Talking them through 2+2

‘I hate maths.” “I can’t do maths.” We hear these ­sentiments frequently from adults and the pre-service teachers with whom we work. Most of these people do not express similar views about other subjects, or at least, not so acutely or emotionally.

Both of us work in mathematics teacher education. The negativity of such sentiments is unhelpful for our work, but we have a dilemma. If you hate maths, you are likely to avoid doing maths. But you cannot move on from hating maths without doing some maths.

It is this dilemma that spurred the development of an initiative within the Wits school of ­education. Called “I Hate Maths”, the ­initiative ­encourages people to “talk maths” around a monthly problem based on primary school mathematics.

The problem is emailed to staff, ­students and external email lists, and is ­carried within The Teacher — the Mail & Guardian’s monthly ­newspaper for teachers. We ­encourage our audience to share the problem and to submit their solutions.

We live in a culture where book clubs are relatively common. Friends read a book together and then meet socially to talk about it.

Meet socially to talk about maths
The “I Hate Maths” initiative aims to ­encourage this kind of activity around ­mathematical ideas — try a problem together and share your thinking.

One problem we sent out was this: “You need to visit your aunt who is sick, but do not have much time. Would it be quicker to travel there at 55km/h and back at 45km/h, or travel there and back at 50km/h?”

We received responses from our staff, students, schoolteachers and the public. Many said they enjoyed trying the problem without the fear associated with maths at school. Some acknowledged that they used maths-avoidance strategies by ­saying things like: “It depends which ­highway you’re on.”

In discussion forums and on our website we follow up on different solutions. The best solutions and commentary on the concepts involved are carried on our website and in The Teacher.

Two weeks ago Professor Mike Askew, an international expert in primary mathematics from Monash University in Melbourne, Australia, ran a public “I Hate Maths” ­seminar at the Wits school of education. Teachers, parents and teacher ­educators sat together and worked on primary school maths problems.

Fear of maths has been widely documented
Openings to talk through and explain mathematical ­thinking are particularly ­critical for ­primary school teachers because, both in South Africa and ­internationally, fear of maths has been widely documented among them.

This fear, predictably, has consequences for maths teaching in primary schools. Evidence points to highly “procedural” teaching approaches that involve directions on what to do, with little emphasis on why particular methods are selected, the types of problems they are ­useful for and alternative processes that could be used.

Our own experience indicates that where teachers feel unsure of their mathematical competence they will stick rigidly to routine ­questions, ­steering clear of those that might open the door to ­genuine ­mathematical thinking.

This has consequences for how maths is ­experienced in ­classrooms — namely, as endless ­prescribed routines to be memorised.

The “I Hate Maths” problems provide spaces to break with this approach. Our problems do not have obvious or unique paths to the ­solutions and we ask people to explain the processes they choose.

A cycle begins
For the teacher, hearing these ­processes provides evidence of ­present understandings and begins a cycle of development-focused ­teaching.

In the example above some responses we received said that it would make no difference going faster one way and more slowly on return because the gain in time going faster would be offset by the slower time getting back. Development-focused teaching might look like this:

Teacher: “So the overall time is the same both ways?”
Solver: “Yes.”
Teacher: “So let’s say that your aunt lives 100km away. How long would the journey time be with 55km/h there and 45km/h back? And how long with 50km/h there and back?”
Solver: “Well, the time for there and back at 50 km/h is two lots of 100/50 which is 2 x 2 hrs = 4 hrs.”
Teacher: “Okay, so you think that the time taken at 55km/h will be ­offset by the time taken at 45km/h, so we get 4 hours overall here too?”
Solver: “Yes.”
Teacher: “How would you check that?”
Solver: “We can get the time to travel 100km at 55km/h by dividing distance by speed, 100 ÷ 55, and the time to travel back would be 100 ÷ 45.”
Teacher: “Okay, so when you work out these values and add them together you get 4 hours?”
Solver: “Yes, we would, because of the offset.”
Teacher: “Can you check that?”
Solver (using a calculator): “100 ÷ 55 = 1.818181 … And 100 ÷ 45 = 2.2222 — But when we put these together we get a bit more than 4 hours …?”
Teacher: “Mmm, we do. Can you draw a picture to help you see why it seems to take longer to go faster one way and slower on the way back than doing a consistent speed does? And I wonder whether this is always true, or only true for a journey of 100km at these speeds?”

Here we see aspects of ­skilful ­primary mathematics ­teaching — following up on pupil’s ­thinking, encouraging explanation, ­representing ideas in mathematical language and in diagrams, ­making choices about when to ­narrow the problem and ­challenging ­learners to think beyond the ­immediate ­question.

We believe that it is ­possible to move on from hating maths by encouraging people to have fun by “talking maths” more often. The “I Hate Maths” initiative aims to provide accessible problems and social spaces for enabling this shift.

Professor Hamsa Venkat is the South African numeracy chair at Wits University and leads the five-year Wits Maths Connect Primary project, ­working with 10 primary schools. Lynn Bowie is a lecturer at Wits and leads the “­Concepts and Literacy in Mathematics” BEd course. For the “I Hate Maths” problems, solutions and commentary mentioned in this article, see wits.ac.za/academic/humanities/education/primary%20maths/14101/i_hate_maths.html

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