Mathematical working space relations with conversions between representations and problem solving in fraction addition

Abstract

The present study is focused on the cognitive level of Mathematical Working Space (MWS) and the component of the epistemological level related to semiotic representations in fraction addition. A test measuring students’ conversion and problem-solving ability in fraction addition was developed and administered to 388 primary and secondary school students (about 11-14 years old) three times. Multivariate analysis of variance (MANOVA) for repeated measures and implicative method revealed that the students’ performance improved as they move within primary school and within secondary school. A hiatus in performance progress is indicated, though, when the students moved from primary to secondary school. This finding is in line with a compartmentalized way of thinking indicated for this age group. Didactical implications are discussed.