Page 66 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 2
with the development of their arithmetic fluency. These results suggest that the mathematics teaching self-efficacy of teachers may depend on the subdomain of mathematics in question and whether, for example, they are being asked to stimulate arithmetic fluency or more abstract mathematical problem-solving. Teachers may not recognize the complexity of mathematical problem-solving for children and what the teaching of this requires. It is apparently difficult for teachers to identify what is necessary and apply this in more advanced mathematics teaching situations.
According to Hiebert and Grouws (2007), a number of factors can hinder the development of effective mathematics teaching behavior, such as a lack of not only subject matter knowledge but also the necessary pedagogical knowledge to teach mathematics flexibly, and the absence of a useful knowledge base for teachers to improve their mathematics teaching practices.
The Dunning-Kruger effect (Kruger & Dunning, 1999) might also be at play: less competent teachers fail to recognize their incompetency in teaching mathematical problem-solving. Self-assessment of mathematics teaching self-efficacy by particularly teachers with a lower level of mathematics teaching competence can actually lead to overestimation of their capacity to promote the development of mathematical problem-solving on the part of children.
In the models in which we combined child and teacher factors with control for the possible influences of teacher/class on mathematical development, the results resembled those for the models in which child-related factors and teacher-related factors were distinguished.
Study strengths, limitations, and directions for further research
The present study involved a large sample of more than 500 children but a relatively small sample of 31 teachers. Caution is thus warranted when generalizing the results to other teachers.
First, we measured math self-concept, math-self-efficacy, and math anxiety in the manner used by others, namely by administration of a written self-perception questionnaire (e.g., Joët et al., 2011; McWilliams et al., 2013; Pajares & Kranzler, 1995; Ramirez et al., 2016). It is nevertheless possible that some of the fourth grade children had