Connections that confuse

In my previous post I wrote aboutĀ using puns as nemonics. Drawing pupils attention to connections between words they understand and mathematical vocabulary is a useful tool for helping students remember technical terms. However a note of caution is also needed.

Many words have common English meanings and also precise mathematical definitions. This is a rich source of confusion for students who may for example think of a right angled triangle as ‘regular’ in the standard English definition though it is not mathematically a regular polygon. These misunderstandings can easily happen whether or not the teacher explicitly makes connections between the common word and the mathematical term, but teachers need to be aware of the danger of creating or cementing unhelpful connections. I think the best course of action is to connect technical terms to their non technical meanings and them spend time explicitly addressing the differences between technical and standard usage. In the case of ‘regular’ this could involve talking about shapes like right angled triangles and rectangles and explaining when they are mathematically regular.

Another issue to be aware of is that in exam questions technical terms can work as a cue, giving students a clue about what techniques the examiner would like to see. Students see common English words like ‘similar’ or ‘difference’ and can fail to interpret these as cues. Therefore it’s vital that students recognise these words as technical terms. One strategy is to ask students to underline technical terms in questions and ensure they are underlining words like ‘similar’ when they are being used with their mathematical meanings.

Puns as nemonics

I’ve talked in other posts about tricks forĀ learning to remember names. Here I’m going to explain how puns can help your students learn technical volcabulary or even formulas. The idea is to connect the new thing you want to learn with something you are already familiar with so that your brain has a way to relate to the new fact.

So perhaps you have a student who knows everything there is to know about pirates, but can’t remember the formula for the circumfrance of a circle. Help them connect what they know with what they need to learn with this joke. “What do pirates take to eat when they sail around the world? Two pies arrr!”

This is just one way to help students remember this formula. The best way to help them learn it us so give them as many different ways to remember it as possible, including pictures, arguments about units, proofs and puns. If students have multiple ways to connect to a fact they are more likely to understand it deeply and be able to apply it correctly in new situations.