Filling the gaps in teachers’ maths skills

Training must be transferred to classrooms, write Hamsa Venkat and Jill Adler

TEACHERS’ mathematical content knowledge is central to our work in mathematics education at the University of the Witwatersrand.

We agree with the central thrust of Nic Spaull’s recent article, “It’s the teachers’ lack of subject knowledge, stupid” (August 18) — that there is a problem with significant gaps in teachers’ mathematical knowledge, and particularly so at the primary and junior secondary levels. But our experience suggests that traditional mathematical content courses may not work to address the problem of poor pupil performance. This example illustrates what we mean:

Grade 2 class: The task is to work out half of 26. The teacher draws 26 circles on the board and explains: “Count out 13 of the balls. Now check there are 13 on the other side. There are 13? Okay. So 13 is half of 26.”

This teacher knows that the answer is 13, but rather than working it out with the 26 circles and an action that involves sharing into two groups, the teacher presents 13 as the answer and then checks if it is correct.

In scenarios like this, children do not learn to work out answers to similar problems on their own. They either have to know the answer or they have to guess and check.

Our point is that teachers need more than mathematical knowledge. Being able to calculate an answer or solve an equation is necessary but not sufficient for teaching mathematics.

And teacher education needs to work from where the teachers are — even if this means working from the low-level gaps that Spaull’s article and other evidence have pointed out.

Spaull criticises the lack of “transfer from training to classroom” and the lack of rigorous in-service education.

Teacher upgrading such as the advanced certificates in education have been criticised for wide variations in quality and impact. But there has rarely been funding to study the impact on classroom practice or build practical components into course work.

If we want in-service teacher education to impact on classrooms, we need time and funding for the study of mathematics that goes beyond content.

We agree that mathematical knowledge is central.

What we need to build are opportunities for teachers to learn and do mathematics as teachers, with the emphasis on transferring this learning into classroom teaching.

This does not fit simply with the qualifications traditionally offered in universities. Nor does the need to study impact over time fit well with the time and funding imperatives of corporate social investment.

The path from acquiring mathematical knowledge to changing classroom practice is neither inevitable nor straightforward. Criticising teacher knowledge, calling for teacher testing and admonishing universities are all currently in vogue.

The problem is that they entrench our poor educational self-perception, and do not move us forward.

Venkat is South African Numeracy chair and Adler is First Rand Foundation Mathematics Education chair at Wits University