How acquiring knowledge is like learning a language
This is a blog about the mental models with which teachers make sense of teaching and learning. Tom Sherrington has argued that a schema-building model is the best we currently have available. He argues that this model is “good enough as a concept to deal with quite a lot of the things we want to achieve in the field of education.”
I disagree. As Sherrington notes in a separate blog, “I have seen many examples of poor lesson activities that stemmed from the teacher’s dodgy model for learning.” Here I agree with him, but only in part. Many of the worst lesson activities I have observed have been planned on the basis of the very model he advocates.
Knowledge & Language
Rightly, Sherrington demands that any critique of his schema-building model is accompanied by a suggestion of something better. This is what I will attempt to lay out in this blog. My suggestion is that we should consider the process of acquiring knowledge as being analogous to learning a language. This, I believe, gives us a much clearer account of what makes for effective teaching.
The major limitation of the schema-building model is that it doesn’t account for the differences between subjects. Teachers operating within this model run the risk of reducing their teaching practice to a series of generic techniques, which focus on superficial memorisation but do little to develop deep disciplinary knowledge. This is what the language analogy aims to address.
Facts & Concepts
The first point we must observe about a language is that it can be thought of in terms of its vocabulary and its grammar. To understand vocabulary, we must recognise the difference between facts and concepts.
A fact is something that can be memorised as an item of information. Examples of facts include: the sky contains atoms; the Archduke Franz Ferdinand was shot in June 1914; the angles in a triangle add to 180o.
A concept can also be memorised, but does not mean much on its own. It is more of a generalising rule than a specific item of information.
Facts are made up of concepts: the concept of matter being visualised as if it can be broken down into atoms; the concept of Empire encapsulated in Franz Ferdinand’s title ‘Archduke’; the concepts of lines, angles and planes upon which any geometrical statement must be based.
Facts can thus be thought of as sentences uttered within a language, with concepts forming the vocabulary that makes them up.
To learn a concept is not merely to learn its definition, it is to learn how it functions within a sentence. Hence a student may be able to repeat that hubris means ‘excessive pride’, but they cannot be said to be knowledgeable unless they can identify hubris in the actions of Icarus, Napoleon or Lear, and construct their own sentences accordingly.
By failing to make clear the difference between facts and concepts, Sherrington’s model runs the risk of leading teachers into overly simplistic practices. Just as memorising a dictionary does not imply the ability to speak a language, memorising a knowledge organiser does not, whatever the name might suggest, imply knowledge.
Scientific Grammar
Another aspect of language is its grammar. Sentences are made meaningful by a language’s grammar: learning a sentence has limited value unless one understands the rules that allow the sentence to function.
Take an example from physics: ‘as the temperature of a gas increases, pressure increases.’ This is a fact, one which is certainly worth students remembering, but asking them simply to remember it, without drawing their attention to the grammar that ties the concepts of gas, temperature and pressure together, is to deprive them of any meaningful understanding of the scientific enterprise.
What is that grammar? Scientists are fond of phrasing sentences in the manner of the statement above: as x changes, y changes. What is implied in this construction is the idea of a causal process: the change in x always and inevitably leads to the change in y.
Causation in science, at least in the classical sciences studied at school, is thus mechanistic. It is assumed by the scientist that every observable effect must have one specifiable cause; the task of the scientist is to discover the mechanism by which cause and effect are related in each case.
‘As …’ sentences encapsulate this process nicely, as do ‘If …, then …’ sentences or those linked together by words like ‘consequently’, ‘as a result’ or ‘therefore’. It is in these phrases, which link ideas together, that the deeper disciplinary knowledge of science is made manifest.
Sherrington’s model gives no account of this. Teaching based on his model would focus on the facts and concepts but not on how a scientist would link them together.
Some students may pick up these relations between concepts intuitively, just as a speaker may grasp a language without being able to state its grammatical rules explicitly. Problems are likely to arise, however, when students are asked to switch between subjects.
Historical Grammar
Consider this sentence from history: ‘the first world war was caused by four factors: imperialism, nationalism, militarism, and alliances’. Here we have the idea of causation, but of a completely different order to the mechanistic model described above.
It would be nonsensical to attempt to turn the historical sentence into a scientific-sounding: ‘as imperialism increased, the likelihood of the first world war increased.’ To do so would be to demonstrate a fundamental misunderstanding of how historians develop arguments, and therefore how we may come to know anything about the past.
