
06528411
j
2016a.00290
Palha, Sonia
Dekker, Rijkje
Gravemeijer, Koeno
The effect of shiftproblem lessons in the mathematics classroom.
Int. J. Sci. Math. Educ. 13, No. 6, 15891623 (2015).
2015
Springer Netherlands, Dordrecht
EN
D34
D44
E54
D54
G44
I54
collaborative learning
geometric proof
integral calculus
mathematical reasoning
mathematical tasks
secondary education
student thinking
textbook
doi:10.1007/s107630149543z
Summary: It remains difficult to foster problemsolving and mathematicalreasoning capabilities in classrooms where students and teachers are accustomed to the more traditional forms of education. Several studies suggest that this difficulty might be related to the kind of knowledge students acquire in such environments, which could be fragmented and superficial. In our research, we developed specific tasks that might improve student's learning and consequently the kind of knowledge when used in small group work. The learning process we aimed at in this setting is directed at strengthening, grounding and integrating students' fragmented and pseudomathematical knowledge. We called the lessons in this approach  shiftproblem lessons  and we investigated the effect of learning arrangements that replace some of the regular lessons with shiftproblem lessons. We conducted two quasiexperimental studies: one in geometric proof and another in integral calculus with 16/17yearold students in preuniversity education. Each study involved three experimental classrooms and three comparable classrooms. The results indicate that the learning arrangement seems to have a positive influence on the students' performance as the experimental group outperformed the control group in particular tasks. We also found that, with regard to small group work in the shiftproblem lessons, the groups of students' success in solving the tasks throughout the course followed different patterns in the integral calculus and geometricproof courses. These results and the implications of the study for mathematics educators and researchers are discussed.