Teachers can’t teach what they don’t know

| October 30, 2013 | 0 Comments

By Nicholas Spaull

The fact that there is an ongoing crisis in South African education isn’t a particularly new revelation. An objective outsider would have to conclude that the weight of available evidence is heavily stacked in favour of the judgement that our education system is in a dire state. Whether one chooses to use local or international assessments, the picture that emerges is the same – thousands of South African schools that are academically bankrupt. By this, I mean schools where there is practically no learning taking place during the year.

Teachers can’t teach what they don’t know Some may protest that such statements are too harsh, but even a cursory analysis of the data would suggest otherwise. For example, one question in the National School Effectiveness Study (2010) showed Grade 5 South African students a picture of three grocery items with three prices attached to them, and asked students: “How much will these items cost altogether?” (The prices were R5.10, R4.20 and R1.30.)

Even though this is a Grade 2 level question, 70% of quintile1 one, two and three students in Grade 5 could not answer it correctly. After at least 500 hours of scheduled mathematics instruction, most Grade 5 students still did not have basic fluency in arithmetic. This is verified by a number of other items and different assessments. How is it possible that the majority of Grade 5 South African students are actually operating at a Grade 2 level? An increasingly popular response to that question in academic circles is that too many South African primary school maths teachers have very low levels of content knowledge themselves. One does not really need to explain why this is a fundamental problem: teachers cannot teach what they do not know.

It is perhaps helpful to provide a few examples of what Grade 6 mathematics teachers in South Africa know relative to teachers in other African countries. The Southern and Eastern African Consortium for Monitoring Educational Quality (SACMEQ) 2007 tested a nationally representative sample of Grade 6 students, and also tested their teachers (a sample of 401 Grade 6 mathematics teachers in South Africa). Question 6 of the SACMEQ Grade 6 mathematics teacher test asks teachers to calculate the following sum:

Question 6) 10 x 2 + (6 – 4) ÷ 2 =

a) 11
b) 12
c) 20
d) 21

The correct answer is ‘d’. This is an application of the Brackets- Of-Divide-Multiply-Add-Subtract (BODMAS) rule for choosing the order in which to perform operations. This is part of the Grade 6 curriculum. However, only 46% of Grade 6 maths teachers in South Africa could answer this correctly and, in the Eastern Cape, only 30% of Grade 6 maths teachers could answer this correctly. This is only marginally above what teachers would get if they just guessed the answer, since they would get it right 25% of the time on a four-choice test item.

Unsurprisingly, only 22% of Grade 6 students in South Africa can answer this correctly – equivalent to random guessing. Question 35 asked: To mix a certain colour of paint, Enni combines 5 litres of red paint, 2 litres of blue paint, and 2 litres of yellow paint. What is the ratio of red paint to the total amount of paint?

a) 5:2 b) 5:4 c) 5:9 d) 9:4

The correct answer is ‘c’. This question is well within the Grade 6 maths curriculum, yet only 33% of the South African Grade 6 maths teachers could answer it correctly, again only slightly better than guessing. In contrast, 82% of Kenyan Grade 6 maths teachers and 64% of Tanzanian Grade 6 maths teachers could answer it correctly. In fact, given that this question was also asked in a previous international student assessment, The Trends in International Mathematics and Science Study (TIMSS, 1995),2 we also know how Grade 8 students from around the world performed on this question.

While an astonishingly low 16% of South African Grade 8 students could answer this question correctly, 87% of Korean Grade 8 students and 95% of Singaporean Grade 8 students could answer it correctly. That is to say that the average 14- year-old child in Singapore or Korea would perform better on this item than the average Grade 6 maths teacher in South Africa. In fact, of the 16 questions that were common to both the Grade 6 maths teacher test (SACMEQ, 2007) and the Grade 8 student test (TIMSS, 1995), South African teachers only scored 30% correct after adjusting for guessing. The figure for Kenyan Grade 6 maths teachers is 72% and for Singaporean Grade 8 students it is 71% (both also adjusted for guessing).

