
06545037
j
2016b.00642
Caglayan, Gunhan
Olive, John
Izs\'ak, Andrew
How middle school students understand polynomial sums and products using algebra tiles model in a ``{\it cours dialogu\'e}".
Rech. Didact. Math. 33, No. 3, 267306 (2013).
2013
La Pens\'ee Sauvage, Grenoble; Association pour la Recherche en Didactique des Math\'ematiques (ARDM), Institut Henri Poincar\'e, Paris
EN
H23
algebra tiles
conceptinaction
models and modeling
multiplicative reasoning
operational invariant
polynomials
{\it cours dialogu\'e}
Summary: This study examines 8thgrade students' understanding and sensemaking of polynomial sums and products modeled with algebra tiles. We base this research within a framework of operational invariants. Our data consist of videotaped classroom lessons and one teacher interview. Ongoing 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 conceptsinaction in the process of representing polynomial sums and products with algebra tiles were available to most students; however, constructing viable theoremsinaction required connections between algebra tile representations and algebraic expressions. Moreover, students who were successful in generating viable theoremsinaction 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.