Visual manipulatives for proportional reasoning

The use of a visual representation in learning about proportional relations studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability sixth-grade mathematics students using the Jasper Adventure Series of problems. The first research question was whether the provided visual representation would influence student understanding of proportion. Students spontaneously transferred an extrapolation strategy to a second problem domain, suggesting that instruction facilitated a recognition of the structural equivalence in the two domains. The second question was whether the visual representation would interact differently with student reasoning on the part/whole and rate problems. Students were more successful using the representation presented during rate instruction on part/whole problems than vice versa. Differences in student reasoning tentatively suggest a sequence of instruction in which visually-mediated instruction with rate problems precedes that of part-whole problems. Three figures present study findinz,s. (Contains 8 references.) (SLD) *********************************************************************** * Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** Paper presente,, at the Annual Meeting of the American Educational Research Association, New Orleans, LA, April, 1994. U.S. DEPARTMENT OF EDUCATION ("dice OI Educat...inl Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) This document has been reproduced as recemd from the person or organtzabon Onginahng d 0 Miner changes have been made to improve reproduction quality Pomts of new or opinions stated in this doc meet do not necessarily represent olitcal OEM position or policy 1. Objectives The current experiment investigates the use of a visual representation in learning about proportional relations. In particular, we examine student understanding of two kinds of invariance that play a role in proportional reasoning: (1) the invariance of a multiplicative relation on both sides of a proportion equation; and (2) the invariance of the structural relations that exist in different semantic types of proportion problems. The goal of our work is the design of learning environments that facilitate a move from implicit to a more explicit understanding of proportionality. Visual manipulatives for proportional reasoning Joyce L. Moore and Daniel L. Schwartz Vanderbilt University "PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY