“We need more than a stab in the dark” – Hamsa Venkat & Nic Spaull
[This article first appeared in the Mail & Guardian on the 8th of August 2014.]
Almost everything that is associated with mathematics 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 the fact that only 3% of Grade 9 students reached the “High” or “Advanced” mathematics benchmark in the 2011 round of international student testing in Timss. However it is not our intention to bang the now familiar drum of low and unequal performance – the refrain that best characterises our schooling system. 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.
In grappling with these issues 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 student and the teacher in the presence of content. Harvard’s Professor Richard Elmore has argued again and again that there are really only three ways to improve student learning at scale: (1) raise the level of content that students are taught, (2) increase the knowledge and skills that teachers bring to the teaching of that content, or (3) increase the level of students’ active learning of the content. In the South African context the evidence points towards huge deficits in the latter 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 mathematics teachers in South Africa have shown that teachers do not have the content knowledge of mathematics needed to impart to students 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 SACMEQ 3 (2007) data – the most recent nationally representative data on teacher content knowledge. At the end of their paper they concluded that, “The subject knowledge base of the majority of South African grade 6 mathematics teachers is simply inadequate to provide learners with a principled understanding of the discipline.” In a paper we published this week we extended Taylor and Taylor’s work and analysed the nationally representative SACMEQ data from a curricular perspective. We wanted to know what grade 6 mathematics teachers know relative to the curriculum that their students are expected to master (CAPS).
This is important to determine what level in-service and pre-service teacher training should focus on. Preliminary results from a Joint Education Trust study show that pre-service training courses offered by five South African institutions had large differences in the amount and the nature of mathematics on offer. Furthermore, in-service education is commonly piecemeal, and frequently related to ‘managing’ the curriculum and assessment rather than with promoting understanding and communication of mathematics.
The findings from our analysis were sobering. Based on the 401 Grade 6 teacher responses in the SACMEQ 3 sample, we found that 79% of South African grade 6 mathematics teachers have a content knowledge level below the grade 6/7 level band even though they are currently teaching grade 6 mathematics. It is also worth noting that our definition of grade-level-mastery was a relatively low benchmark – teachers only needed to score 60% of the items in a grade band correct to be classified as competent in that band. Breaking this grade band analysis down further, the following patterns of results were seen:
- 17% of the teachers had content knowledge below a grade 4 or 5 level
- 62% of the teachers had a grade 4 or 5 level of content knowledge
- 5% of the teachers had a grade 6 or 7 level of content knowledge
- 16% of the teachers had at least a grade 8 or 9 level of content knowledge
Our analysis also confirmed particular weaknesses on 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.
While sobering, this analysis is useful for policy purposes and useful for thinking pragmatically about primary mathematics teacher education and development. The results suggest the need to begin work at the level of concepts at lower levels (Grades 4 and 5) in order to build more solid foundations of key ideas, rather than starting with higher-level mathematics.
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 students’ opportunity to learn. Gaps in content knowledge also lead to highly disconnected mathematics teaching. This works against helping students to see connections between mathematical ideas, connections that are important for flexible and efficient problem-solving.
There are some signs of mobilization in the education field. The Association of Mathematics Educators of South Africa established a mathematics teacher education group in 2013 and has begun gathering information on pre-service course offerings. The Joint Education Trust study nearing completion is doing the same for the Intermediate Phase level. The Department of Basic Education has started preliminary work on developing tests which 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 programs.
We know that content knowledge is not the whole story: good mathematics 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 mathematics teacher content knowledge at any scale in South Africa. Not a single one. Programs 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.
There are moves towards more open discussions about problems related to teachers’ mathematical knowledge and greater consensus around the need for longer term interventions and evaluation of our development models and efforts. We believe that our findings and those of others, contentious as they might be, are important to face and acknowledge if we are to develop intervention models and content that build from the ground as it currently stands towards the improved mathematical outcomes that we all so desperately want to see.
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Professor Hamsa Venkatakrishnan holds the position of SA Numeracy Chair at Wits University. Nic Spaull is an education researcher in the Economics Department at Stellenbosch University. Their joint research paper can be found at: http://www.ekon.sun.ac.za/wpapers/2014/wp132014/wp-13-2014.pdf
Nic Spaull 