When it’s a guess.
If you can dream, and not makes dreams your master;
If you can think, and not make thought your aim.
- Rudyard Kipling
Last week I wrote about what I perceived as ‘fervour around understanding’ in education, and talked about how I worried that a blinkered charge towards understanding could ironically be preventing it.
This week I would like to discuss a related issue; a similar fervour that I see with respect to ‘thinking.’
First, I would like to mount a defence on ‘thinking’s’ behalf, and offer two huge benefits to encouraging students to ‘think’ during lessons.
Daniel Willingham describes memory poetically as ‘the residue of thought.’ To paraphrase his work: ‘Think about something and you will remember it. Don’t, and you will forget it.’
I have nothing to reference here, but colloquially I think it is believed that ‘thought’ is necessary to develop understanding. Just sitting in my armchair, I can buy into that idea. The more I personally think about something, the more I seem to understand about it. In part this involves giving me time to consider whatever I am studying from different angles, and to pose different questions to myself and try to answer them. Also, the longer I spend thinking about something, the more time I have to recall knowledge from my long-term memory to which it may be related. If that happens, I can link the two ideas together, and understand each in greater depth than I did previously. For these reasons, I’m sold on the idea that thinking leads to understanding. If anyone has a reason to disagree with that, I’d like to hear it, and so would encourage you please to add to the comments below.
As far as I’m concerned, thinking is desirable. It builds both memory and understanding. What conclusion might we now draw from this? How about something along these lines:
“We must try to get kids to think as much as possible during lessons.”
It seems to cover our needs. The more thinking they do, the stronger their memories and greater their understanding.
Let thinking commence!
I would now like to give three examples of how I’ve seen this translated into the classroom. Two will actually come from adult education, but still within the education sector (as opposed to corporate training programmes for example.) The third will be an example for a maths activity I’ve heard about.
Example 1 – Masters Reading
A friend of mine is a teacher doing a Masters in education part-time. On their first meeting, they were provided the specification for the programme. It was a single A4 sheet, chopped into pieces. Rather than being handed the sheet and given five minutes to read it over, they were asked to spend fifteen minutes reading each separate piece, and then to rearrange them into the correct order. The reason for doing this, they were told, was because it would promote ‘thinking.’
Example 2 – Coaching
From my own experience, I went to a training session on mentoring and coaching. I happened to have quite a bit of experience with mentors and coaches already, since it was an integral part of the service my pre-teaching employer provided. Other people at the session had never heard before of a coach or a mentor, in any formal sense of the word. A long list of attributes of coaches and mentors was presented on the board; a single list. We were asked to sort each attribute as to whether we thought it was something related to coaching, or something related to mentoring. We were given half an hour to complete this task. We were told nothing about coaching or mentoring.
In mathematics, eventually you need to learn the notation we use to describe algebraic models. You need to learn, for example, that a letter can represent an unknown number, e.g. n, and that by convention we never write the multiply symbol between a coefficient and the unknown, i.e. we write 2n, not 2 × n. One lesson I’ve seen for teaching this involves a series of twelve worded statements. Students are asked to represent each statement using algebra. Up to this point, they have been told none of the conventions of algebraic notation. Once they have done this, the next part involves providing students the model solutions. Students are then asked to pair up the model solutions with each worded statement, and then compare the model solution with their own interpretation.
This is just one example of many suggested activities for maths lessons that I’ve seen. At the core of each lies the same principle: tell them nothing; they must be made to think.
Learning algebra is a challenge for many novices
So what’s the problem?
Starting with the first example, if a person reads, they are thinking. You can offer a sheet of A4 for someone to read, and as they read it, they will be thinking about it. To do so would have taken a third of the time, so arguably time here was wasted. There’s another problem: were the Masters students here thinking about the right thing? With regards to memory, Willingham specifies that it’s not merely ‘thinking per se’ that needs to happen – thinking for thinking’s sake – but thinking precisely about what it is we hope to remember. The Masters students needed to think about the content of the paper; instead they were thinking about the order the sections should go in. The ‘mix and match’ is also a problem that can be solved with knowledge of grammar and sentence structure alone; it requires no knowledge or understanding of the content of the paper. In addition to this, the Masters students were arguably given extraneous things to think about. Daniel Willingham talks about ‘minimising cognitive load,’ meaning it’s important when teaching to minimise the number of things the student has to think about. This view is supported by Kirschner et al. amongst others. In this example, the students were asked to think about how to arrange the pieces of paper in addition to the hope that they would read and think about the content. If the content were already complex, adding this additional cognitive work could induce overload, preventing any thinking from taking place.
One may argue that it is possible to read without thinking; I’m sure we’ve all done that thing where you’re reading a novel, you’ve gone through a page and a half and only then do you realise you were thinking about something completely unrelated, and you’ve no idea what just happened in the story! The argument here would be that the activity guarantees the student has to read properly, in order to complete the activity. In response to this I would suggest that if you can’t simply trust an adult learner to read what they’ve been given, you have bigger problems to worry about than can be solved by a card sort. However, as already mentioned, this is immaterial since the activity doesn’t even guarantee that students are thinking about the right things, and furthermore makes them think about things that have nothing to do with the learning.
In the second example, about coaching, we were reduced to guesswork. In a minute or two we could have been told what defines and distinguishes between a mentor and a coach. If communicated well, this concept could be easily and quickly understood. In our case, we were asked instead to spend thirty minutes where I watched as people guessed what they thought may or may not be correct. At the end of a few minutes deliberation, it was concluded, correctly, that no-one really knew; there was much uncertainty. I explained the distinction based on what I knew, clarified in response to a few questions, and we then spent the remaining time discussing unrelated issues. After the event I expressed my concerns with the trainer, and asked why the activity had been set up that way. Her response was ‘to encourage us to think.’
