How to solve mathematical word problems better? : the role of identification of the schema and the semantic role of unknown

Abstract

Schema identification, a process to identify the semantic structure from the problem scenario and applies the corresponding meta-equation, and semantic role of unknown identification, a process to identify the semantic role of the unknown in the word problem, are the two important processes that affect word problem solving performance (Bednarz & Janvier, 1996; Lesh, et al., 1987; Martin & Bassok, 2005; Ng & Lee, 2009). However, previous studies investigated the roles of the two processes in mathematical word problem solving separately. The current study developed an Advanced Word Problem Reasoning task to examine fourth, fifth, and sixth-grade Chinese students' ability and development of schema identification and semantic role of unknown identification within the same study, and their unique contributions to word problem-solving performance. Fourth to sixth graders (n=259) were tested on their ability to identify schema and semantic role of unknown, their mathematical problem solving as well as some potential confounding variables (i.e. non-verbal intelligence and visual-spatial working memory. The ability to identify schema and semantic role of unknown were shown to be significantly predictive of children’s mathematical problem solving even after controlling for the effects of covariates. In addition, there was a differential developmental pattern in the two key processes, which while schema identification was well-established by grade 4, semantic role of unknown identification continued to develop across grade 4 to 6. The current study showed that schema identification and semantic role of unknown identification played unique and crucial roles in students’ word problem solving abilities. It also provided insight into optimizing the timing and emphasis of schema-based instruction.