From soundbite to sound practice

The blog this week comes from Corinne Angier, secondary maths consultant with Trinity MAT, the home of the West Yorkshire Maths Hub, Trinity Teaching School Alliance and White Rose Maths.

A month ago the education press was full of headlines like these. They were a response to one of the findings of the EEF funded evidence review that was commissioned to inform the previously published guidance to improving maths in key stages 2& 3.

It was perhaps particularly newsworthy because in 2011 the schools minister Nick Gibb had made it clear that calculator use should be reviewed:“Children can become too dependent on calculators if they use them at too young an age. They shouldn’t be reaching for a gadget every time they need to do a simple sum.” The DFE subsequently decided that calculators would no longer be allowed in KS2 tests. A few years later the new GCSE specification was to have 2 out of 3 of the papers as calculator allowed.

This research finding is timely because it coincides with primary schools considering whether to reduce, and secondary schools considering whether to increase, the use of calculators. In both cases this is in response to assessment requirements. It would be more professionally satisfying to explore the issue from the standpoint of wanting all our children to have the best possible opportunity to develop as mathematicians.

The debate about calculator use has been going on for many decades (see for example this guidance from 2000) and there is a danger it might become akin to the debate about eating red meat or wearing a cycle helmet. As teachers we need to go beyond the soundbite of the day and explore what the research is saying in the light of our own experience.

What’s your story?

We are not blank slates as we read research. We have all learned maths ourselves and it is important to pause and put a marker in the sand that acknowledges our experience. I was one of the first pupils to be allowed to use calculators in exams (O’Levels!) and the machines we had were nothing like as intuitive as those on the market now. I remember learning to use the reciprocal button to ease the hassle of substitution into formulae in physics. Through this I made sense of the inverse relationship between multiplication and division.

As a beginning teacher I used calculators, BBC computers (for the programming language LOGO) and later PCs (for spreadsheets and dynamic geometry) on a regular basis in lessons. There was an acknowledgement of the importance of IT tools for learning mathematics and teachers were expected to be proficient in using them.

What was your experience at school and in your teacher preparation? How has this impacted on what you do in your classroom?

Responding to the research findings

Calculators (Section 7.1 of the EEF evidence review)

What are the effects of using calculators to teach mathematics?

Calculator use does not in general hinder students’ skills in arithmetic. When calculators are used as an integral part of testing and teaching, their use appears to have a positive effect on students’ calculation skills. Calculator use has a small positive impact on problem solving. The evidence suggests that primary students should not use calculators every day, but secondary students should have more frequent unrestricted access to calculators. As with any strategy, it matters how teachers and students use calculators. When integrated into the teaching of mental and other calculation approaches, calculators can be very effective for developing non-calculator computation skills; students become better at arithmetic in general and are likely to self-regulate their use of calculators, consequently making less (but better) use of them.

Strength of evidence: HIGH

(Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation p11)

The narrative above provokes two very important questions:

Why might calculator use help students to develop their skills?
How should they be used in the classroom?

Our responsibility as teachers is to explore this issue further through reading (see suggestions below), reflection on our experiences, and discussion with our colleagues and learners.

I tend to encourage calculator use when I want my learners to focus on something other than arithmetic e.g. when they are finding the mean of a set of data given to 2 decimal places. I want to use genuine data such as measurements or prices in my lessons and this can make calculations quite arduous.

I also expect calculators where I offer no other method e.g. to find √10 or sin^-1 (0.4567). This is perhaps worth thinking a little bit more about. Why do we sometimes expect 34783/17 to be computed by hand but never root √10? Should we work with exact trig values for much longer? These are the kinds of discussions that can happen in maths team meetings.

The value of calculators as a learning tool.

When learners use calculators they often get surprising results that don’t seem to make sense. This may be because the calculator protocol is not understood, or it could stem from misconceptions about number. The unexpected answers can be used to seed discussions and may also spark some exploration.

Learners can also use calculators to generate a lot of results quickly. This allows them to conjecture and to generalise. With a graphical calculator this can be extended beyond the structure of the number system to exploring functions. The recognition and description of structure is an important mathematical learning behaviour.

Activities like these can be found in resources from a few decades ago such as the SMILE booklet calculating which can be downloaded from the stem centre elibrary. This may look a little bit dated but the carefully crafted tasks explore key mathematical themes. They could very easily be given a visual makeover.

Your classroom, your team, your school.

The EEF findings are an opportunity to start a conversation about calculator use in your setting. You might want to identify the topics where you will introduce and teach the key functions. This could be in science or geography lessons in primary schools. If you decide to embed calculator work across the school the evidence report might be useful should you need to present a case for buying a few more or investing in one that projects onto the board.

I am left wondering whether I might need to dust off my LOGO and spreadsheet resources in the near future.

Further reading

https://www.stem.org.uk/resources/elibrary/resource/29222/guidance-paper-use-calculators-teaching-and-learning-mathematics

https://www.tes.com/news/school-news/breaking-views/why-we-need-fall-back-love-calculators-primary#

https://nrich.maths.org/2553

http://www.cambridgemaths.org/Images/416450-how-does-the-use-of-calculators-in-primary-schools-affect-mathematics-learning-.pdf

For information about Maths Hub activities go to:

http://www.mathshubs.org.uk/find-your-hub/west-yorkshire-maths-hub/

For information about courses run by the teaching school go to:

http://www.trinitytsa.co.uk/

White Rose Maths materials are free on TES and diagnostic questions. For information about White Rose Training go to:

http://whiterosemaths.com/