We examined the role of visuo-spatial working memory in different types of arithmetic ability in children. Previous research had suggested that arithmetic is not a single entity (Dowker, 2005, 2015), and also that visuo-spatial working memory is specifically involved in mathematical cognition (McKenzie et al., 2003) There has, however, been little research on the relationships between visuo-spatial working memory and different types of arithmetic. We tested 39 children in Year 2 (6 to 7 years) and Year 4 (8 to 9 years), taking measures of written arithmetic, mental oral arithmetic, and derived fact strategy use (the ability to derive unknown arithmetical facts from known facts, by using arithmetical principles). We also measured visuo-spatial working memory, verbal comprehension, and spelling ability. We investigated the relationships between visuo-spatial working memory and our three arithmetic measures, as well as spelling and verbal comprehension, to test whether these effects were specific to mathematical abilities. We found that visuo-spatial working memory was specifically associated with both verbal oral and mental written arithmetic, and but not with spelling or derived fact strategy use.
How teachers interpret and express fractions critically influences their teaching and their students’ fraction knowledge. Internationally, the mathematics education community has been studying ways to enhance pre-service elementary teachers’ rational number knowledge, particularly fractions. To address the challenge of augmenting pre-service teachers’ fraction knowledge warrants theoretical and empirical revisions to standardized practices for teaching fractions. This study investigates how reexamining fractions from a distinctive measuring perspective influences pre-service teachers’ reasoning about fractions. For four 75-minute sessions, 46 pre-service teachers enrolled in a teacher preparation program at a university in the United States revisited fractions from a measuring perspective. They engaged in tasks that focused on comparing continuous quantities and identifying relative magnitudes. The data for this study comprise their pre- and post-tests that assessed how they identify and represent fractions with discrete and continuous models. For each model, we analyzed participants’ reasoning by attending to their written strategies. Findings revealed three main strategies: partition, construction, and symbolic manipulation. In general, participants expressed more strategies on the post-test for all fraction models. Partitioning was the most frequent strategy on the pre- and post-tests. However, the frequencies of strategies changed after the intervention. For example, with all models, there was an increase in partitioning strategy and a decrease in symbolic manipulation strategy. The results highlight affordances of a measuring perspective to support participants to shift from procedural strategies such as symbolic manipulation to more conceptual strategies to identify and represent fractions.
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