Understanding the key words and language of mathematics is central to becoming a confident mathematician who can solve multistep problems. In school, we successfully pre-teach, teach and revise vocabulary. It has been a well-used tool and tactic for supporting and scaffolding learning. However, we need to recognise that while key words are vital they are only a part of the whole. Problems arise when the meaning of a word may be understood but how we use the word changes.
What we have discovered is that when teachers apply reading comprehension strategies to other subjects, including maths, pupils of all abilities are able to better understand maths problems. Pupils need opportunities to visualise, make connections, predict, ask questions and build vocabulary to develop a deeper conceptual understanding of maths.
For example, a pupil may be able to confidently tell and show you they know ‘more than’ means quantifiably more, but they may not understand how to solve a word problem that uses that vocabulary if they don’t understand the meaning of the term.
For example, Katy has 56 Maths — No Problem! tests to mark which is 12 more than Natalie. How many papers does Natalie have to mark?
If pupils identify the key mathematical term ‘more than’ as a signal to add the numbers, i.e. 56 (more than) + 12 = 68, they would be wrong because that’s not what the question asks. This is where reading and vocabulary really come into play.
If your learners only think of ‘more than’ as ‘to add’ they will only apply that principle to the problem and won’t comprehend what’s being asked of them. This is an example of what Dr. Yeap Ban Har has shown as procedural rather than contextual learning.
A better approach to help pupils understand the meaning of key words is to use visualisation as in Jerome Bruner’s Concrete, Pictorial, Abstract (CPA) approach. For example, a more visual approach to the questions posed above is ‘Can you imagine Katy sitting down at her desk with a pile of 56 papers to mark? They are stacked in 5 piles of 10 papers with 6 papers left over. Katy has 12 more papers to mark than Natalie. Can you see Katy with her 56 papers? Can you see Natalie? How are we going to find out how many papers Natalie has to mark?’
By using this approach and consistently modelling how to read a question, pupils will understand how to use the term in question, rather than just understand what the word means. This will lead to a deeper conceptual understanding and the ability to see the term in the context of the whole problem.
Reading a maths problem well is a skill that all teachers at Saltdean have explored and used consistently, and one pupils need to be taught in all year groups. Reading strategies such as choral and echo are great for practising fluency in reading problems, but the key is for pupils to truly understand the meaning and context of key words in order to successfully solve maths problems.