id: 06545037
dt: j
an: 2016b.00642
au: Caglayan, Gunhan; Olive, John; Izsák, Andrew
ti: How middle school students understand polynomial sums and products using
algebra tiles model in a “{\it cours dialogué}".
so: Rech. Didact. Math. 33, No. 3, 267-306 (2013).
py: 2013
pu: La Pensée Sauvage, Grenoble; Association pour la Recherche en Didactique
des Mathématiques (ARDM), Institut Henri Poincaré, Paris
la: EN
cc: H23
ut: algebra tiles; concept-in-action; models and modeling; multiplicative
reasoning; operational invariant; polynomials; {\it cours dialogué}
ci:
li:
ab: Summary: This study examines 8th-grade students’ understanding and
sense-making 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. 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-in-action 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.
rv: