The Dangerous Fantasy of Generalised Understanding

Michael Fordham and Greg Ashman have recently blogged about the distinction between knowledge and understanding, a distinction which has often been used to denigrate what is referred to as ‘mere’ knowledge.

Michael Fordham points out that the supposedly ‘higher’ cognitive phenomenon which is labelled understanding actually means more detailed and more complex knowledge, as well as the knowledge of how one fact links to another. At the highest level, this detailed and complex knowledge, along with the knowledge of relevant connections, is achieved by experts over many years of study.

In contrast, the type of abstract of conceptual knowledge which is often labelled ‘understanding’ is low on detail. It might be termed generalised knowledge, and it is actually much quicker to master than the large amounts of detail which a genuine expert has at his fingertips. It’s so short on content that you might even learn it through group work, with a few prods to point you in the right direction.

Even at a basic level, we can see this in operation. If we consider arithmetic, we can say that mastering the concept of addition requires very little specific knowledge. On the other hand, it takes lots of laborious practice to make number bonds truly automatic, because there are so many, and automacity takes so long to build.

The idea of addition, the concept that by combining two numbers you end up with a higher number that is the sum of the numbers added, is quite abstract, and it might seem more sophisticated to articulate this concept than to memorise number bonds. But a general definition is much less valuable than the ability to return an answer to a number bond automatically, without thinking. And as Michael Fordham points out, these are not two fundamentally different things, knowledge and understanding: they are just two different types of knowledge, one generalised and abstract, the other much more concrete and applicable to specific situations.

The idea that generalised concepts are somehow higher than specific applications, and that general knowledge is more valuable than large amounts of detail, is an idea which privileges management over technical ability, as I have written about here. It is not an idea which encourages hard work and application; instead, it elevates those who present smooth and credible vagueness and generalisation and leave the hard work of the details to others.

Ultimately, praising so-called conceptual knowledge over hard, specific information encourages us to live in a fantasy world, in which the boring details can always be left to somebody else. In fact, it is the world of television and film, which always edit out the tedious effort of piecing together details in a criminal investigation, or piecing together evidence in scientific research. Instead, a fictional Stephen Hawking gazes into glowing coals and the next day has a eureka moment and comes up with his theory of everything.

This is the fantasy of the individual Romantic hero, questing for the transcendent and the sublime, or the revolutionary guerilla, transforming society with just a Kalashnikov, a colourful bandanna and a few glamorous slogans; it is dangerous nonsense.

As Hannah Arendt does, we should ask the deeper question about why these ideas are so popular. Why should a culture embrace concepts that undermine hard work and the mastering of objective knowledge? Could it be that we have privileged the subjective over the objective, and ceased to believe that there is any definite and certain knowledge to master?

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4 thoughts on “The Dangerous Fantasy of Generalised Understanding

  1. Enjoyed this although having taught addition to my own children I’m pretty sure that appreciating what it means in different contexts is actually quite hard. Also I’d say that often procedural fluency is needed to facilitate knowledge/ understanding of addition.
    For example, my neice was struggling with addition at end of year one. She could count two groups and tell you the total but was unable to ‘count on’. It became clear that this bright little girl had never been taught the idea of ‘one more’, so essential to a full grasp of addition. I say she was never taught but the idea must have been wafted in her direction at some point in the context of a sand pit or some toy dinosaurs… Anyway , I think I’m basically agreeing with you!

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  2. I know this post isn’t about addition but I thought I would throw this in. I know GCSE students who will probably get a C in maths, and yet when they are asked 29 + 46 may well reply 65 or even 74 or 76 – to these last two answers I tend to ask incredulously ‘how can you be one out!’ There is something seriously wrong when an odd plus an even equals an even. (I suspect it is the use of number lines and fingers for too long). I have lots of examples in which middle set kids will call out seemingly random answers! Something has gone wrong somewhere.
    Thanks for letting me get that off my chest.

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Thoughtful and reasonable discussion is always welcome.

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