How to develop maths resources that challenge students to think

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When I first started out as a teacher, I always made my own resources and that’s a habit I have continued throughout my teaching career.

From 1990 onwards, I worked full-time as a maths teacher in comprehensive schools around the country. My roles have included maths teacher, Head of Mathematics and Assistant Head, with experience of schools in Essex, Havering, Knowsley, Liverpool and Thurrock. I have always managed to improve results in maths at each of these schools, often achieving the best ever results in that school’s history.

Nowadays I author maths materials and deliver training courses for teachers nationally. I try to apply all of that experience when developing new resources, particularly focusing on how maths can do more to challenge students.

Since I started teaching, my approach to developing resources has changed quite a bit! In the early days my worksheets were produced using a spirit duplicating machine, also known as a Banda machine. The technology we have now is incredible, and much better for producing good-looking worksheets. Of course, that experience has also helped to improve the quality of my resources over time.

I have noticed that some maths teachers will make the work difficult by using larger numbers or decimals when producing worksheets. I used to do that years ago, but I have progressed to focus more on the promotion of thinking skills.

This isn’t necessarily an easy task – not least because some students do not want to think! They may want to simply get the correct answer and then move on. But the educational benefit of that approach can be limited.

Teaching with a purpose

I believe maths teachers must make an important decision about the resources they are going to produce. Please pause and ask yourself: What is the aim of this resource? Is it to enable learning, teach a topic or practice a technique? Every resource that you produce needs a strong answer to that age-old conundrum: Why?

There is also a question about familiarity and repetition when producing resources. Most teachers will use worksheets to supplement textbooks, which is good because pupils will quickly get fed up with one particular resource. However, you need to make sure there’s variety to your own supplementary materials. In the same way you can ruin your favourite meal by eating it every day, teachers can face falling engagement if they’re over-reliant on a single textbook, resource or worksheet.

The same can be said about work that is repetitious in general. This can be a common objection when teaching maths, so it’s important to ensure variety and relatability of your resources. That objection is also one of the reasons why I have shifted towards promoting thinking skills.

Teach pupils to think beyond the right answer

Here are some examples I use when training teachers about how to diversify their maths problems.

When I’m writing a resource about time, I use a clock face and ask for the time shown. The clock face can be used to challenge students’ ability in different ways.

  • First the clock face has just four numbers: 3, 6, 9, 12. This would be a standard setup.

  • The next clock face does not have any numerals, or it’s reflected in a mirror or a shop window.

  • Can students respond to the same challenge, but without the additional information?

  • For example, can they tell me the correct time when the minute hand is missing, and only the hour hand is showing the time?

Often children are asked questions such as 4 x 3 = ? Or they may be asked to find the factors of 12. However, from a different angle we can ask:

  • Using the numbers 1 to 4 only once, find the largest possible answer to oo x o
  • Find how many numbers under 30 there are with exactly six factors.

This process can be applied to lots of different scenarios. By removing information, we’re illustrating how you can arrive at the correct answer using different methods. These are problem-solving skills that may seem simple, but they are vital life skills for a range of subjects and careers.

By re-focusing on the process you go through to get the correct answer, rather than the correct answer in isolation, I believe we can better support students in developing vital problem solving-skills.

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Gordon Brough is a business coach, trainer, entrepreneur and maths teacher. With 25 years of teaching experience, he has trained PGCE students, been a tutor for The Open University and gained degrees in Mathematics, Mathematics & Economics and Education Leadership & Management.

Follow Gordon on Twitter @gordon_brough