Page 68 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 2
Implications for practice
The present results have shed light on the roles of various child and teacher factors in the mathematical development of fourth grade children. The findings have some clear implications for the practice of mathematics education.
First, prior mathematics achievement was shown to contribute to both arithmetic fluency and mathematical problem-solving, which is in line with the findings of previous studies (Fuchs et al., 2006; Watts et al., 2014). Teachers should more clearly recognize the crucial role that they play in establishing a solid mathematics base for elementary school children to build their further learning on. Teachers should be given a better understanding of exactly which aspects of their teaching are most effective for achieving given math learning goals and thereby making more informed decisions for the achievement of these learning goals (Hiebert & Grouws, 2007). A solid mathematics foundation in the lower elementary school grades or, in other words, early proficiency with numbers and numerical operations is a prerequisite for supplementing, refining, and deepening children’s mathematical knowledge, skill, and understanding (Byrnes & Wasik, 2009; Duncan et al., 2007).
Second, it is important to stimulate children’s learning of new math concepts, the expansion of their mathematical knowledge, and the mastery of more advanced mathematics skills on the basis of prior learning and ability (National Research Council, 2001). Unfortunately, the best means to achieve these objectives are not completely clear. In any case, the results of the present study suggest that teachers must have not only sufficient mathematical knowledge but also sufficient pedagogical knowledge and mathematics teaching self-efficacy to do this.
In addition, teachers should be encouraged as part of their professional development to attend more to the self-concepts of their children in general and their math self-concepts in particular. Once formed, negative self-perceptions can be very persistent (Swann, 2012). A clear association between children’s math self-concept and arithmetic fluency was found in the present study, showing that it is crucial to