Choy, Ban Heng

Orchestrating productive mathematics discussions by building on students’ ideas is challenging. Although certain talk moves involving eliciting student responses are associated with this high-leverage practice, they may not be sufficient for enhancing student reasoning. Telling, on the other hand, may play an important role despite the perception they are contradictory to a more interactive stance in teaching. In this paper, we examined how an elementary school teacher orchestrated a productive whole-class discussion through the skillful interweaving of talk moves and telling.

Every student has different learning needs and teachers cannot simply disregard these differences during teaching. Instead, teachers are expected to pay attention to these differences and adapt their instruction accordingly. This places a lot of demand on teachers and is challenging in the context of a heterogeneous classroom. The key question is: how can teachers plan and adapt their instructional approaches in response to the rich diversity of student profiles? Differentiated Instruction (DI) may offer teachers a means to think about classrooms in ways that honor students’ differences and maximizes students’ learning capacities. In this chapter, we first explore the notion of differentiated instruction and present the key principles of differentiated instruction. We then describe how differentiated instruction has been carried out in our classrooms, and suggest how teachers can begin to think of heterogeneous classrooms as opportunities to hone their teaching craft and pedagogical reasoning.

This article provides a concrete illustration of how teachers in a primary school in Singapore discuss students’ learning in a lesson study cycle and grew professionally as a community. Specifically, we examined how collaboratively analysing students’ work serves as a useful practice for teachers to learn to work with diverse learners.. The findings suggested that open discussions around students’ work helped teachers to reflect upon their unwarranted perceptions of their students and their teaching. The study provided insights into how teachers’ understandings of their students’ diverse backgrounds, as well as teachers’ understanding of subject content and pedagogy, developed as they participated in lesson study activities that were focused on analysing students’ work. Our findings found that lesson study provided the following affordances to foster such changes: (1) eliciting hypotheses in dialogue; (2) creating space for alternative perspectives; (3) collaboratively scrutinizing student learning evidence for follow-up teaching; and (4) identifying problems for further discussion. While the illustration of this case is uniquely Singaporean, implications include concerns about teacher professional learning and teaching for equity common to many other educational contexts.

Typical mathematics problems, such as examination-type questions, are often used in classrooms to develop students' procedural fluency. In this article, we describe and analyse what a secondary school mathematics teacher noticed about the affordances of such a problem, as well as how she orchestrated a mathematically productive discussion using the adapted problem in class. The findings suggest that a teacher's productive noticing of the affordances offered by typical problems can enhance the learning experiences of mathematics students.

Excellence in mathematics education is often linked with high performance in international achievement tests such as TIMSS. In this short paper, I broaden the notion of excellence by considering how the different aspects of mathematics education come together instead of only focusing on what these aspects are. Using confluence as a metaphor to describe excellence, I examine Singapore’s excellence in mathematics education by showing how the “big things” of education such as societal expectations, policy formulation and implementation, and how the “small things” of classroom practices—scheme of work, tasks (especially typical problems), and examinations—flow together towards the same vision of ambitious teaching articulated by the Singapore Mathematics Curriculum Framework.