During a course run by the East Midlands Maths Hub we discussed what is actually meant by the term ‘purposeful practise’.

We were shown the two pictures below and asked to discuss the differences between them:

Both of these sets of questions involve simplifying fractions but the bottom set clearly shows more variety, It contains examples of top heavy fractions, mixed numbers and questions that simplify to 1.

We then were told that purposeful practise contains 4 elements:

1. arithmetic complexity
2. visual complexity
3. multiple steps
4. decoding

The aim is not to cover all 4 of these steps within one set of questions but to try and incorporate them within a whole lesson at some point. Below is greater detail of what each of these elements means:

It could be argued that from the first 2 set of questions shown the bottom set meet the arithmetic complexity and visual complexity. 111 over 3 would meet both as it involves large numbers and 111 could be perceived as a scary looking number. I don’t think I would be surprised if a student mistakenly thought this to be a prime number.

It has certainly made me think carefully about the exercises that I set during lessons and I do aim to meet these 4 elements where possible. This week whilst expanding brackets with my year 9 class I purposefully set a question of expanding a bracket with a fraction (see below). It surprising how many of my students asked me how to handle the 1/4.

I would argue that the above questions meet a lot of the purposeful practise ‘guidelines’. To ensure that multiple steps were then met you could go onto expanding and simplifying two brackets e.g. x(x + 5) + 2x(x – 1).

As teachers it is always important to reflect upon our practise and ensure we set tasks that are making our students think and not just ‘mindlessly practise’. I have found using these 4 elements an excellent tool for making me think about the questions I ask and help me in ensuring my students are being exposed to purposeful practise.