Knowledge: you don't know the half of it

Teach the facts, we're told, and the rest will take care of itself. But when it comes to imparting wisdom, nothing is black and white

Clare Jarmy

Educationalists often highlight the importance of skills over facts, but it cannot be denied that imparting knowledge is vital to what we do as teachers.

This is made clear by the fact that it is repeatedly referenced in curriculum and exam requirements. The first stated aim of England's 2014 national curriculum, for example, is to provide pupils with "an introduction to the essential knowledge they need to be educated citizens".

Knowledge frequently crops up first in assessment objectives, too. In England, GCSE maths students must be taught to "accurately recall facts, terminology and definitions"; in the second year of A-level religious studies, they must show "knowledge and understanding" of philosophical arguments; and GCSE history asks them to "demonstrate knowledge and understanding of the key features and characteristics of the periods studied".

Clearly, knowledge is considered to be the foundation on which high-level thinking is built. If we want students to be able to analyse a concept, evaluate a theory or solve problems, subject knowledge will underlie those skills.

Although it is given importance, however, knowledge is only a first requirement: application, analysis and evaluation come afterwards. The message here is that knowledge is simple. But as many teachers will know, it is a bit more complicated than that. And those complications provide an argument for changing the way we view knowledge and our efforts to teach it.

If you come from a background in philosophy, as I do, then this suggestion that knowledge is basic might seem rather strange. One of the core branches in philosophy is epistemology, the study of knowledge. This asks what we know, what knowledge is and how we gain it. It even entertains questions about whether we can truly know anything at all. It is crucial that we, as teachers, engage in these questions: epistemology can provide us with valuable insights for the classroom.

Philosophically speaking

Philosophers have a habit of starting from definitions. Perhaps this trait originated with our bearded hero Socrates, who rightly pointed out that there wasn't much point in talking about something if you didn't actually know what it was you were discussing. So on that basis, let us decide what knowledge is.

Consider this example: Bert knows that Dunfermline is south of Perth.

How does this constitute knowledge? The first thing to say is that Bert can only know that Dunfermline is south of Perth if it is true that Dunfermline is south of Perth. In other words, all things that are known must be true; you can't know something false. I can't know that Tuesday is Friday, for example, or that a bachelor is married.

But knowledge can't simply be something that is true, because lots of things that are true aren't known. There might be creatures living so deep in the ocean that no one (yet) knows that they're there. Those creatures being there and someone knowing that they are there are two separate things. Truth is only one part of knowledge.

So what might the missing part be? What if, say, Bert came to believe that Dunfermline was south of Perth because he guessed it? In that case, Bert would believe it and it would be true, but you couldn't call that knowledge because he could just as easily have guessed that Dunfermline was north of Perth. That doesn't seem secure enough to be called knowledge.

So what are we left with? How do we know if a student truly does have knowledge? Philosophers agree that knowledge is some particular kind of true belief but that there is a third condition that needs to be added before a true belief can be said to be known, something that makes knowledge more secure than lucky guesswork. Unhelpfully, they disagree about what this third thing is.

Some say that the belief must have a justification; others say it must be gained through a reliable method. There isn't time here to go off on a tangent about all the different possibilities. Nevertheless, philosophers have provided some insights that are useful in understanding what we mean when we say a student knows something.

Facts, familiarity and skills

A student giving the right answer to a question is not sufficient evidence to be sure that they know that answer. Imagine you are taking a geography class and you ask where Dunfermline is. As we said above, a student may state the right answer but he or she might have guessed it or one of their classmates might have whispered it. Philosophers and teachers alike require more than just a true belief to identify knowledge.

But this brings problems because there is more than one type of knowledge. Students are required to "know" in all subjects and at all stages of education, but what we mean by the term varies.

Let's add two more examples to demonstrate this:

l Bert knows that Dunfermline is south of Perth

l Bert knows Brian

l Bert knows how to ride a bike

Here, Bert has three different kinds of knowledge. Bert's knowledge that Dunfermline is south of Perth is knowledge of a fact. Let's call this "knowledge-that".

Bert knowing Brian is not knowledge of a fact; it is an acquaintance with something or, in this case, someone. Bert might know facts about Brian, such as whether or not he wears glasses, but that is not the same as being acquainted with him. To know Brian is to know something more than just the facts about him. I know facts about the Queen but I am not acquainted with her - if I was, that would be a new kind of knowledge. Let's call this "knowledge-of".

Bert knowing how to ride a bike is yet another kind of knowledge: the possession of a skill. When we say that Bert knows how to ride a bike, we mean that he knows how to do the things necessary to be riding a bike. Let's call this "knowledge-how".

