The vital importance of vocabulary in maths

Editors note: Article originally written for the wonderful people over at

For some students, learning maths can feel like assembling a particularly tricky piece of IKEA furniture. 

Now this might not seem that challenging to you: for teachers and experts, the pieces are all there and the instructions are in English and you know who to ask when you get stuck.

Unfortunately, many students have foundational gaps in their knowledge and hit a brick wall. You will often see this with students who are trying to add fractions without understanding what fractions are. They just rush ahead with the adding part, on the top and the bottom! Without the key information, this can be understood as trying to put together IKEA furniture without the most important pieces.

But this isn’t the only area where students will have trouble. The language we use to describe mathematical operations is often overlooked, rushed or crudely simplified. If you are taking on a new student or class, you mustn’t blindly trust that their previous teacher has covered vocabulary to a suitable level. 

If they haven’t been taught that the word “substitution” can be understood in terms of swapping out a team member, they may be relying on an unconnected procedural memory alone. Having gaps in vocabulary is like having IKEA instructions in a foreign language!

Asking for help is the final challenge. If your students don’t also understand that the vocabulary is important, they likely won’t persist in asking for the meaning of the vocabulary being used. Whilst we know to ask a friend, family member, or helpline for guidance, they may just decide that furniture isn’t worth having anyway. For many students the whole process is too tiring and pours fuel on the fire of their negative self beliefs. 

Angles on parallel lines is a particularly fraught topic for many key stage 3 students. The mathematical principles are rarely what catch students out. The names of the rules are the usual pitfall. Vocabulary gives us the solution.

Understanding that “corresponding” means “equivalent in character” makes it clearer how that rule works. Knowing that “alternate” means change between contrasting places explains why it refers to different sides of the transversal (crossing line). Understanding that interior means inside might be something we just expect students to know – but by missing the chance to repeat and strengthen this link, we fail any that need this taught explicitly.

Other examples that I often use in my teaching include highlighting the meanings of the words involved in the first stages of trigonometry: opposite, hypotenuse, adjacent. These words are not devilishly complex to connect to their meanings, but we must not just expect students to do this without our help.

A final and important area that we should be looking to incorporate into our teaching is prefixes. Tri-gonometry and equa-tion are just two examples of how vocabulary can help students recall the necessary process – which is one of the most common and heartbreaking struggles of students who have been primarily taught in a procedural manner. It is doubly frustrating when you know that the students have mastery of the procedures!

So here is our key advice: 

Whilst you may think maths is about numbers, learning happens through language. Check for understanding in both key skills and key vocabulary at the start of a topic. Question students on them repeatedly until their responses are automatic. Your students grades will soar.

Further research

Watch –

Read – “Closing the vocabulary gap” by Alex Quigley

Do – Pick five mathematical words and research all the different meanings they can have and all the possible misunderstandings a student could have about their use.

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