What is the unknown? The ability to identify the semantic role of the unknown from word problems longitudinally predicts mathematical problem solving performance

The current study aimed to investigate children's difficulties in word problem solving through assessing their ability to mathematize, or to identify the semantic role of the unknown from word problems. Fifth graders (n = 213) were given an advanced word problem reasoning task in which they had to match word problems with schematic diagrams that depict different processes (multiplication versus division) and the unknown being in different semantic roles (e.g., unit size, number of units, or total in an equal group problem). They were also tested on their mathematical problem solving as well as some potential confounding variables (i.e., intelligence and working memory) and mediators. The ability to identify the semantic role of the unknown was shown to be longitudinally predictive of children's mathematical problem solving performance even after controlling for the effects of covariates and autoregressor. Such a relation was partially mediated by children's ability to convert word problems into the correct number sentences/equations. The findings not only highlight the importance of unknown identification in mathematical problem solving process, but also provide a practical tool to assess such an ability.