Page 182 - Children’s mathematical development and learning needs in perspective of teachers’ use of dynamic math interviews

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Chapter 6
not specified (Rockoff, 2004; Seidel & Schavelson, 2007). The results of the present research (Chapter 4) showed the professional development program and practice with dynamic math interviewing to improve the more advanced aspects of teaching behavior (i.e., use of activating learning, differentiation and adaptation of lessons, explicit teaching of learning strategies and math-specific strategies); only the less complex teaching behaviors did not improve (e.g., safe and stimulating learning climate, efficient classroom management). The teacher-child dialogue conducted as part of the dynamic math interviews and information obtained in these interviews presumably increased teachers’ awareness of the individual child’s math learning needs. In this connection, Stipek et al. (2001) found that teachers who focus largely on product (i.e., correct responding), achievement, and speed of problem- solving during mathematics lessons, teach in a largely prescriptive manner and follow textbooks quite strictly. In contrast, teachers who focus on the underlying understanding of children, their ability to make sense of mathematics, and their adoption of appropriate actions tend to carefully listen, observe, analyze errors, draw connections between ideas and concepts, and ask the right questions — the teachers show, in other words, more complex teaching behavior (Lester, 2013).
The mathematical knowledge for teaching of the teachers in the present research played a predictive role in the development of the children’s mathematical problem-solving but not their arithmetic fluency during grade 4 (Chapter 2). In other research, Campbell et al. (2014) similarly found that teachers’ perceived mathematical knowledge and their awareness of children’s learning needs predicted the mathematics achievement of their students. For the teaching of mathematical problem-solving, Ball et al. (2008) have emphasized the importance of teachers’ mathematical knowledge and knowing how to apply this effectively during daily teaching practice. For grade 4 mathematics instruction, Muijs and Reynolds (2002) indeed found teachers to perceive themselves as having more content knowledge and the necessary teaching skills for early mathematics education than for later instruction (e.g., fractions and proportions). The instrument used in the research reported on here (see Appendix B) asked teachers to rate their pedagogical content knowledge, subject matter knowledge, and