Page 100 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 3
increased (e.g., mastery of basic arithmetic in grade 4; Balhinez & Shaul, 2019; Fuchs et al., 2006). In the present study, we nevertheless expected both visuospatial and verbal updating to continue to play both direct and indirect roles in the changes/development of children’s mathematical problem-solving during grade 4, which did not prove to be the case. The finding of significant roles for inhibition and shifting + inhibition was unexpected. The children in our study had to solve increasingly more advanced, multi-step mathematical fact and word problems, with/ without pictures, requiring a variety of calculations within a single problem. To solve such multiple step problems, inhibition and shifting may be more critical than visuospatial and verbal updating (Bull & Scerif, 2001; Cantin et al., 2016; Verschaffel et al., 2020). For example, when children confront a new domain of mathematics entailing increasingly complex and abstract mathematical problems, inhibition may be increasingly needed to suppress irrelevant information (e.g., irrelevant textual information) and prior learning experiences (e.g., ignoring a counting on strategy when applying a multiplication strategy is more appropriate). In addition, shifting is increasingly needed to switch between procedures (e.g., going from addition to multiplication, shift to another strategy; Wiley & Jarosz, 2012). At this point in the child’s learning then, visuospatial and verbal updating may still be important but not as important as when the child is less arithmetically fluent. In other words, the roles of inhibition and shifting in mathematical problem-solving may increase in grade 4 but remain indirect as they still depend on arithmetic fluency (Cragg et al., 2017). As children learn to solve a wider variety of mathematical problems in grade 4, greater flexibility in the determination of solution strategies and conduct of calculations is needed (Fuchs et al., 2006; 2016; Geary, 2011; Wiley & Jarosz, 2012). The executive function of inhibition and/ or shifting comes to play an increasingly important role in children’s mathematical problem-solving as found in the present study.
Finally, the results of the present study indicate that while the level of mathematical problem-solving at the start of grade 4 is predictive for the development of mathematical problem-solving ability (and therefore used as a control variable in some of our analyses), the level of arithmetic fluency is equally important and continues to be