This study, using a scriptwriting task, examines how 52 Czech pre-service mathematics teachers (PMTs) handled a situation in which a fictional pupil's incorrect reasoning resulted in a correct answer. The participants were asked to imagine and provide a script that reflects how the situation could evolve in response to the pupil's incorrect…

Students' issues dealing with reflection tasks, especially with inclined mirror lines, are widely known. Previous research conducted with primary school students mainly focussed on task difficulty and students' outcomes, especially their errors of reflection. Little is known about which not obviously sustainable understanding of reflection leads…

Interpreting and responding to student thinking are central tasks of reform-minded mathematics teaching. This study examined preservice teachers' (PSTs) interpretations of and responses to a student's error(s) involving finding a missing length in similar rectangles through a teaching scenario task. Fifty-seven PSTs' responses were…

Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students' methods of approaching absolute value inequalities,…

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

Pupils' mistakes, if suitably analysed, may give useful suggestions for improving the teaching/learning process of mathematics. We present here the main issues of an investigation on a population of 732 Italian pupils (9--12 years old), addressed to determine the typology of errors in performing written subtraction. We compared our results with…

This experiment involved 176 London children aged six and seven. Their levels of attainment on subtraction were quickly and accurately established by two questions. Then teaching programs were used to help them attain prerequisite skills. To symbolize too soon is a danger to be avoided. (MNS)

Diagnostic interviews were conducted with third graders to determine why they made mistakes on sixteen arithmetical tasks. A modified version of the Newman method of analyzing errors is discussed and applied to these interviews. (MP)