id: 06528411
dt: j
an: 2016a.00290
au: Palha, Sonia; Dekker, Rijkje; Gravemeijer, Koeno
ti: The effect of shift-problem lessons in the mathematics classroom.
so: Int. J. Sci. Math. Educ. 13, No. 6, 1589-1623 (2015).
py: 2015
pu: Springer Netherlands, Dordrecht
la: EN
cc: D34 D44 E54 D54 G44 I54
ut: collaborative learning; geometric proof; integral calculus; mathematical
reasoning; mathematical tasks; secondary education; student thinking;
textbook
ci:
li: doi:10.1007/s10763-014-9543-z
ab: Summary: It remains difficult to foster problem-solving and
mathematical-reasoning 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 pseudo-mathematical knowledge.
We called the lessons in this approach ‒ shift-problem lessons ‒
and we investigated the effect of learning arrangements that replace
some of the regular lessons with shift-problem lessons. We conducted
two quasi-experimental studies: one in geometric proof and another in
integral calculus with 16/17-year-old students in pre-university
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 shift-problem lessons, the groups of students’ success in
solving the tasks throughout the course followed different patterns in
the integral calculus and geometric-proof courses. These results and
the implications of the study for mathematics educators and researchers
are discussed.
rv: