Teachers' mathematical knowledge

Teachers' mathematical knowledge


Maths teachers in the sample were given five simple mathematical tasks to do, drawn from the Grade 6 curriculum. The results show that more than half of the students in the NSES sample were taught by teachers who could answer only two of the five questions correctly. Two-thirds of the teachers could answer only three questions, and just 12% of teachers could answer all five. For teachers who scored anything less than five, the mean achievement of students was very similar. However, those students taught by teachers who could answer all the questions correctly performed noticeably better, scoring an average of 47% on the learner test, compared with an overall average of 34%. 

The recent SACMEQ III results, which involved a longer teacher test of items comparable to those on the Grade 6 learner test, show a low correlation between teacher knowledge and learner scores.

This is a common finding even in developed countries, where teacher knowledge, as measured by relatively simple tests, correlates only weakly, at best, with the performance of their learners. However, scores on more complex teacher tests devised by Heather Hill and her colleagues in the USA, which assess deeper levels of mathematical understanding, emerged as a significant predictor of student gain scores in maths.

The authors conclude that efforts to improve teachers’ maths knowledge through content-focused professional development and preservice programmes will improve student achievement. This work suggests that in order to be effective a teacher needs to have a thorough conceptual understanding of the principles of the subject, and that different degrees of a relatively shallow understanding have no marked effect on learner performance. The NSES data gives some support to this hypothesis.

An interesting interaction between the time spent on teaching and teacher knowledge was noted in our modelling exercise.

Students taught by teachers who scored less than 100% in the mathematics test, and who reportedly taught for less than 18 hours per week, had lower numeracy achievement in Grade 4 on average than students with any other combination of these two teacher characteristics.

Students taught by teachers with either better knowledge or more time spent teaching, but not both, performed somewhat better than the poorest performing group.

However, students whose teachers scored 100% and reportedly spent more than 18 hours a week teaching performed substantially better on average (mean of 54% on the maths test) than the other students (mean of 35%). These pupils also exhibited higher gain scores in Grade 5. Unfortunately, only 7% of students were in this fortunate position.

The National School Effectiveness Study was designed and managed by JET Education Services, and subsidised by the Royal Netherlands Embassy and JET. Aneesha Mayet led the fieldwork. The final research report is currently being written under the editorship of Nick Taylor, Senior Research Fellow, JET Education Services; Servaas van der Berg, Professor of Economics, University of Stellenbosch; and Thabo Mabogoane, Performance Monitoring and Evaluation, The Presidency.