I’ve written before on the normative principles behind minimizing cognitive load – i.e. to what extent should teachers design teaching so that learners’ cognitive load is minimized? This post, however, will focus on something foundational I’ve observed, that’s been in the background of these previous posts.
In my previous post I described the phenomenon where:
students are able to accurately reproduce a process, while being simultaneously completely unaware of the WHAT they are doing.
Similarly, the conclusion of another post was:
to enable students to learn x, I believe we should include desirable difficulties in tasks to ensure that students are required to use everything they need to know about x in order to solve the task; students are thus forced to think about everything they’re meant to be think about to understand x correctly, and they thus embed those thoughts.
I believe the underlying principle that explains these two recommendations is the following descriptive observation: whilst listening to instruction and doing tasks, learners aim to achieve ‘success’ while experiencing as little cognitive load as possible. This often has negative learning consequences and must be counteracted.
Here are some examples and suggestions related to this observation:
I mentioned the common examples in previous posts of students accurately reproducing procedures & achieving ‘successful’ answers, without engaging with what those procedures were for. As I’ve detailed, this has several adverse effects, including an understandable lack of memory-building and retention of this process. So, make tasks impossible for learners to do without engaging with the name of the process.
Another example is activities such as code-breaking tasks (where solving problems gives you another letter or clue for the code) – as well as any sort of ‘parallel’ task where answers to one task then yield the clue for solving the other task (like those calculated colouring worksheets). I’m sure anyone who’s ever used one of these has experienced the frustration of children finishing in record time by cleverly guessing words and spotting patterns in the words. Learners want the ‘success’ of breaking the code without the unnecessary cognitive load of actually working out the maths problems. This is a really interesting example of where engagement and motivation with the task is actually sabotaging the key practise aim and learning objective. If you want to include something a bit more ‘engaging’, make sure it’s impossible to attain success by skipping the maths – because learners will skip it otherwise.
Another example is when teaching advanced methods that aren’t necessary for learners to be successful in the subsequent task. Teaching equation solving is the classic example, especially when teaching it to a class that have seen it before. The balance method is superior, but requires lots of difficult conceptual shifts; therefore, if it’s taught, but then practised with questions such as: 3b + 4 = 12
then many students will minimize their cognitive load by using much inferior, though still successful methods, such as by ‘undoing’ operations from the RHS, or by using their number sense + trial & improvement to work out what b must be. No! If you want them to use the balance method, give them questions where it’s actually easier to use balance methods to gain success: something like 6b + 4 = -12, where learners will feel much less confident in using their number sense and/or trial & improvement.
Other examples of this type of issue: teaching trial & improvement for equation solving, when students could just solve the equation accurately using non-numerical methods. More generally, don’t teach any sort of numerical estimation method unless the questions used are going to be ones where learners have to use those methods. That applies whether you’re talking about estimation simple calculations, or whether you’re using the trapezium rule. Or, teaching students to solve quadratics: if you want them to practise using the quadratic equation, don’t make the mistake (that I did) of using factorisable quadratics in your task.
Learners also minimize their cognitive load when given non-ideal scaffolds and memory aids. BIDMAS is a great (/terrible?) example of this. BIDMAS makes perfect sense to those who already understand the order of operations, but brings a whole host of misconceptions to those who first encounter it. The classic one is to see addition as prior to subtraction, or division as prior to multiplication. Yet why on earth would learners think otherwise, when they’re presented with BIDMAS? If one is taught that BIDMAS tells you the order of operations, and brackets are first, followed by indices… well, ‘of course’ division comes before multiplication. The biggest danger, too, is that BIDMAS will often give learners enough success (e.g. for Qs like 3 + 4 x 2) for them never to doubt it again. Understanding that learners seek to minimize their cognitive load suggests: don’t use a memory aid if it doesn’t, in itself, say the whole picture. Otherwise the memory aid will be remembered, and the full picture will be forgotten.
One final suggestion: this principle can be exploited positively, too, rather than just guarded against. My original definition clarifies that while learners do want to minimize their cognitive load, they nonetheless only do this to the extent that they can still be successful in tasks. A great way to exploit this is by loudly including ‘trick questions’, i.e. unanswerable/non-example questions in tasks – for example, throwing in questions like simplify 3a + 6b; simplify 2^4 + 2^3. It’s amazing how much more careful, thoughtful and focused students become as you announce ‘do not make this idiotic mistake! I’ve put in some trick questions to see if you’ll make it!’