Dr Ems Lord, Director of the University of Cambridge’s NRICH initiative, shares three activities to try in your classroom, to help learners improve their use of mathematical vocabulary.

Like many academic subjects, mathematics has developed its own language. Sometimes this can lead to humorous clashes when mathematicians meet the real world. After all, when we’re calculating the “mean”, we’re not usually referring to a measurement of perceived nastiness (unless it’s the person who devised the problem we’re trying to solve!). 

Precision in our use of language within mathematics does matter, even among school-aged learners. In my experience, issues frequently arise in geometry sessions when working with pyramids and prisms, squares and rectangles, and cones and cylinders. You probably have your own examples too, both within geometry and the wider curriculum. 

In this blog post, I’ll explore three tried-and-tested ways to improve the use of mathematical vocabulary in the classroom.

1. Introduce your class to Whisper Maths

“Prisms are for naughty people, and pyramids are for dead people.” Even though I’ve heard that playground “definition” of prisms and pyramids many times before, it never fails to make me smile. It’s clear that the meanings of both terms cause considerable confusion in KS2 and KS3 classrooms. Don’t forget, learners often encounter both prisms and pyramids at around the same time in their schooling, and the two words do look very similar. 

One useful strategy I’ve found is using an approach I like to refer to as Whisper Maths; it’s an approach which allows individuals time to think about a problem before discussing it in pairs, and then with the wider group. For Whisper Maths sessions focusing on definitions, I tend to initially restrict learner access to resources, apart from a large sheet of shared paper on their desks; this allows them to sketch their ideas and their drawings can support their discussions with others. 

This approach helps me to better understand their current thinking about “prismness” and “pyramidness” before moving on to address any misconceptions. Often, I’ve found that learners tend to base their arguments on their knowledge of square-based pyramids which they’ve encountered elsewhere in history lessons and on TV. A visit to a well-stocked 3D shapes cupboard will enable them to explore a wider range of examples of pyramids and support them to refine their initial definition. 

I do enjoy it when they become more curious about pyramids, and begin to wonder how many sides a pyramid might have, because this conversation can then segue nicely into the wonderful world of cones! 

2. Explore some family trees 

Let’s move on to think about the “Is a square a rectangle?” debate. I’ve come across this question many times, and similarly worded ones too. 

As someone who comes from a family which talks about “oblongs”, I only came across the “Is a square a rectangle?” debate when I became a teacher trainer. For me, using the term oblong meant that my understanding of what it means to be a square or an oblong was clear; at primary school I thought about oblongs as “stretched” squares. This early understanding made it fairly easy for me to see both squares and oblongs (or non-squares!) as both falling within the wider family of rectangles. Clearly this is not the case for everyone, so having a strategy to handle the confusion can be helpful. 

Although getting out the 2D shape box can help here, I prefer to sketch the “family tree” of rectangles, squares and oblongs. As with all family trees, it can lead to some interesting questions when learners begin to populate it with other members of the family, such the relationship between rectangles and parallelograms.

3. Challenge the dictionary!

When my classes have arrived at a definition, it’s time to pull out the dictionaries and play “Class V dictionary”. To win points, class members need to match their key vocabulary to the wording in the dictionary. For the “squares and rectangles” debate, I might ask them to complete the sentence “A rectangle has...”. Suppose they write “four sides and four right angles”, we would remove any non-mathematical words, so it now reads “four sides, four right angles.” Then we compare their definition with the mathematics dictionary.

They win 10 points for each identical word or phrase, so “four right angles, four sides” would earn them 20 points. It’s great fun, and well worth trying out if you feel your classes might be using their mathematical language a little less imprecisely than you would like.

More free maths activities and resources from NRICH…

A collaborative initiative run by the Faculties of Mathematics and Education at the University of Cambridge, NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering early years, primary, secondary and post-16 education – completely free and available to all. 

The NRICH team regularly challenges learners to submit solutions to “live” problems, choosing a selection of submissions for publication. Get started with the current live problems for primary students, live problems for secondary students, and live problems for post-16 students.