Page 16 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 1
Arithmetic fluency contributes to children’s ability to use a variety of cognitive procedures appropriately and efficiently, which is essential for the development of more advanced mathematical problem- solving abilities (Gersten et al., 2005; Träff et al., 2020). Conceptual understanding in combination with the efficient application of strategies and extended practice are needed to speed up the calculation process. Automaticity facilitates working memory and allows children to further develop their mathematical problems-solving ability and acquire new mathematical concepts and skills (Geary, 2004). A lack of arithmetic fluency for basic mathematical facts can clearly hinder children’s progress in mathematical problem-solving (Geary, 2011; Träff et al., 2020).
To solve a mathematical problem, children must be able to read the problem, distinguish relevant from irrelevant information, identify key words, devise a solution plan, determine underlying numerical relationships, select and apply required operations and algorithms, manipulate numbers, and — in doing all of this — call upon a variety of representations (Boonen et al., 2013; Kintsch & Greeno, 1985). Mathematical problem-solving further calls upon a variety of cognitive abilities including updating, inhibition, and shifting with each of these cognitive actions requiring specific conceptual, procedural, and factual knowledge and skills (Baddeley, 2000; Bull & Sherif, 2001; Lester, 2013). Gaining the necessary problem-solving experience is thus crucial for children’s mathematics learning and development (Lester, 2013).
Beliefs and emotions
Children’s mathematical development does not rely on cognitive factors alone but also on math-related and general learning beliefs and emotions (Chinn, 2012; Lebens et al., 2011; Giofrè et al., 2017). Math self-concept, math self-efficacy, and math anxiety have all been shown to relate to mathematical development (Ashcraft & Moore, 2009; Beilock & Maloney, 2015; Lee, 2009; Prast et al., 2018; Usher & Pajares, 2008).
Self-concept and self-efficacy both concern self-perceived competence but are distinguishable. Self-concept encompasses beliefs about one’s competence and thus self-esteem (Bong & Clark, 1999).