“I don't understand what they want me to do.” I hear this phrase a lot during revision lessons.
In the past, my response was to interpret the question for students while drawing their attention to the mathematical processes. But with some students, this method just didn't seem to work and they stumbled over the same difficulties each time.
I wondered whether teaching common words and phrases explicitly would enable my students to be more successful in exams. So, in a research project last year, I reversed my approach. Instead of emphasising the maths, I worked with my students on exam language.
As well as carrying out whole-class tests, I asked learners to complete exam questions out loud − in my presence, but without my input. This proved to be enlightening. Where one student mispronounced certain words or phrases or ignored them altogether, it showed me that he had not fully understood what he was reading.
However, after the vocabulary teaching, this student was able to tell me precisely what the question wanted him to do. Even though he couldn't always do what was being asked, his improved understanding made it easier for me to determine exactly what was holding him back mathematically and to suggest topics for him to revise.
This example exam question illustrates the process:
The quadratic equation (k + 1)x2 + 4kx + 9 = 0 has real roots.
a) Show that 4k2 – 9k – 9 > 0
b) Hence find the possible values of k.
When faced with this question, students could struggle with:
1) “Has real roots”
This is a mathematical term with a precise meaning. You will be unable to answer the question without understanding what it means, however good you are at algebra.
This means that you must use working to reach the equation or inequality given by the question, rather than using the equation as your starting point.
If you haven't managed to do anything with part a), you might think you can't do part b). But “hence” is a clue to use what came immediately before. By solving the inequality, which you can do even if you weren't able to “show” it, you will find the possible values of k.
4) “Possible values”
This means that you need to find more than one answer, none of which are definite. We therefore know that the question is asking for inequalities, rather than equations.
Next year, I intend to make this a greater part of my teaching. My classes will be annotating exam questions to identify the processes that certain words should prompt. In your own classroom, you could also try vocabulary lists, posters on the walls, discussions and tests.
Poor literacy should not hold anyone back from showing the maths they can do. GCSE exam language has been extensively reworked to this end, but students are now arriving at A-level unprepared for a jump in linguistic as well as mathematical challenge. By confronting the issue early on, we can help learners to fulfil their long-term potential.
Julia Treen is a maths teacher at Old Swinford Hospital school in the West Midlands