Learning Opportunities to Promote Conceptual Understanding in Singapore Secondary School Mathematics Instruction

Abstract

AbstractIn the teaching of mathematics, experienced and competent teachers in Singapore secondary schools go beyond merely teaching facts, skills and conceptual structures. They use a repertoire of teaching approaches. Instructional activities in their lessons show a very systematic choice of variation and clear focus of teaching a specific concept. As teaching plays a major role in shaping students’ learning opportunities, the opportunity for students to engage in constructing concepts depends largely on the nature of interaction generated by the teacher’s pedagogical moves. This chapter discusses learning opportunities enacted by two experienced and competent teachers when they introduce concepts to students or engage students in constructing concepts in well-structured lessons. Distilling the learning opportunities requires a careful analysis of the classroom events that are instructionally guiding students’ learning of mathematical concepts. Specifically representations and attending explicitly to concepts can facilitate conceptual learning among learners. In this chapter drawing on three excerpts of classroom instructions we discuss how two experienced and competent mathematics teachers create learning opportunities when they introduce concepts to students or engage students in constructing concepts. The teachers used their planned frames and enacted teacher-directed lessons that engaged students in making sense of concepts. Though the lessons were teacher-directed, the student–teacher classroom discourse was integral for the creation of knowledge by the students.KeywordsLearning opportunitiesExperienced and competent mathematics teachersMathematical conceptsClassroom instructions