Language in mathematics

A full four years ago (where does time go?) I wrote this post on the importance of vocabulary, where I argued for including subject-specific (what we tend to refer to as ‘tier 3’) vocab more in our lessons.

Since then I’ve obviously thought more about this and, following on from conversations with David Didau this week, I wanted to get down another observation.

In my experience, maths teachers can have a tendency to underestimate two things:

  • The vocabulary our pupils can cope with.
  • The effect of bypassing the correct vocab.

Let me elaborate.

The vocabulary our pupils can cope with

Our pupils are capable of learning lots of words. They learnt to speak as youngsters and acquired thousands of them, but we know that many of them don’t move past the basic or intermediate literacy skills to those they need to access more advanced material (Shanahan and Shanahan, 2008). Something happens to many students at secondary age whereby their language acquisition falters. If that is the case, then it falls to us to accept that we’re not teaching them this as well as we could. We must maintain the highest of expectations of all our pupils and part of that is building language acquisition into our lessons such that it is both integral and normal.

What do integral and normal look like? Integral means you value language acquisition as an essential part of your teaching, that you understand its necessity in an education. You seize every opportunity to teach new words, you make pupils practice them – saying them out loud, using them in sentences in context – and you carefully build this into what you do. Normal means language acquisition teaching isn’t an add-on and it’s not over-complicated. We don’t need fancy worksheets and analysis of etymology (although etymology is fascinating and all students should meet it). If we make the teaching of language (or anything, for that matter) too onerous or time-consuming it won’t happen properly. It must be a simple, everyday occurrence, as normal as anything else we do.

When the teaching of language is integral and normal you see that pupils are able to learn really rather complex and specific vocabulary very well and this, in turn, allows them to think more precisely and to communicate more clearly.

Returning to the paper referenced earlier, the authors spent some time talking to mathematicians, scientists and historians to determine what reading looked like in each discipline. There were specific elements of reading that were valued to a different extent by each. The mathematicians valued close reading and re-reading, specifically because reading in mathematics is linked to precision, accuracy and proof. I particularly like this quote:

Students often attempt to read mathematics texts for the gist or general idea, but this kind of text cannot be appropriately understood without close reading. Math reading requires a precision of meaning and each word must be understood specifically in service to that particular meaning.

If we want to take our students on a pathway to being mathematical, thinking like a mathematician, we should build in language acquisition and precision reading as a principle of this.

The effect of bypassing the correct vocab

Something I see very regularly in classrooms is teachers avoiding using correct vocab, I think (from conversations I’ve had) because they are worried that particular vocab will make it harder to understand a concept. This is best explained with an example:

Teacher: A factor is a number that goes into another number.

How many times have you said this? I know I have! I think it happens because of a perception that a “simplified” definition makes this word accessible to more pupils. However, I would argue that we are making the word specifically less accessible in doing this.

What does ‘goes into’ really mean? As a novice without a strong mathematical background I could interpret this in a number of ways. However, if my teacher tells me, “A factor is a number that divides another number with no remainder”, or similar, and accompanies this with examples and non-examples, I can make more sense of the word from the start. Moreover, if my teacher regularly refers to the word ‘factor’ alongside this definition, and asks my peers and me this definition, and gets us hearing it and rehearsing it, then I start to associate the word ‘division’ with ‘factor’ and I am less likely to confuse it with ‘multiple’. Eventually, it will become part of my fluent vocabulary.

In ‘dumbing down’ a definition, we work against understanding rather than for it. That doesn’t mean we have to go all-out Wolfram Mathworld1 on our pupils, but it does mean we have to consider the implications of our own use of language and how we can make small changes that have a positive impact. It’s worth taking some time with your team to discuss where else we have a tendency to bypass proper vocabulary or definitions, and think about the specific negative effects this will have on our pupils. How can you, as a team, work towards increasing your pupils’ language acquisition and precision? What ideas or concepts do you want them to automatically associate a certain word with? Design your instruction towards that aim.


1 “A factor is a portion of a quantity, usually an integer or polynomial that, when multiplied by other factors, gives the entire quantity.” Mathworld

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