Why have none of the many attempts to improve maths teaching worked?
Almost everything that is associated with maths in South Africa is either contentious or depressing or both.
One could talk about the flawed World Economic Forum rankings, the confusion around the pass mark in matric, or that only 3% of grade nine pupils reached the “high” or “advanced” maths benchmark in the 2011 round of pupil testing in the Trends in International Maths and Science Study (better known as Timss).
However, it is not our intention to bang the now familiar drum of low and unequal performance. Of course we need to know how bad things really are, but we also need to know why they are so bad, and perhaps, more importantly, how we get ourselves out of this quagmire.
We believe that the national discourse around schooling needs to turn towards our most critical resource: teachers. No education system can move beyond the quality of its teachers. At its most basic level this is essentially what schooling is: the pupil and the teacher in the presence of content.
Harvard University’s Professor Richard Elmore has argued again and again that there are really only three ways to improve pupil learning at scale: raise the level of content that pupils are taught; increase the knowledge and skills that teachers bring to the teaching of that content; or increase the level of pupils’ active learning of the content.
In the South African context, the evidence points towards huge deficits in the last two areas: teacher content knowledge and pedagogical skill as well as low levels of curriculum coverage and cognitive demand.
Without ambiguity or the possibility of misinterpretation, all studies of maths teachers in South Africa have shown that teachers do not have the content knowledge of maths needed to impart to pupils even a rudimentary understanding of the subject. Unfortunately, almost all of these studies have been small-scale localised initiatives aimed at testing teachers in only a few schools or, at most, in one district.
One recent exception was the 2013 analysis by Nick Taylor and Stephen Taylor of the 2007 Sacmeq 3 (Southern and East African Consortium for Monitoring Educational Quality) data, released in 2010 – the most recent nationally representative data on teacher content knowledge. They concluded: “The subject knowledge base of the majority of South African grade six maths teachers is simply inadequate to provide pupils with a principled understanding of the discipline.”
In a paper we published this week we extended their work and analysed the nationally representative Sacmeq data from a curricular perspective. We wanted to know what grade six maths teachers know relative to the new curriculum (known as Caps) that their pupils are expected to master.
This is important to determine what level in-service and preservice teacher training should focus on. Preliminary results from a Joint Education Trust study show that preservice training courses offered by five South African institutions had large differences in the amount and the nature of maths on offer.
Furthermore, in-service education is commonly piecemeal, and frequently related to “managing” the curriculum and assessment – rather than with promoting the understanding and communication of maths.
The findings from our analysis were sobering. Based on the 401 grade six teacher responses in the Sacmeq 3 sample, we found that 79% of South African grade six maths teachers have a content knowledge level below the grade six to seven level band even though they are currently teaching grade six maths.
It is also worth noting that our definition of grade-level mastery was a relatively low benchmark – teachers only needed to score 60% correct of the items in a grade band to be classified as competent in that band.
Breaking down this grade band analysis further, we found the following patterns of results:
• 17% of the teachers had content knowledge below a grade four or five level;
• 62% of the teachers had a grade four or five level of content knowledge;
• 5% of the teachers had a grade six or seven level of content know-ledge; and
• 16% of the teachers had at least a grade eight or nine level of content knowledge.
Our analysis also confirmed particular weaknesses in problems relating to ratio and proportion, and multiplicative reasoning more generally – the kind of thinking that underlies many tasks involving fractions and decimal working as well.
Though sobering, this analysis is useful for policy purposes and useful for thinking pragmatically about primary maths teacher education and development. The results suggest the need to begin work at the level of concepts at lower levels (grades four and five) in order to build more solid foundations of key ideas, rather than starting with higher-level maths.
We would argue that many of the problems we see in South African schools often have their roots in low levels of teacher content knowledge. When teachers lack confidence in the subject they are teaching, this leads to two consequences.
Either they do not cover those parts of the curriculum with which they are uncomfortable or they restrict classroom interactions to low-level problems that limit pupils’ opportunity to learn.
Gaps in content knowledge also lead to highly disconnected maths teaching. This works against helping pupils to see connections between maths ideas, connections that are important for flexible and efficient problem-solving.
There are some signs of mobilisation. The Association of Maths Educators of South Africa established a teacher education group in 2013 and has begun gathering information on preservice course offerings.
The Joint Education Trust study, nearing completion, is doing the same for the intermediate phase (grades four to six). The basic education department has started developing tests that can be used to identify which teachers have critically low levels of content knowledge.
All these initiatives are commendable and show promise, but the key obstacle to progress remains a lack of evaluation of in-service teacher training programmes.
Content knowledge is not the whole story: good maths teaching requires a host of practical and interactional skills, but deep and connected content knowledge is a critical base.
In researching our paper, we were unable to find evidence of any intervention that has been shown to raise maths teacher content knowledge at any scale in South Africa. Not a single one.
Programmes need to be piloted and evaluated before they are scaled up – and only scaled up if they actually work. They should also be evaluated at different scales. Models that work for 10 schools may not work for 100 schools. What works in Gauteng may not work in the Eastern Cape.
In the absence of rigorous evaluation, we are shooting in the dark, on a wing and a prayer. Our teachers deserve better.
Professor Hamsa Venkat occupies the South African Numeracy Chair at the University of the Witwatersrand. Nic Spaull is in the economics department at Stellenbosch University. Their paper can be found at ekon.sun.ac.za/wpapers/2014