Page 84 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 3
al., 2007). The mixed findings with regard to particularly the roles of inhibition and shifting in arithmetic fluency may be due to the increasingly quick and easy retrieval of stored arithmetic facts from long-term memory, making inhibition less needed and facilitating the shifting required for more complex mathematical problem-solving (Bull et al., 1999; Bull & Scerif, 2001; Cragg et al., 2017).
Executive functioning in relation to mathematical problem-solving
Mathematical problem-solving requires the following skills, among others: identification of relevant information and key words after the reading of a problem and selection and application of most suitable strategies, operations, and algorithms across multiple contexts (Boonen et al., 2013; Fuchs et al., 2008; Verschaffel et al., 2020). School textbooks typically have children solve mathematical problems involving real world contexts depicted using mathematical notation, text, and/or pictorial representations (Verschaffel et al., 2020). Visuospatial and verbal updating have indeed been found to help children integrate the information identified as relevant to thereby solve advanced mathematical problems requiring multiple steps (Cragg et al., 2017). Inhibition and shifting may also be required when learning new concepts and mastering the procedures needed for new domains of mathematics and for solving more complex mathematical problems as is the case in grade 4. To prevent irrelevant information from interfering with a new and otherwise unfamiliar problem-solving process, for example, inhibition is needed. In addition, children must be able to readily shift between various procedures for more advanced mathematical problem-solving, such as applying conceptual knowledge of fractions and factual knowledge of addition and multiplication when solving a multi-step problem (Lee et al., 2009).
The roles of visuospatial and verbal updating in mathematical problem-solving appear to be most consistent. Studies consistently report significant associations of visuospatial and verbal updating with not only simple, single-step mathematical problem-solving (Swanson, 2011; Swanson & Beebe-Frankenberger, 2004; Swanson et al., 2008; Zheng et al., 2011) but also more complex, multi-step mathematical problem-solving (Agostino et al., 2010; Cragg et al., 2017; Fuchs et al.,