Monthly Archives: August 2014

We need more than a stab in the dark (M&G article co-authored with Hamsa Venkat)

maths teacher

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.


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: 

My new Working Paper with Hamsa Venkat on Mathematics teacher content knowledge in SA


My new working paper (co-authored with Hamsa Venkat) was released today:  “What do we know about primary teachers’ mathematical content knowledge in South Africa? An analysis of SACMEQ 2007”  (Stellenbosch Economic Working Paper 13/2014)


Primary school mathematics teachers should, at the most basic level, have mastery of the content knowledge that they are required to teach. In this paper we test empirically whether this is the case by analyzing the South African SACMEQ 2007 mathematics teacher test data which tested 401 grade 6 mathematics teachers from a nationally representative sample of primary schools. Findings indicate that 79% of grade 6 mathematics teachers showed content knowledge levels below the grade 6/7 band, and that the few remaining teachers with higher-level content knowledge are highly inequitably distributed.

Full paper HERE.

Picture from an excellent NYT article on mathematics in the US – see here.

Links I liked…


“On our own, when we’re furious, we don’t shout, as there’s no one there to listen – and therefore we overlook the true, worrying strength of our capacity for fury. Or we work all the time without grasping, because there’s no one calling us to come for dinner, how we manically use work to gain a sense of control over life – and how we might cause hell if anyone tried to stop us. At night, all we’re aware of is how sweet it would be to cuddle with someone, but we have no opportunity to face up to the intimacy-avoiding side of us that would start to make us cold and strange if ever it felt we were too deeply committed to someone. One of the greatest privileges of being on one’s own is the flattering illusion that one is, in truth, really quite an easy person to live with.” You cut me deep Shrek. 

  • The no-baby boom” – Really interesting and insightful social commentary on how older women without children navigate society’s expectations and why they have to.
  • “What no one could have predicted is that women born in the ’60s and ’70s would become what Day terms the “shock absorber” cohort, living through the most extraordinary changes in dating and mating in one generation. That’s the result of a confluence of forces—the pill, women’s access to higher education and professions—running headlong into a rigid corporate model that remains based on the husband-provider, male-fertility model—working hard in your 20s and 30s to establish a reputation, leaving kids to the stay-at-home wife. “But that doesn’t work for women,” says Day. “If you make it work, it’s as much luck as good judgment.” (via @KelseyWiens).

  • Why do Americans stink at Math?  – great NYT article about comparing Japanese and American approaches to learning and teaching.
  • Thankfully the Ugandan anti-gay law has been struck down by their Constitutional Court on a technicality
  • Just the facts about sexual orientation & youth: A Primer for Principals and Educators

CS Lewis on the Church’s response to its gay members

lines guy

“Of all tyrannies, a tyranny exercised for the good of its victims may be the most oppressive. It may be better to live under robber barons than under omnipotent moral busybodies. The robber baron’s cruelty may sometimes sleep, his cupidity may at some point be satiated; but those who torment us for our own good will torment us without end for they do so with the approval of their own conscience. They may be more likely to go to Heaven yet at the same time likelier to make a Hell of earth. Their very kindness stings with intolerable insult. To be ‘cured’ against one’s will and cured of states which we may not regard as disease is to be put on a level of those who have not yet reached the age of reason or those who never will; to be classed with infants, imbeciles, and domestic animals.” From C.S. Lewis “God in the Dock”

When I read this quote from C.S. Lewis I could not help but think that this was an apt description of the relationship between the church and its gay members. I have often tried to understand how it is that patient, loving, and compassionate people – like those that I encountered in the church – can cause so much unintentional harm. I have never thought that there is some sort of conspiracy of horrible people aiming to exclude and marginalize gay people, yet this is the effect of conservative theology – intended or not. With a tilt of the head, and an earnest facial expression the pastor sighs, “It’s for your own good.” How much pain and suffering has been justified and morally rationalized under that treacherous slogan? How do pastors wash their hands of the blood of suicidal teenagers or the tears of their parents? The answer is that they do not claim responsibility even as they walk away culpable as fuck. This is the thing that makes me really angry. When confused children and youngsters seek help from their well-intentioned pastors and all they get is a subtle re-shaming cloaked as pastoral advice. “It’s perhaps best not to tell too many people about this” he says, trying to spare his charge some pain or public humiliation. Yet he does not think what this advice actually accomplishes. This suggestion to cover-up, to hide, to conceal only confirms to his charge that somehow he is to blame for this. This is his fault. So he walks away internalizing the guilt and shame with every step. The next session the pastor will re-assure his charge of God’s unconditional love and acceptance while he utters the words “There is nothing to be ashamed of”, as if these seven words could somehow counteract all the things he has heard or felt both inside and outside his church. As if it could negate all the things that have been insinuated and suggested by friends and family and pastors and preachers. No, it is not that easy to negate the secrecy and self-denial promoted by the evangelical church. You really have to be wilfully ignorant or just plain stupid not to see how the church’s current approach leads to self-loathing and shame for those who cannot match up to the unworkable and inhumane expectations placed on them.

William Easterly has written a fantastic paper about the ill effects of foreign aid on developing countries and refers to the situation as a “Cartel of good intentions.” A great description of what I am talking about here. “Cartels thrive when customers have little opportunity to complain or to find alternative suppliers.” And these facts together – Lewis’ tyranny exercised for the recipient’s benefit and Easterly’s lack of voice or exit means that we are stuck with a horrible equilibrium. More blood and more tears even as the church prays more fervently and tries to “help” to “care” to “pastor.” What they do not realize is that they are the solution to their own problems, indeed they are the problem.

Things will change, they always do. “The arc of history is long but it is bent towards justice.” We have more precedent than we have need for – slavery, women’s rights, civil rights, what more do you need? I believe two things are changing and they will be the straw that breaks this obstinate camel’s back: changing attitudes and beliefs of church members and increased compassion from pastors themselves. I have yet to see a pastor who has kicked his own child out of the church for being gay. Funny that, how one’s firmly held theological beliefs change so radically when the letter of the Law and the spirit of the Law collide, as they sometimes do.

Obviously most people do not lead churches or mosques or synagogues. They are not the bastion of intolerance and rejection that gay people regularly come up against. But that doesn’t mean there is nothing they can do. There is always something you can do. Speak. Act. Listen. Advocate. Vote. Empathize.

Washing one’s hands of the conflict between the powerful and the powerless means to side with the powerful, not to be neutral. ” ― Paulo Freire