Bringing cognitive science into the Maths classroom
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by Greenshaw Research School
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One of the most common challenges in teaching is transitioning from teacher-led activities (such as modelling or worked examples) to student independent practice.
I’m sure this scenario will be familiar to colleagues up and down the country:
You’ve done your best modelling, shown students a series of examples that you’d painstakingly put together the night before. You broke it down step-by-step, explained your thinking, and got students to copy them into their own books. You feel confident that students have ‘got it’, so you set them off on their independent task. And yet, almost as soon as you’ve finished telling them the questions they need to complete, the first hands start going up and you can almost predict the “Sir/Miss I don’t know what to do.”
This is an almost universal experience in teaching, it’s something I’ve experienced and something I’ve had conversations with many colleagues about when supporting them to reflect on their practice.
In a previous series of blogs, we started to look at how worked examples and models can be so useful for our students as they build a solid foundation.
In this blog, we’re going to delve deeper into understanding the problem, get stuck into the theory, and finish by thinking about classroom applications (to get the most out of this blog, I’d recommend reading the linked blogs first).
In order to understand the solutions, we first need to understand the problem and why it happens. To do that, we need some shared language to describe what takes place.
Cognitive load theory is a theory about how we process and think about information when learning1. The theory suggests that there are two* types of load that we experience: intrinsic and extraneous.
Intrinsic load relates to the difficulty or complexity of the to-be-learnt material and will depend on the material as well as a person’s existing knowledge2 (eg reading this blog is likely putting a relatively small load on you due to your existing familiarity with the English language, but for someone learning to read English for the first time it would place a far higher load).
Extraneous load relates to the way information is presented3 (eg having a question split over two pages requiring you to flick back and forth is likely to place a higher extraneous load than the full question being on one page).
When we’re using worked examples and models, we’re able to moderate the intrinsic load by doing the ‘heavy-lifting’ for students and instead just focusing on getting them familiar with the concepts/procedures etc we’re trying to teach.
When pupils then switch to independent practice, there’s a significant jump in intrinsic load because they’ve gone from being able to off-load the thinking to someone else, to suddenly having to do it all themselves.
This jump can overwhelm our working-memory4, which can often result in things like students not attempting the questions, or putting their hands up and asking for help almost immediately.
So let’s refine our challenge: it’s not just the case that students struggle with the transition, what they’re actually struggling with is the sudden increase in intrinsic load. So, how can we make that increase more manageable?
A solution is to use some of the suggestions from the EEF’s FAME approach as, crucially, they limit the intrinsic load placed on working-memory (relative to not having those approaches). Take the ‘Alternation’ aspect for example:
The problem with the traditional way of giving students a sequence of worked examples before setting them off is that, even if the first question is easy, it likely relates to an example students saw 4/5 examples earlier.
The alternation approach allows students to look at a technique, practice that technique, and then gradually build up to more and more complex ones. Consider the sequence of examples below:
The alternating approach allows students to become familiar with each type of solution process before the difficulty increases (ie the intrinsic load increases).
To use a construction analogy, rather than constructing a building and removing all scaffolding all at once, we gradually remove the scaffolding so the building has support and, should need be, it’s easier to nudge back into place.
Now that we have more understanding of the problem, we can think deeper about Intrinsic and Extraneous loads and what this means as we transition from teacher-led activities to student independent practice. We must bear in mind that classroom applications need to be tailored – and this doesn’t just mean that any questions are suitable for this approach.
If you would like to explore this in more depth, and look at more examples (and non-examples) of how these ideas can impact the maths classroom, please join our Bringing Cognitive Science into the Maths classroom webinars on 13th and 20th January.
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