To collate these concerns:
- There is a false assumption that a reader, or listener, is not actively thinking
- People were not necessariy thinking about the right things
- People were given extraneous things to think about
- People were asked to guess, rather than really think
- People were left in a state of serious doubt
- Time was wasted that could have been spent thinking about the knowledge to be learnt
Thinking, or guessing?
In the third and final example, I believe the flaws I’ve highlighted to be combined in the school classroom. In trying to analyse the intention of the activities at each stage, this is how it seems to me: the students are asked to ‘think’ about how they might be able to write the worded statements algebraically; they’re not told how to do it. Why; because thinking is good. There’s an implied assumption: if we tell people something, they won’t think about it. It’s the same assumption made when the Masters students were asked to sort the pieces of paper, and the same assumption made when our trainer at the session on coaching refused to tell us anything about what separates coaches from mentors. I would argue that the school students here face the same problem we did in the training on coaching – they are being asked to guess at something to which they cannot possibly divine the answer. Without something to go on, a student might at best conjure up ‘2 × n’ but will never write ‘2n’. Next, if the intention is for students to learn and remember how to write algebraic expressions, what they need to spend their time thinking about according to Willingham is the correct way of writing algebraic expressions; we need them for example to be thinking again and again ‘If I want to write 3 times a number, then I write 3n.’ In this activity, they can’t be thinking that, since they don’t yet know the right way of writing the algebra!
It seems to me that the first part of the activity reduces to useless guesswork. This would also be accompanied by unnecessary uncertainty. I’m all in favour of resilience, and openness to making mistakes, but even as an adult, when dealing with novel concepts I want somehow to feel I’m on the right track; I feel frustrated if left in a state of doubt.
What about the second part of the activity then, matching the model solutions with the worded statements? Here again I think the simple argument in its favour would be that it encourages students to really ‘think’ about the expressions, and how they relate to the worded statements. Then, in comparing the models with their own efforts, they could see how ‘2 × n’ in their version became ‘2n’ in the model expression. I can see some merit to the idea that matching the expressions with the worded statements will help them to ponder how the words and symbols interrelate – though I would want to keep the number minimal, to avoid cognitive overload. Where I worry, is in the idea that this is necessarily a better way of learning that 2 × n should be written ‘2n.’ It’s taken the students a long time to come to this realisation; a long time spent not thinking about it, and for what alternative gain? It’s also a roll of the dice; what happens to the kid who misses that realisation? We’ve also now induced excessive cognitive load; we’re asking the students to simultaneously think both about which expression matches which worded statement and asking them to try to spot the conventions of algebraic notation. Had they first been told the conventions, and practised that separately, they would now be free to work on the conversion between words and symbols.
Overload is never comfortable.
I wonder if there’s uneasiness here at simply ‘telling’ kids something. Are there teachers who fear the children are never listening, or would never listen to them, and so through activities like this they free themselves from the burden of exposition? The argument against exposition appears to be that young people cannot learn from it, or that they won’t be thinking if we’re talking; they will be ‘passive receptacles.’ This is simply not a priori true. I have invested hundreds of hours in watching video lecture series in which a lecturer speaks, and I listen. I spend a great deal of time thinking about the things they say. Being told something does not necessarily mean the listener is not thinking; that they are passive. But okay, it can be the case that a person is not listening; activities of this kind help us to ensure that students think. Well, as already noted at length, they don’t, necessarily; to reiterate, many of the activities I have in mind seem either to reduce to guessing rather than thinking, or else leave students thinking about the wrong things. Perhaps this is reductionist, or otherwise not an exhaustive representation – feel free to comment – but I would put forward that ‘thinking’ is making connections between things that are known, whereas it seems to be often interpreted as ‘creating new knowledge from the ether.’
“The reasoners are like spiders who make cobwebs out of their own substance” – Bacon
There’s something else that perhaps unsettles me. If one were to form the argument that I think during or after those lectures I mentioned only because I’m an adult, or an ‘independent learner,’ does that reveal our latent bias against and low expectations of our students? ‘Children cannot possibly be thinking about something a speaker says.’ Or, they could not possibly want to think, or otherwise be interested in listening and thinking. I suspect anyone who’s worked with young people must know this isn’t the case; they crave learning and understanding, even if they sometimes speak to the contrary. So where does this anxiety come from? I’m not sure I know; thoughts everyone?
What’s the alternative? I think if I were to run a lesson along the lines of this one, I might keep it similar, but cut out the first part completely. I believe it wastes time, and promotes guessing, not thinking.
The master of this craft, in my opinion, is Michel Thomas, a language instructor. In brief, he explains a new word, phrase or rule, he provides an effective mnemonic to memorise it, he offers examples of it in practice, and he then asks the learner to combine their knowledge in new ways, by asking them to translate into the foreign language, a sentence they have not heard before. At every step, time is maximised and the learner is always thinking about what needs to be learnt. There is never any guesswork; every problem he asks you to tackle can be solved by applying the knowledge he has given. In this sense, every act of thought undertaken by the learner involves making connections between the knowledge Michel imparts, rather than ‘creating from the ether.’
As an aside, Michel Thomas is someone for whom I have immense love and respect as an educationalist, and I expect I’ll write more on him in the future.
Here’s what I’d like the key takeaway to be from this post: I am concerned that, heedless of Kipling’s words, we have made thought our aim. Instead, I would suggest that when designing any instructional activity, we should ask ourselves the following questions:
- Is this really thinking, or is it guessing?
- What will students be thinking at each point; will they be thinking about what it is that I would like them to learn?
- Have I minimised the number of new things they have to think about?
- Is this the most time efficient method of learning?
I’d be interested to hear what other people think about this issue.
Daisy Christodoulou writes at length on the second point here: