Teaching geometry through problems: opportunities and challenges -

Abstract

Early secondary (12 to 15 years) and higher secondary (16 to 18 years)

What are the opportunities and challenges of teaching geometry through problems? In this workshop, I will share some lessons that demonstrate what teaching geometry through problems means and how they can increase students’ participation in classroom discussions. These lessons have been developed by geometry teachers collaborating in a process we call StoryCircles where teachers learn from each other as they prototype lessons using storyboards with cartoon characters and receive feedback from colleagues.

The workshop will characterise problem-based instruction and identify difficulties teachers face when infusing classroom discussion into problem-based lessons. We will then consider possible ways of promoting classroom discussion through different ways of eliciting students’ work and responding to it by highlighting aspects of the work that contribute to the goal of the lesson. We’ll look at how teachers from the US and other countries have collaborated to build prototypes of these lessons and discuss possible applications in the Aotearoa New Zealand context. I will then share some specific contributions from our research that support the development of problem-based, discussion-intensive lessons. These include categories of perception that teachers can use to notice what students bring to the discussion and responding moves that teachers can use to weave those contributions into a classroom dialogue.