ABSTRACT
This chapter describes the four different types of Mathematical Imagining tasks, including construction tasks, problem-solving tasks, reasoning tasks and paradox tasks. It discusses the information and comments that accompany the imagining tasks. At minimum, every exercise in Mathematical Imagining seeks to help students engage with and visualize a mathematical topic. To achieve these goals, the task is framed in a context of objects and actions. The chapter explains how the exercise leads to the mathematical idea. All exercises in Mathematical Imagining have been implemented in classrooms numerous times, so teachers should be able to use the instructions with their students as they appear. Depending on what students want to accomplish with them and/or the prior knowledge of their class, they may need to modify the wording to suit their situation. •Many images that students construct during an exercise in Mathematical Imagining hinder the continuation of the imagining process.
