Page 37 - 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
Introduction
The main goal of mathematical education today is to develop the knowledge and skills needed for later professional and personal lives (OECD, 2010; Tout & Gal, 2015). Two essential subdomains are arithmetic fluency (i.e., the ability to add, subtract, multiply, and divide fast and accurately) and mathematical problem-solving (i.e., solving problems using mathematical notation, text, and/or pictures) (National Research Council, 2001; Powell et al., 2013). Mathematics is known to be hard for some children due to such factors as low mathematical self- esteem and no appropriate mathematical education (Mazzocco, 2007).
To understand the development of children’s mathematical skill, research has paid more attention to cognitive, information- processing, and neuropsychological factors and less attention to child self-perceptions and beliefs about mathematical skill. However, children’s math self-concept (Bong & Clark, 1999; Timmerman et al., 2017), math self-efficacy (Bandura, 1997; Joët et al., 2011; Pajares & Miller, 1994), and math anxiety (Ashcraft & Moore, 2009; Ramirez et al., 2016) have been shown to significantly correlate with mathematics achievement. In general, better mathematics skill positively correlates with math self-concept and math self-efficacy while poorer mathematical skill negatively correlates with math anxiety. Similarly, children’s mathematical development has been shown to be significantly associated with the observed mathematics teaching behavior of teachers (Muijs & Reynolds, 2000, 2002; Stronge et al., 2011), mathematical knowledge for teaching (Baumert et al., 2010; Hill et al., 2005), and teachers’ mathematics teaching self-efficacy (Klassen et al., 2009; Tella, 2008).
Research has yet to consider the roles of both child and teacher factors together for understanding children’s mathematical development. In addition, arithmetic fluency and mathematical problem-solving are not distinguished clearly in most research despite the involvement of different underlying skills. In the current study, we therefore investigated the influences of two sets of factors on the development of the arithmetic fluency and mathematical problem- solving abilities. We examined, in particular: 1) the math self-concept,
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