Scaling up of Continual Professional Development for Mathematics Problem Solving in Singapore Schools     

Leong  Yew Hoong  Toh  Tin Lam  Tay  Eng Guan  Quek  Khiok Seng  Toh  Pee Choon  Jaguthsing  Dindyal 《International Journal of Science and Mathematics Education》2021,19(6):1291-1310

The more ambitious an educational innovation, the greater the challenge in scaling up. In this paper, we focus on the scaling up of an ambitious pedagogical practice—mathematics problem solving as a regular feature in the classroom. We adopt a long-term approach to continual professional development (CPD) that began with intensive work with one school before we broadened the programme to four other schools which span the spectrum of schools in Singapore. To evaluate this overall design, we examine the current state of each school’s capacity in sustaining mathematics problem-solving instruction. In particular, we study and report findings on these areas: the readiness of teachers, the instructional materials and supporting structures. Based on the findings, we reflect on our CPD strategies and our theory of action which guided the CPD programme.

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The Interplay of Teacher and Student Actions in the Teaching and Learning of Geometric Proof     

Tami S. Martin  Sharon M. Soucy McCrone  Michelle L. Wallace Bower  Jaguthsing Dindyal 《Educational Studies in Mathematics》2005,60(1):95-124

Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify factors that may be related to the development of proof understanding. In this paper, we identify and interpret students' actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures, justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on the students, analyze student arguments, and coach students as they reason, creates an environment in which participating students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively participate in the classroom discourse are supported as they engage in proof development activities. By examining connections between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students' understanding of proof.  相似文献