Page 81 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Role of executive functioning in mathematical development
system that supports factual knowledge, procedural knowledge, and conceptual understanding also plays a crucial role in advanced mathematical problem-solving. In light of that hierarchical structure, studies presenting both simple, single-step mathematical problems and more complex, multi-step problems have demonstrated clear associations between arithmetic fluency and mathematical problem- solving (Fuchs et al., 2006; Viterbori et al., 2017; Zheng et al., 2011). In other words, arithmetic fluency or knowing key arithmetic facts accurately and quickly (addition, subtraction, multiplication, division) has been shown to be crucial for more advanced mathematical problem-solving.
Role of executive functioning
Along with domain-specific factual knowledge, procedural skill, and conceptual understanding, domain-general cognitive skills also contribute to mathematics achievement. Many studies involving primary school-aged children have shown consensus on at least three components of executive cognitive functioning that are critical for advanced mathematical problem-solving: updating of information, inhibition of information, and shifting of attention (Bull & Lee, 2014; Miyake et al., 2000).
With regard to the updating of information, a distinction can be made between visuospatial and verbal updating (see also Baddeley, 2000). Visuospatial updating refers to the ability to monitor, manipulate, and retain information presented in a visual form or as objects in space, while verbal updating involves the ability to monitor, manipulate, and retain information presented in a verbal auditory form. Inhibition is the ability to suppress irrelevant information and/or inappropriate responses. Shifting is the capacity for flexible thinking and adeptly switching between alternative tasks or strategies (Miyake et al., 2000).
Executive functioning has been found to be linked to both arithmetic fluency and mathematical problem-solving in several ways. During the mathematical problem-solving process, information must be held in memory, manipulated, and regularly updated (Best & Miller, 2010; Bull & Lee, 2014). A representation of the required problem-solving strategy
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