Are representations to be provided or generated in primary mathematics education? Effects on transfer

Abstract

With regard to transfer, is it better to provide pupils with ready-made representations or is it more effective to scaffold pupils' thinking in the process of generating their own representations with the help of peers and under the guidance of a teacher in a process of guided co-construction? The sample comprises 10 classes and 239 Grade 5 primary school students, age 10-11 years. A pretest-posttest control group research design was used. In the experimental condition, pupils were taught to construct representations collaboratively as a tool in the learning of percentages and graphs. Children in the experimental condition outperformed control children on the posttest and transfer test. Both high-and low-achieving pupils profited from the intervention. This study shows that children who learn to design are in a better position to understand pictures, graphs, and models. They are more successful in solving new, complex mathematical problems.Keywords: mathematics education; learning; transfer; collaborative learning; providing versus generating; models; primary school Introduction In most research that focuses on the use of strategies in learning and problem solving, ready-made representations or models provided by the teacher or a textbook are regarded as proper objects of study (Hattie, Biggs, & Purdie, 1996). Research findings support the idea that representations are important for the learning of science and mathematics (Ainsworth, 2006;Gilbert & Boulter, 2000;Greer, 1997;Lehtinen & Hannula, 2006;Mayer, 1989;Perkins & Unger, 1999). Moreover, learning to design representations can be expected to promote problem solving in relation to both familiar and new problems. When students are actively involved in the construction and collaborative evaluation of representations, they develop mathematical knowledge that enables them to generate new solution processes. This article reports on a research project aimed at describing and analyzing the effects of an experimental mathematics program that focuses on the construction and use of student representations in primary mathematics education.

Emergent mathematical thinking in the context of play

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Young Children’s Representations of Addition in Problem Solving

“…When students generate representation/representations themselves, they are focused on the structure of the problems as they constructed representations, which promotes the students' use of metacognitive skills, thus contributed to understanding that later supported the solution performance (Manches & O'Malley, 2016;Terwel, van Oers, van Dijk, & van den Eeden, 2009). As previous researchers highlighted, although multiple representations facilitated problem solving (Elia et al, 2007), students still struggle in utilizing it (Yang & Huang, 2004), thus they tend to utilize only a single form of representation (Beyranevand, 2010).…”