakes represent the deepest errors. Heat as a substance. Force as a thing. These aren't just wrong; they're robustly wrong. As Chi explains, "many misconceptions are not only 'in conflict' with the correct scientific conceptions, but moreover, they are robust in that the misconceptions are difficult to revise, so conceptual change is not achieved." These don't yield to contradiction or accumulation of facts. They require a categorical shift, a rebuild from the ground up.

“Well-organised misunderstanding"

The problem, then, is not that students don't know something. As Chi emphasises, "this is not an ignorance problem; this is about well-organised misunderstanding." I love this phrase, it perfectly captures what teachers experience countless times: students who can articulate complex explanations for phenomena, demonstrate sophisticated reasoning, and defend their ideas with internal logic and yet arrive at completely incorrect conclusions. This is why the 'show your working' heuristic is so powerful: You can't repair a model you haven't seen.

Chi's insight about robust misconceptions is particularly striking. She describes a study by Law and Ogborne where students used computer programming to model their understanding of motion. What's fascinating here is that the students had immediate, explicit feedback; either their programs either worked or they didn't. Despite this clear correction mechanism and being willing to revise individual rules, students maintained their underlying misconceptions about force and motion. As Chi notes, "even though the student willingly modified individual rules or beliefs as a result of external feedback... the revised beliefs, cumulatively, did not transform the mental model into the correct model, in that the implicit underlying core hypotheses were still incorrect."

This resonates deeply with my own experience of marking student work. I've seen students make surface-level corrections while maintaining the same fundamental errors across multiple attempts. The student wasn't resistant to change per se; they readily revised their rules. But the multiple belief revisions didn't add up to correct understanding because "the core hypotheses underlying the mental model are not addressed." In other words, they were rearranging furniture in a house built on faulty foundations.

This is what I find so compelling about Chi's work. It explains why simply pointing out errors often fails. We're addressing symptoms, not causes. This is what Chi calls the "robust misconception problem", in other words, misconceptions that are "not only 'in conflict' with the correct scientific conceptions, but moreover, they are robust in that the misconceptions are difficult to revise, so conceptual change is not achieved."

Effective instruction reveals the student's model, compares it to the correct one, and creates enough conflict to prompt change. This is why explicit instruction proves so powerful. You're not just delivering content; you're checking for understanding, diagnosing thinking, exposing faulty models, and helping students rebuild them from the ground up.

Why Teaching "‘Critical Thinking Skills’ Often Fails

So it’s true that facts alone are not enough but Chi’s work also helps explain why so many attempts to teach “critical thinking skills” in isolation fail to produce much change in student understanding. Critical thinking is often presented as a transferable skill, something you can cultivate in the abstract and then apply to any subject matter. But if a student’s underlying mental model is flawed, sharpening their reasoning skills will just make them better at defending the wrong conclusion.

In other words, reasoning skill alone doesn’t guarantee accurate reasoning. As Daniel Willingham has pointed out, critical thinking is not a generic set of moves that float free of content. We think critically about something, and the quality of that thinking depends on the accuracy and depth of the knowledge we bring to bear. If a student has miscategorised evolution as a purposeful process that works toward a predetermined goal rather than as the result of variation and natural selection, they can construct beautifully logical arguments within that mistaken framework, exactly the kind of “coherent but incorrect” reasoning Chi describes.The critical thinking isn’t broken; it’s just operating on the wrong inputs.

This is why the “skills over knowledge” mindset is so misguided. Without accurate background knowledge and correct conceptual categories, there’s nothing for the critical thinking process to work with. Worse, when misconceptions are robust, students may use their reasoning skills to assimilate new facts into the wrong model rather than confront the model itself.

If we want students to think critically, we must first make sure they are thinking with the right concepts. That means identifying, surfacing, and, when necessary, dismantling flawed mental models, not just teaching abstract heuristics about argument and evidence. Otherwise, we risk creating highly articulate students who can argue brilliantly… for things that aren’t true.

The Challenge of Category Mistakes

For the most stubborn misconceptions, Chi argues that the problem runs deeper than flawed models. The issue is categorical. Students have assigned concepts to the wrong fundamental category entirely.

Take heat, which Chi uses as a key example. Students often think of heat as "physical objects such as 'hot molecules' or a material substance such as 'hot stuff' or 'hotness'... as indicated by phrases such as 'molecules of heat' or expressions such as 'Close the door, you're letting all the heat out.'" They've categorised heat as an Entity - something that can be contained like marbles or water.

What strikes me about this example is how reasonable the student thinking appears. Our everyday language reinforces these misconceptions. We do say "let the heat out" and "trap the heat in." The error isn't in the logic; it's in the fundamental categorisation that makes that logic possible. But scientifically, Chi explains, "heat or the sensation of 'hotness,' is the speed at which molecules jostle: the faster the speed, the 'hotter' the molecules feel. Thus, heat is not 'hot molecules' or 'hot stuff' (an Entity), but more accurately, the speed of molecules (a Process)."

This kind of category mistake creates what Chi calls "incommensurate" concepts. When students categorise heat as an Entity and scientists understand it as a Process, "they conflict by definition of kind and/or ontology." You can't fix this with simple contradiction because the very foundations of understanding are different.

As Chi puts it, "if misconceptions occur as the result of category mistakes, then instruction needs to focus at the categorical level. When students' misconceived ideas conflict with correct ideas at the lateral category level, then refutation at the belief level will not promote conceptual change." In other words, when student and teacher are operating from fundamentally different conceptual categories, they're essentially speaking different languages. No amount of corrective feedback will bridge that gap until the student recognises they need to shift categories entirely.

Why Smart People Believe Dumb Things

Chi's work reveals something profound about the nature of learning itself. We don't simply add new information to an empty vessel (this is what many people seem to think explicit instruction is). We construct understanding within existing frameworks, and sometimes those frameworks need dismantling before reconstruction can begin. This has implications far beyond the classroom. In an age of misinformation and polarised debate, understanding how people hold onto false beliefs becomes crucial.

One thing I’ve learned working in the evidence-based/science of learning space is that evidence is not enough. If it was then we wouldn’t have so many people still believing in homeopathy, astrology or learning styles.

It's not enough to present facts; we must understand the mental models that organise those facts. As Chi observes, "part of the difficulty of shifting categories for many science concepts has to do with lack of awareness, in that students do not realize that they have to shift their assignment of a concept to a different category."

Chi's research suggests that truly effective teaching requires two steps for the most stubborn misconceptions: "First, students have to be aware that they have made a category mistake, which amounts to confronting their ideas at the categorical level; and second, students must be knowledgeable about the category to which a concept actually belongs."

This is challenging because, as Chi notes, "miscategorization is rare in everyday life." We don't routinely need to re-categorise things. "The fact that these category mistakes rarely occur in real life makes it difficult for learners to recognize that their understanding or lack of understanding of new concepts may originate from a category error." To me, this explains why these deep misconceptions can persist even in bright, motivated students. They're not making obvious errors that everyday experience would correct.

The solution? Chi argues that instruction must "begin by making students aware that they have committed category mistakes" and then help them build new categories with "distinct set of properties." Only then can students begin to assimilate new instruction into the correct conceptual framework. This is demanding work (both intellectually and emotionally) because it requires us to understand how our students think, not just what they should think. What does this look like in practice?

Three Paths to Conceptual Change

The diagram below, from Chi’s 2008 chapter, illustrates how different kinds of misconceptions require different forms of instruction. It’s deceptively simple, but it gets at something profound: the location of the misconception within a student's mental framework determines what kind of conceptual change is possible—and what kind of teaching is needed to bring it about.

On the left, we see cases where the misconception lives within the correct hierarchical category. For example, a student understanding photosynthesis as something plants do, but wrongly believing it happens at night. These can often be corrected through experience or instruction that clarifies or revises aspects of the idea without upending the whole structure.

In the middle, partial refutation might be needed; more deliberate and targeted, but still working within the existing conceptual frame. Think of a student who understands that force causes motion but has a naive view that heavier objects fall faster. Here, you correct part of the misconception while reinforcing the rest.

But the right side of the diagram is where the real trouble lies. These are misconceptions that involve ontological miscategorisation. In other words, when a student puts a concept into the wrong category altogether. Force isn’t a thing, it’s a relationship. Heat isn’t a fluid, it’s a transfer. These misconceptions won’t shift with correction alone. They require what Chi calls total explicit rejection: a dismantling of the old category and construction of a new one that doesn’t overlap with the original. This is the kind of deep reorganisation that requires careful, explicit instruction.

This then is why effective instruction doesn't just deliver content. It checks for understanding, challenges mental models, rebuilds faulty frameworks, and helps students change their minds, not just their answers.

It’s also precisely why a model like Direct Instruction has such robust evidence behind it, and why Chi's framework helps explain its effectiveness. When teachers use Direct Instruction properly, they're not simply transmitting information, they're actively diagnosing student thinking at every step. The constant checking for understanding ("What sound does this letter make?" "How do we know the character is feeling angry?" "What's the first step in solving this equation?") serves a dual purpose: it ensures students are following along, but more importantly, it reveals their underlying mental models.

Chi's research explains why this approach is so effective with students who have been failed by other methods where minimally guided students are left to their own devices. Many of these students don't have missing knowledge, they have “well-organised misunderstanding”. Their previous educational experiences may have layered new information on top of flawed foundations, creating increasingly complex but fundamentally incorrect mental models. Direct Instruction's systematic approach allows teachers to identify these foundational errors early and address them explicitly.

For example, the "I do, we do, you do" structure isn't just about gradual release of responsibility, it's about gradual revelation of student thinking. During the "we do" phase, teachers can observe student responses, catch misconceptions early, and provide immediate corrective feedback before errors become entrenched. This is conceptual change in real time.

This is also why being explicit about what is to be learned works particularly well for disadvantaged students, a claim that E.D. Hirsch has dedicated his life’s work to. These students often lack the background knowledge and conceptual frameworks that more privileged students bring to school. Without explicit instruction that builds these frameworks systematically, they're left to construct their own, often flawed, mental models. Explicit Instruction doesn't assume they already have the right categories; it builds them deliberately.

The Shape of Thought

As Chi's research demonstrates (indeed, as 70 years of evidence from cognitive science demonstrates), the mind is not a blank slate but an active constructor of meaning. Sometimes, the most sophisticated thinking can lead us astray. (Again, this is why a focus on skills rather than knowledge is so misguided). The mark of truly effective teaching is recognising when students need not more information, but better ways of organising the information they already have.

Chi's framework reminds us that behind every persistent error lies a logical system trying to make sense of the world. So I guess our job isn't to dismiss that logic but to understand it well enough to help students build something better. In doing so, we acknowledge that learning is partly about acquiring facts, but also about understanding and transforming the very categories through which we understand reality.

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Reference: Chi, M.T.H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In S. Vosniadou (Ed.), Handbook of research on conceptual change (pp. 61-82). Hillsdale, NJ: Erlbaum.