Now that we have seen there are three kinds of knowledge, we might question whether we all mean the same thing when we talk about knowledge in the classroom.

The hows and the whys

Many subjects require students to have factual knowledge (knowledge-that). This is perhaps the kind of knowledge most associated with what is learned in school. In geography, you need to know the names for different areas in a settlement; in maths, you need to know the sine rule; in chemistry, you need to know the formula for calculating moles.

However, there are also areas where "knowledge-of", an acquaintance with something, best captures what is taught. It seems natural to say that the knowledge involved in learning languages is "knowledge-of", not "knowledge-that". Learning to speak Spanish involves immersing yourself in a way of life, a culture. Knowledge of a language is to be acquainted with it.

It might also be natural to think of knowledge in history in the same way. Yes, there are dates to remember and terms to learn and these are factual pieces of knowledge. But sensitive historical study can take place only when one understands a period of time or political situation. After all, isn't this why schools put on "dress up as a Victorian" days and the like? If nothing was gained by acquainting yourself with a historical era, surely they wouldn't bother.

Subjects such as art and design will lean heavily towards knowledge-how. Again, they have their factual knowledge, such as terms for different techniques, media and tools, but at their core, art and design are know-how subjects. Knowing how to paint is very different from knowing that Dunfermline is south of Perth.

Deduction and experience

Viewed like this, you realise that students go around school having to adapt to very different kinds of knowledge. If you have ever shadowed a pupil for a day, you will have seen this in action. They go from knowledge-that in biology to knowledge-how in swimming via knowledge-of in French, then back to knowledge-that in maths - and all before lunch.

Usually, students navigate these differences surprisingly well, but the presence of different types of knowledge can go some way towards explaining how things can go wrong in their work. Occasionally a student will give me a philosophy essay that is good, but is not a philosophy essay. When this happens, it is not simply the style that is wrong. The student has struggled to see what kind of knowledge is required for the essay I have set.

So should we try to use just one kind of knowledge in schools? Even if we disregard knowledge-of and knowledge-how and focus purely on factual knowledge, we are still not clear of confusion. When we consider how it is that we come to know facts, we are again requiring different things in different areas of the curriculum.

Philosophers delineate between things known a priori (from before) and a posteriori (from afterwards). A priori knowledge can be known without experience, whereas knowledge a posteriori is known only through experience. I can know that all bachelors are unmarried without doing a survey of all bachelors. By definition, any bachelor cannot be married, so I can know this without experience. On the other hand, if I wanted to know how many people got married in Britain last year, I couldn't work it out myself. I would either have to consult the records or ask someone who already had.

Science deals with experiential, a posteriori knowledge. It takes the world around us as subject matter and demands that conclusions be reached by physically finding things out though experiments. This is a posteriori study.

Maths, so often grouped with science, couldn't be more different. In maths, conclusions are established not through experience, but a priori. If you know the concept 2 and the concept 4 and you know what addition is, then you can work out that 2+2=4. You don't need to go out into the world to see that it is so - if you understand the concepts, you can calculate the answer.

Of course, primary school students might well use blocks and cubes to enable them to see the maths happening in front of their eyes, but this is an aid. You don't have to have experience to find out the answer to a maths problem.

Imagine if we applied these epistemological discoveries to curriculum policy. What kinds of decisions might we make?

Perhaps it would give students a clearer sense of what was expected if similar kinds of knowledge were timetabled together so they didn't continually have to adapt. Alternatively, it might make sense to do the opposite and have as much variety as possible, because changing between different kinds of knowledge could be more engaging for students.

And what about the grouping of different subjects? Some schools have faculties of maths and science, and students frequently take the two in combination. Given that maths and science have different ways of acquiring knowledge, does it make sense to think of them as similar? Doesn't maths, especially at the higher levels, sit more naturally with computing than biology? Perhaps PE and theatre studies departments should have more to do with each other. Both are know-how centred; both are physical; both involve, in their different ways, performance under pressure. Perhaps languages and RE have common ground because they involve knowledge-of, imaginatively entering into different cultures.

I am not advocating these as watertight suggestions for curriculum policy. The point is that epistemology can lead to creative new ways of thinking about our own teaching and the curriculum as a whole. After all, simply asking what is going on with knowledge has helped us to understand that the subject is by no means simple.

Clare Jarmy is head of philosophy and religious studies at Bedales School in Hampshire. She is the author of Arguments for God, published by PushMe Press, and forthcoming study guides on the miracles and attributes of God

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