Al-Ghafri, Mohammed Said
(2002)
Learning to teach algebra : secondary trainee-teachers' knowledge of students' errors and difficulties.
*University of Southampton, Doctoral Thesis*.

## Abstract

This study investigates secondary trainee-teachers' knowledge of students' errors and difficulties in algebra. We noted that, on the one hand, there is a great deal of research about student's errors and difficulties in algebra. On the other hand, there are only few studies of teacher knowledge about student's errors. There are even fewer studies of secondary mathematics trainee-teachers' knowledge of student's errors and difficulties. This area of research therefore forms the focus of this study because it is less well-documented by research despite the fact that secondary trainee-teachers constitute the next generation of teachers.

To investigate what trainee-teachers know about students' errors and difficulties in algebra, we carried out a national survey in which we asked the participants to explain given students' errors and then suggest ways for helping students who make the errors. We also asked them to predict the most likely errors that students might make when working out given algebra problems. In addition, we asked them to rank order the problems in a way suitable as a teaching sequence. Finally, we asked them to give their expectations about students' success in working out the problems.

This study suggests that secondary mathematics trainee-teachers are able to suggest a teaching sequence that takes into account the relative difficulty of the algebra ideas that are part of the high school mathematics curriculum. For example, most can correctly identify rank-order algebra questions from those that particular groups of students find the easiest to those they find most difficult. the trainee-teachers are also able to predict the most likely errors that secondary students are known to make when encountering algebra in secondary school.

On the other hand, the study indicates that less than one-fifth of secondary mathematics trainee-teachers are able to identify major sources of students' errors (i.e. the reason why such errors occurred). Consequently, most secondary mathematics trainee-teachers are unable to suggest ways that challenge students' thinking and make the students realise their faults in advance of the teacher attempting to add additional knowledge. Instead trainee-teachers are likely to devote time and energy to explaining the whole topic again.

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