TY - JOUR
TI - How middle school students understand polynomial sums and products using algebra tiles model in a « cours dialogué »
AU - Caglayan, Gunhan
AU - Olive, John
AU - Izsák, Andrew
T2 - Recherches En Didactique Des Mathématiques
AB - This study examines 8th-grade students’ understanding and sensemaking of polynomial sums and products modeled with algebra tiles. We base this research within a framework of operational invariants (Vergnaud 1996). Our data consist of videotaped classroom lessons and one teacher interview. On-going analyses of these data were conducted during the teaching sequence. The dataset was analyzed using constant comparison methodology and analytic induction. Our analysis indicates that students’ (mis)interpretation of the tiles in the process of generating polynomial products was an obstacle to their multiplicative thinking. We found that concepts-in-action in the process of representing polynomial sums and products with algebra tiles were available to most students; however, constructing viable theorems-in-action required connections between algebra tile representations and algebraic expressions. Moreover, students who were successful in generating viable theorems-inaction were the same students who suggested the use of the negative sign combined with the addition operation rather than the subtraction operation, when negative quantities were involved in representing polynomial sums and
products via algebra tiles. We also postulate that the structural aspect of algebra tiles has been the source of many student misconceptions, which could be explained by the effects of the didactical contract between the teacher and her students.
DA - 2013///
PY - 2013
VL - 33
IS - 3
SP - 267
EP - 306
J2 - RDM
LA - EN
SN - 0246–9367
UR - https://revue-rdm.com/2013/how-middle-school-students/
ER -