Study of two other questions from the test (question 21 and 25) further reveal how low South African mathematics teacher content knowledge really is.

21. < 7 is equivalent to…

A. x >14
B. x < 14
C. x > 5
D. x < 25.

These triangles are congruent. The measures of some of the sides and angles of the triangles are shown. What is the value of x?


A. 52°
B. 55°
C. 65°
D. 75°

Low levels of teacher maths content knowledge

Unsurprisingly, the international report on the SACMEQ study states that only 32% of Grade 6 maths teachers in South Africa had desirable subject knowledge in mathematics. This is in stark contrast to many other African countries with much higher proportions of maths teachers with desirable levels of content knowledge – for example, Kenya (90%), Zimbabwe (76%) and Swaziland (55%). The situation is also highly variable by province in South Africa, with Mpumalanga having almost no maths teachers with desirable content knowledge (4%). The figure for the Eastern Cape is 17%, Gauteng is 41% and the Western Cape is 64%. Yet, the South African SACMEQ report written by the Department of Basic Education does not discuss these very low levels of maths content knowledge. It is unclear why the department has not already identified this as a major priority and taken decisive action. The evidence base is large, consistent and unambiguous. Whether it is small qualitative studies or large nationally representative surveys, the results are the same: too many South African teachers have shockingly low levels of mathematics content knowledge.

Too little transfer

It should be noted that teachers should not be blamed for this situation, since they are the victims of inadequate apartheid-era training and ineffective post-apartheid in-service teacher training. Post-apartheid in-service teacher training has not worked because there is too little transfer from training to classroom practice. Unless training influences the forms of teaching and learning that happen in the classroom, there is little reason to believe it should increase student learning. Teachers in academically bankrupt schools need to be tested to identify content knowledge gaps and then given high-quality training and support that has been proven to work. It is one of the scandals of higher education that after almost two decades of democracy, our education faculties have not managed to create an in-service training programme that has been rigorously evaluated and proven to raise teacher content knowledge. As an aside, one must remember that content knowledge is a necessary, but by no means sufficient, condition for improving student learning – teachers also need to be able to convey that knowledge. Nevertheless, it is widely accepted that teachers need a thorough mastery of mathematics several grades beyond that which they are expected to teach.

Long road ahead

The longer it takes to provide teachers with high-quality training (which has been proven to work), the longer the children in their care will remain illiterate and innumerate.

When maths teachers have such low levels of content knowledge, should we really be surprised when there is virtually no learning taking place in these schools?


1. South Africa’s schools are divided into five categories or ‘quintiles’, according to their poverty ranking. The poorest schools are included in quintile 1 and the least poor in quintile 5. Source: http://www.ci.org.za/depts/ci/pubs/ pdf/general/ gauge2008/part_two/quality.pdf.

2. See, for example, http://timssandpirls.bc.edu/timss1995.html.


1. Hungi, N., Makuwa, D., Ross, K., Saito, M., Dolata, S., Van Capelle, F., et al. (2010) SACMEQ III Project Results: Pupil Achievement Levels in Reading and Mathematics. Paris: Southern and Eastern Africa Consortium for Monitoring Educational Quality.

2. Moloi, M. and Chetty, M. (2011) The SACMEQ III Project in South Africa: A Study of the Conditions of Schooling and the Quality of Education. Pretoria: Department of Basic Education.

3. Taylor, N. and Taylor, S. (2013) ‘Teacher knowledge and professional habitus.’ In: Taylor, N., Van der Berg, S. and Mabogoane, T. What Makes Schools Effective? Report of the National Schools Effectiveness Study. Cape Town: Pearson Education South Africa, pp. 202-232.

4. Taylor, N., Van der Berg, S. and Mabogoane, T. (2013). What Makes Schools Effective? Report of the National Schools Effectiveness Study. Cape Town: Pearson Education South Africa.

Category: Summer 2013

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