Bokhove had some great comments on my post on minimizing cognitive load vs. desirable difficulties which clarified the debate for me. As he says,

Squaring [the circle of minimizing load vs. desirable difficulties] is not necessary.

Cognitive Load Theory does not state that less load=best… it should beabout successful integration into schemas.

This fits in with all kinds of worthwhile processes Didau set out in his blog on fading, scaffolding etc. One mechanism can also be ‘desirable difficulties’ or intentional crises (perturbations, cognitive conflicts, productive failure). Yes they might (intentionally)spark loadbut they areconducive to schema building. (Emphases mine)

The phrase of ‘germane load’ stands out to me. It was emphasized again in this great blog post, which goes into much more detail:

encouraging learners to engage in conscious cognitive processing that is directly relevant to the construction of schemas benefits learning. For example, varying the conditions of practice appears to have beneficial effects upon learning, despite the fact that the presence of that variety would raise the loading on working memory. They called this germane cognitive load.

Since then post I’ve been thinking a lot about such day-to-day teaching strategies that might be conducive to sparking germane load: i.e. strategies which build students’ mathematical schemas. Hopefully there’ll be more such ideas in this series.

I’m sure I’m not alone in seeing this phenomenon: encountering a student(/whole classes) struggle with a starter question that was literally done yesterday, even when the whole class were getting it 100% right yesterday.

As many have said, evidence of a student performing a process accurately does not imply they’ve learnt it securely. Performance and learning just aren’t the same. Memory is crucial too.

Due to the fact we did it just yesterday, I think it’s more complex than a memory problem. Sometimes the problem starts **even whilst students were getting all the questions right. **From some of my observations, sometimes the problem is that *students are able to accurately reproduce a process, while being simultaneously completely unaware of the WHAT they are doing.*

Let me be clearer: here I’m not even talking about ‘understanding’ what they’re doing. What I mean is, students can be thinking deeply *‘so I multiply this number here with this one, then I add these ones all up, then I divide that by this total… let’s check if I have the same as my partner – yes! Great, I’m doing it right!’* And yet, all the while, they have no trace of the thought ‘I am currently finding the mean from a frequency table’.

This happened for some of my students in a recent lesson. Their pages were filled with ticks, yet when I was asking them ‘so what is this number? What have you just found?’, such students had absolutely no idea. It’s no surprise, then, when it comes to next lesson’s question asking them to ‘find the mean’, they’ve forgotten what to do. ** They never thought of it as finding the mean in the first place**. In the terms used in the literature, they were failing to even begin building a schema; they were simply replicating a process, detached from any sense of what it was for.

I decided to blog on this as it seemed such an obvious and yet subtle issue with my pedagogy. And a problem that’s so easily correctable as well.

Next time round, I taught finding both the mean and the mode from frequency tables in one go; then the questions required them to find both measures from each. The students were then forced explicitly to label their answers: ‘mean = ….’ and ‘mode = ….’; they thus **had to link the process** of finding the mean **with its name**.

This solution can be used where there’s another similar easy-to-do process that can be lumped alongside the other process you’re trying to teach. I mentioned a very similar one in my previous post on finding areas and perimeters together in the same task. I think one could do similar things with fraction operations, angle facts, index laws, other statistics, and undoubtedly many other topics.

I do have some slight reservations with this strategy, however, due to it violating the principle of ‘separating minimally different concepts’. But from what I’ve seen so far, it’s worked better for medium/long-term retention than whatever I did before.

Undoubtedly there are other ways of linking processes with their names. I think this principle might lend itself usefully to plenaries too: e.g. a 1-minute ‘discuss with your partner: what have we learnt to do today? So, how do I find the MEAN and the MODE from a frequency table?’

I’m also a big fan of rhymes and chants as memory aids, and I think these have an even more powerful effect than simply lumping several processes together. I also think testing students on knowledge organisers might be the best way to do this in general (give them and expect them to learn the exact schema you want them to have in their mind!). However, effective memory aids and knowledge organisers take some careful thought and energy. When it comes to daily lesson planning in a sequence of work, lumping together several similar processes together is relatively easier to implement.

To bring it back to my original post, this strategy undoubtedly increases cognitive load, yet in a way that encourages schema-building. It seems to be working well so far.

Hi Hin-Tai. Couple of things:

Germane Load: one to be careful with. Although I’m on board with the idea in principle, I’ve read some criticism that argued that GL undermines CLT as it renders its predictions unfalsifiable. Take a scenario in which Cog Load is relatively ‘high’. Did it lead to effective learning? (By whatever measure) No. Why not? Extrinsic load was too high. Yes. Oh, the high cog load must have been ‘Germane’.

In other words, what is deemed GL is defined after the fact, dependent on whether or not the activity was successful.

I haven’t cared enough to dig deep into this and pick it all apart yet, but something to be aware of.

Re: Separation of minimally different concepts – there’s a distinction I think between concepts and processes. If teaching ‘mean’ and ‘median’ as concepts, I would suggest separating them out. If teaching a new process to calculate each of these concepts, they can probably be taught alongside each other, as the concepts are by now well understood.

Likewise with area and perimeter – I’m still on the side of separating them out by a long way, but there are then lots of methods for calculating various perimeters and areas later on (think area and perimeter of a sector, for example) which can of course be taught side by side.

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