Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making

Abstract

Two-hundred and thirty-one students in 6 Grade 9 classes in 2 secondary schools in Thailand attempted 54 pencil-and-paper tasks related to linear equations and linear inequalities immediately before and after they participated in 13 lessons on those topics. Students’ written responses, and transcripts of pre- and postteaching inter- views with 18 interviewees (a high-performer, a middle-performer, and a low-per- former, from each of the 6 classes), were analyzed, the aim being to identify changes in student understanding. At the postteaching stage, students improved their perfor- mance and had a better understanding of associated concepts than they had at the preteaching stage. However, many remained confused about the meaning of an in- equality and about what solutions to an inequality represented. Six months later, stu- dents in low- and medium-stream classes performed only slightly better than they had performed at the preteaching stage.