What is learning? – Part 2

Clearly, I was being ‘ambitious’ when I said ‘tomorrow’!


But doesn’t this lead to a risk of rote learning?

Only insomuch as there’s ever a risk that any given teacher will promote knowledge acquisition that is rote in nature.

In an earlier post I talked about Ben Orlin’s criticism of mnemonics.  One example always stuck with me:

 “We could teach that during the civil war, ‘Maryland was a part of the union because marriage is a union.’  The mnemonic is easy to remember, but provides no understanding of the situation….”

I don’t know much about US history.  It’s with the greatest of ironies that, in speaking with friends about this example, I have always first used Orlin’s mnemonic to recall the states to which he was referring, and that they were a part of the union, and then used that recalled knowledge as a cue to remember the reasons why Lincoln wanted to keep Maryland on side.

In other words, a teacher could just teach the mnemonic, and a child might answer a simple question correctly on a poorly designed standardised test, but clearly have no understanding of the situation; their knowledge is rote.

Another child could use the mnemonic to recall the facts, but have also been given knowledge then about the connections between facts, the why which we perceive as understanding.  It is fundamentally down to the teacher to apply these principles intelligently; a teacher who looked at my view of understanding in the previous post and then only ever taught factual knowledge in a rote disconnected fashion has been lazy, and not applied the principles intelligently.  They have also failed to appreciate the importance and implications of the second bullet point: ‘Understanding is the knowledge of connections between knowledge.’

But what about questioning, inquiry and critique?

Surely we don’t want kids to just accept everything we tell them!

Well… if you don’t want your pupils to accept what is it you’re teaching them, I would pause to think carefully about what it is you’re teaching them.

Granted, we share a sense that we don’t want them to accept it ‘mindlessly;’ we fear this image of unthinking drones who accept anything an authority says to them.

Previously, I painted a picture of the pupil who questions and challenges the causal knowledge provided.  I said that that child would be capable of doing so only because of their yet even broader range of interconnected knowledge.  In other words, if you’re serious about wanting pupils who can question or challenge what you tell them, then you must be prepared to furnish them with as much interconnected knowledge as possible so they can do so, and you must be prepared to wait.  Simply asking them to ‘question’ or ‘analyse’ or ‘critique’ something is an exercise in futility if you haven’t given them the means to do so; it’s like asking someone to lay siege to the citadel with no army, no armour, and no armament.  To continue the metaphor, raising an appropriately equipped army is something that takes time, and likewise building a mind that can properly question and critique is something that takes time.

Think for yourself

Think for yourself, or mindlessly challenge authority?

It’s with the deepest of ironies that focussing on producing students who ‘question authority’ will lead to unthinking drones, mindlessly churning out ‘But maybe not!’ unable then to substantiate their criticism.

But what about skills?

There are at least two broad kinds of what we might call a ‘skill’ in the intellectual sense.

Knowledge is sometimes categorised as being either factual, know that, or procedural, know how.  Thinking about mathematics, we teach a lot of procedural knowledge.  Being able to solve a certain type of equation is one example, and it could be seen as a kind of skill; it’s something that one has to practise over and again, getting better each time until the skill is mastered.

There are other, more ethereal kinds of skill in mathematics though; the biggest catch-all for these would be ‘problem solving.’  In history and English there is concern over whether people can analyse, interpret, synthesise or ‘write to persuade’ et al.  There are similar ideas in geography.  In science there is also some focus on analysing and interpreting data, or the wonderful catch-all ‘thinking scientifically.’

As before, these ‘skills’ won’t manifest without the requisite knowledge.  In mathematics, I came to realise that what I perceived as my ‘problem solving ability’ was actually me thinking very quickly, and often subconsciously, through solutions I’d seen in the past to problems that shared similar properties to the one I was working on.

In the humanities I would argue it’s pointless telling someone how to ‘infer’ or ‘interpret,’ giving them some kind of generalised framework or conceptualisation of what that means and then expecting pupils to be able to apply it.  That general framework may be a piece to the puzzle, but it’s a small piece; what’s really needed is lots, and lots of examples for pupils to read and think about in which a person has inferred or interpreted or analysed or compared and contrasted something.  It’s the same way mathematicians develop problem solving skills: see lots of different problems and their solutions, and slowly, over time, be able to replicate parts of that process.

Likewise, in science the ‘skill’ of interpreting data manifests, I would argue, as the result of having seen many types of data set be interpreted in many different ways.

Still, all of this hinges on the right knowledge having been accumulated, and its links between.  A pupil can only solve a mathematical problem if they have to hand the pieces of mathematical facts and processes that form a necessary part of its solution.  A history pupil can only infer or analyse something if they know enough about the historical narrative, the context, the characters and so forth to be able to make the appropriate new links between the knowledge they already have.


Skills or knowledge?  Or skills are knowledge… ?


Learning is:

  • The accumulation of knowledge
  • Knowledge of the connections between the knowledge


This is not ‘mere transmission teaching.’  This is powerful learning.


About Kris Boulton

Teach First 2011 maths teacher, focussed on curriculum design.
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3 Responses to What is learning? – Part 2

  1. I like this kind of thinking aloud post. What interests me is how this manifests itself in discussions at your school. Is this a line of argument you pursue in department meetings about schemes of work or about day to day practice? Does anyone disagree? Are there examples of practice in your school which suggest this isn’t well understood?

  2. Kris Boulton says:

    I guess something like this is pretty ‘high-level conceptual’ in nature, meaning that it’s many steps removed from what we actually do in the classroom, and takes a long time to filter down into practice. It’s an idea that might be held in mind and underpin future thinking.

    It’s something I’ve only mooted in passing a few times, and since it’s so removed from our immediate necessities, it’s not something that’s necessarily led to significant debate, or a furore of activity to change how lessons are planned.

    To plan a curriculum to take full advantage of this kind of thinking: building knowledge ‘chunks,’ then later connecting them together, is an enormous undertaking. We’re lucky, I think, in that our curriculum certainly allows for a lot of this connectivity to take place, but if it happens it’s largely at a teacher-level, and so isn’t necessarily planned for departmentally.

    It informs what I do personally, and how I think about long-term planning. I consider it something of a ‘working hypothesis.’ Whether the model leads to deep mathematical understanding over time, we will see!

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