Ban Heng Choy

Innovative and Powerful Pedagogical Practices in Mathematics Education

Powerful and innovative pedagogical practices are necessary for all students to learn mathematics successfully and equip them for the future. In this chapter, we review Australasian studies that provide evidence of pedagogical practices that support creative and flexible mathematical thinkers for the 21st century. The review is structured around three key themes that were evident in the research literature. The first theme is the need to develop innovative learning environments that benefit all learners. The second theme is centred on how both tasks and tools can be used to support powerful pedagogical practices. Finally, the third theme reviews the challenges of developing innovative mathematical learning environments. We argue for the need for effective pedagogy for all learners and a need for ambitious, future-focused teaching in mathematics education.

Mathematical Teacher Noticing: The Key to Learning from Lesson Study

Lesson Study has been adapted by many countries in support of teachers’ learning from their practice. However, learning from Lesson Study does not come naturally and it is unclear how teachers can be supported in such learning. Moreover, lesson preparation, a critical component of mathematics teaching, is still largely under-explored in the study of teacher noticing. This chapter presents an analysis of what and how teachers notice when they make instructional decisions during the planning and reviewing stages of Lesson Study. It compares and contrasts two groups of elementary school teachers: one group of pre-service teachers (PSTs) from the United States, and the other group of in-service teachers (ISTs) from Singapore, in terms of what they see and think about their students’ mathematical reasoning during Lesson Study. Using a notion of productive noticing, we provide snapshots of mathematics teacher noticing, which highlights the key role noticing plays in learning from Lesson Study, and offer insights as to how teacher noticing can be supported in the context of lesson planning and reflection.

Mathematics Teacher Noticing: Expanding the Terrains of This Hidden Skill of Teaching

This paper was published in the Proceedings of the 13th International Congress on Mathematical Education held at Hamburg, Germany from 24 - 31 July 2016

The FOCUS Framework: Characterising Productive Noticing During Lesson Planning, Delivery and Review

Enacting the work of diagnostic teaching is challenging and demands that teachers pay attention to mathematical details when designing tasks, orchestrating discussions and reflecting on their lessons. This chapter presents the FOCUS Framework on teacher noticing, which can be used to characterise teachers’ efforts to notice productively during all three phases of diagnostic teaching: lesson planning, delivery and review. Using the two key components of the framework, the focus and its focusing, we provide snapshots of a teacher’s mathematical noticing in each of the phases. The findings from this research suggest that productive noticing in all the three phases is highly consequential, and illustrates how the FOCUS Framework can be used to analyse a teacher’s mathematical noticing.