A thread on maths vocabulary:
I've seen a fair few resources in my career that attempt to associate mathematical words with specific operations. I've also observed numerous mathematics lessons where UKS2 children are taught to associate given words with operations and... 1/14
I've seen a fair few resources in my career that attempt to associate mathematical words with specific operations. I've also observed numerous mathematics lessons where UKS2 children are taught to associate given words with operations and... 1/14
...to solve word problems on this basis. (Nonsense like RUCSAC encouraged such superficial strategies.) Unfortunately, such associations are, at best, often misleading. Take this question: "Amy has some cakes. She adds them to a pile of 3 cakes, making 10 in total... 2/14
...How many cakes did Amy have?"
The only discernible maths vocabulary here is "adds" and "total", and yet this is a question that requires subtraction.
When I have discussed this with other teachers, separating mathematical vocabulary from its context has often been... 3/14
The only discernible maths vocabulary here is "adds" and "total", and yet this is a question that requires subtraction.
When I have discussed this with other teachers, separating mathematical vocabulary from its context has often been... 3/14
... described as a way to tackle children's apparent difficulties with word problems. This is, however, only superficially useful, and doesn't deal with the underlying issue - children's inability to parse the meaning of the word problem, i.e. to construct a mental... 4/14
...model of what the words mean in practice. So how should a teacher help children deal with word problems in a short space of time? The disappointing answer is that it can't be done. As I said earlier, supporting children to comprehend 'word problems' means... 5/14
...helping them to construct a mental model of what is going on. (This is a fairly common definition of reading comprehension, and naturally has overlapping elements relating to vocabulary, syntax, background knowledge, etc). While the eventual mathematics that children... 6/14
...will undertake may be deeply abstract, it is initially built on their ability to visualise what is going on in a given word problem. Teaching mathematics well in primary schools is dependent on scaffolding children's ability to grasp the underlying mathematics of... 7/14
...these word problems, and this doesn't come from nowhere. It is based on the physical and visual representations of 'what is going on' in a given mathematical situation. Take the question asked earlier about Amy's cakes. It can be visualised at first with actual cakes. 8/14
Taking children to a more abstract representation of what is going on in the word problem might then involve using counters to represent the cakes, as here: 9/14 
It might then involve a bar model, such as this: 10/14
The exact representation is less important than the attempt to visualise in some form what is going on in the initial word problem. The idea isn't to have children grow to rely on such representations, but to scaffold their journey by showing them that constructing some... 11/14
...form of mental model is what interpreting word problems is all about. There will be many children who seem quite comfortable in the world of abstract mathematics, capable as they are, for whatever reason, to construct these mental models for themselves without support. 12/14
However, this is not the case for many children. The familiar refrain from primary teachers that "they just can't do word problems" is testament to this fact. The good news is that we absolutely can support children to comprehend and solve word problems. The bad news... 13/14
...is that this is a complex process that begins at the very beginning of primary school, requiring high levels of maths-specific pedagogical knowledge and a whole-school approach. Loose associations between mathematical vocabulary and word problems really won't cut it. 14/14
