A Study on the Responsive Teaching Practices of an Elementary School Teacher Teaching Pattern Generalization

A mathematics teacher needs to understand students’ mathematical thinking and to provide them with appropriate learning opportunities. This study explored how an elementary school teacher taught pattern generalization on the basis of what she identified regarding students’ various mathematical thinking during her lessons. In particular, the teacher’s responsive teaching practices were analyzed in relation to whether or not she had anticipated the student’s specific mathematical thinking before the actual instruction. Regarding a student’s mathematical thinking the teacher had anticipated in advance, she faithfully implemented the core instructional elements to be emphasized to teach pattern generalization. However, regarding a student’s mathematical thinking the teacher had not anticipated, the teacher first checked whether such thinking would be meaningful to teach pattern generalization and then used it in the subsequent classroom activities or improvised her initial teaching plan on spot on the basis of her professional knowledge. Building on these results, this paper discusses the characteristics and implications of responsive teaching practices to teach pattern generalization.