Page 39 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

Impact of child and teacher factors on mathematical development
pictures. Mathematical problem-solving is taught in mainly the upper grades of elementary school. From about fourth grade (children aged 8-10 years), the focus of mathematical education shifts to advanced mathematics (e.g., fractions, proportions) and the abstractness and complexity of mathematical tasks increases. Mathematical problem- solving requires children to be able to read the problem, distinguish relevant from irrelevant information, identify key words, derive underlying numerical relationships, select and apply required operations and algorithms, and manipulate numbers procedurally (Fuchs et al., 2008; Goldin, 1998; Kintsch & Greeno, 1985). The brain’s central executive system of working memory plays an important role in the integration of information for the solution of mathematical problems and has thus been found to be an important predictor of developing mathematical problem-solving ability (Swanson & Beebe- Frankenberger, 2004).
Several longitudinal studies have shown strong associations between early and later mathematics achievement (Byrnes & Wasik, 2009; Duncan et al., 2007; Watts et al., 2014). And the developments of both arithmetic fluency and mathematical problem-solving have been shown to be highly stable with early mathematical skill critical for the development of later mathematical skill (Fuchs et al., 2006; Watts et al., 2014).
There is nevertheless evidence that additional child and teacher factors are crucial for the development of mathematical skill.
Roles of children’s math self-concept, math self-efficacy, and math anxiety
As already mentioned, children’s mathematical development depends on several factors with cognitive factors receiving the most attention in previous research. Mathematical development has also been shown to relate to children’s mathematical self-beliefs (Bandura, 1997; Pajares & Miller, 1994). In the first years of elementary school, children have positive and even at times unrealistic perceptions of their abilities. These early self-beliefs are relatively unstable (Wigfield & Eccles, 2000). By the age of seven/eight years, children have become more
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