Page 15 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Arithmetic fluency and mathematical problem-solving can be distinguished but are also related to each other (Fuchs et al., 2008). Children who are not arithmetically fluent can have problems with the retrieval of basic arithmetic facts from long-term memory while trying to solve mathematical problems (Andersson, 2008; Duncan et al., 2007; Fuchs et al., 2016; Geary, 2011; Träff et al., 2020).
Child predictors of mathematical development
The mathematical development of children can be facilitated (and hindered) by general cognitive systems and domain-specific cognitive competencies, on the one hand, and by emotions and beliefs, on the other hand (Chinn, 2012; Fuchs et al., 2016; Lee, 2009). Hierarchical models of the role of cognitive systems in the development of mathematics (Cragg et al., 2017; Geary, 2004; Geary & Hoard, 2005) assume roles for the central executive control system, the visuospatial system, and the auditory-based phonological system (Baddeley, 2000). In addition, math self-efficacy and math self-concept along with math anxiety have been shown to be associated with mathematics achievement (Lee, 2009).
Cognitive predictors
The executive functions of visuospatial and verbal memory updating, inhibition, and shifting are all cognitive skills that are part of the central executive control system and thus provide crucial support for children’s development of the domain-specific mathematical processes (i.e., conceptual understanding, factual knowledge, procedural skill) (Baddeley, 2000; Cragg et al., 2017; Cragg & Gilmore, 2014). Updating is the ability to monitor and manipulate task-relevant information held in mind; inhibition is the ability to suppress irrelevant information and inappropriate responses; and shifting is the capacity for flexible thinking and smoothly switching between tasks and strategies (Miyake et al., 2000). And all of the various executive functions have been shown to contribute to the individual differences observed in children’s mathematical development (Bull & Scerif, 2001; Cragg & Gilmore, 2014).
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General introduction
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