This is the danger of leaving the grammatical rules of a discipline implicit: students may attempt to link ideas together in ways that are simply not appropriate for the subject matter.
To avoid this issue, the history teacher must draw students’ attention to the way individual words can imply causation, a causation that is different in kind to the mechanistic conception characteristic of science.
Consider the sentence: ‘the first world war was triggered by the assassination of the Archduke Franz Ferdinand.’ Here the word ‘triggered’ implies a form of causation, but one which is categorically distinct from the mechanistic link between the temperature and pressure of a gas.
If a student is to speak both languages and be comfortable in switching between them, therefore, teachers of both subjects must make the grammatical rules of their discipline explicit. Again, these are issues that Sherrington’s schema-building model overlooks.
Substantive & Disciplinary Knowledge
So far, I have argued that the facts generated by a discipline are comparable to sentences, which can be understood in terms of their concepts (the vocabulary), and the ways in which those concepts are linked together (the grammar). This account may serve to clarify the meaning of some terms commonly used by teachers when thinking about knowledge and the curriculum.
Substantive knowledge can be thought of as the concepts of a discipline, whereas disciplinary knowledge can be thought of as the rules that link those concepts together.
In other words, substantive knowledge is like the vocabulary of a language and disciplinary knowledge is like its grammar.
What is likely to be overlooked by teachers operating within Sherrington’s schema-building model is that facts must be considered as distinct from concepts, i.e. substantive knowledge. These two ways of thinking about knowledge are often conflated, leading to students memorising definitions like ‘hubris means excessive pride’ fruitlessly.
A mental model based on language does not lead to such reductive practice. It implies that every fact can be understood in terms of both its substantive and disciplinary aspects.
Take the two facts examined above: ‘as the temperature of a gas increases, pressure increases,’ and, ‘the first world war was triggered by the assassination of the Archduke Franz Ferdinand.’
Both of these can be understood in terms of their concepts — temperature, pressure, particles, kinetic energy and force in the former; imperialism, nationalism and alliances in the latter — as well as in terms of subject-specific conceptions of causation, as outlined in the paragraphs above.
This implies that, just as speaking a language fluently requires a person to master both its vocabulary and grammar, knowledge of physics or history requires a person to master both the concepts and the rules governing how those concepts link together.
In other words, substantive and disciplinary knowledge are not two separate things that students need to learn; they are two sides of the same coin. Both aspects are present in the items of information Sherrington’s model focuses on.
Subject Communities
This is better understood by some subject communities than others. The history education community has done a lot of work translating these ideas into practice (the terms first and second order concepts are often used, with first order concepts rightly being treated differently to historical facts).
The science education community, on the other hand, typically treats disciplinary knowledge as merely another set of concepts and procedures to be memorised. These usually are related to the so-called scientific method, i.e. experimental and laboratory work.
I have seen very little written, especially in the cogscisci blogosphere, about the deductive and inductive links between concepts that are characteristic of scientific reasoning.
Rims, Hubs & Spokes
It is not just science teachers who have struggled to grasp the subtleties of the substantive-disciplinary distinction; advocates of cognitive science in the classroom often ignore it altogether.
Let’s return to Sherrington’s schema-building model. A schema is said to be a network of information clustered around a key idea. It may be argued that this indeed captures the distinction between facts and concepts, even if it doesn’t make this distinction explicit.
The facts are the many, diffuse nodes of the networks; the concepts are the key ideas around which the facts cluster. To use another metaphor, if the facts are arranged around the rim of a bicycle wheel, the concepts sit in the hub.
This begs the question, however, what about the spokes? How exactly are the facts linked together by those concepts? How does that look different when we think about scientific concepts (particles, temperature, pressure) as opposed to historical ones (imperialism, nationalism, alliances)?
To put it another way, what do all those little lines between the dots actually mean?
As far as I am aware, Sherrington’s model provides no answer.
Conclusion
This is where the language model offers a much clearer picture. By describing facts as sentences, resolvable both in terms of their vocabulary and their (subject-specific) grammar, we obtain an account of knowledge that is much less liable to mutate into generic teaching techniques.
Consequently, I hope it might help teachers move towards practices that develop deep disciplinary knowledge, and away from those that lead to little more than superficial memorisation.
As Sherrington notes, with a nod to Carlo Rovelli, the only way knowledge can develop within a field is if people are willing to call current ideas into question. This is what I have attempted to do in this blog. I look forward to hearing Tom’s response.
