The Ingredients of Complex Tasks

In a lot of ways, the next two blog posts are the culmination of all the learning we’ve been doing on applying cognitive science to our curriculum, teaching and learning (and in a lot of ways, that’s perfectly appropriate for the topic at hand!)

In terms of using cognitive science to inform our practice so far: we’ve recognised that working memory is very limited, while long-term memory is essentially infinite, so we aim to deal with that bottleneck by ensuring students memorise the key facts – hence the use of knowledge organisers and self-quizzing. We also provide students with retrieval practice regularly, both in lessons and for homework. We do these things because solving tricky problems, or constructing a cogent essay, rely on the automatic recall of basic facts first – only once the basic facts are recalled without significant effort is the necessary bandwidth in working memory freed up to crack the problem or think about the big arguments for your essay.

Let me give an example. Here’s a problem to be solved in a year 8 maths lesson. To be able to solve it, students must recall and use the following facts:

• The meaning of ‘perimeter’ and how to find it

• That opposite sides of rectangles have equal lengths

• Strategies for making sure you include all the sides when finding perimeter (e.g. dot at one corner and draw the path around the shape)

• The fact that x represents a specific value to be found through calculation

• How to add negative numbers

• Converting mixed fractions to top-heavy fractions – how to do this

• How to add fractions (or switching to decimals to add them)

• Like terms can be collected by addition

• How to rearrange an equation to make the unknown quantity the subject (knowledge of reverse operations)…

• And I may well have left things out because I’ve taken them for granted!

There are far more facts here than can be ‘held in mind’ at any one time. Therefore, to be able to solve it, many of the facts and skills have to come automatically. It is a very useful exercise for teachers to identify the key facts and/or skills that contribute to a problem like the above – it is often surprising just how many there are! But this recognition is a vital step in building students’ capacity for tasks like this. Furthermore, although students across subjects need to become better at synthesis and problem-solving (not just because these are new GCSE demands, but because this makes them better at the subjects!), simply practising problems like the above over and over does not lead to improvement on these kinds of problems! It would seem like the logical approach – ‘Students need to get better at problem solving/essays, so they should practise problem solving/essays’. However, when allocating this practice there are two problems. Firstly, we the teachers don’t know where they are going wrong, so we give inaccurate feedback. Secondly, students don’t know where they are going wrong, so cannot improve.

Instead, the far better approach is to spend time breaking down the complex tasks and ensuring students are fluent, even automatic in some cases, at the component skills. All it takes is a little thought, like the example above. It requires us to recognise that, as subject experts, we take so much for granted. We have to show some empathy with novices (our students) and recognise the many things we expect them to do at once when – for example – writing that essay. We have to be alert to the misconceptions and conflations that exist in our subject. For science teachers, at least, there is plenty of literature on this. Once we’ve picked out these components, the key to success on the complex task is to drill these knowledge and skills: the subject of the next post.