ABSTRACT
This chapter explores the construction type of exercises in Mathematical Imagining. These imagining tasks guide students through the construction of a mathematical scenario so that learners are then able to answer a mathematical question. Few students have a mental image of an icosahedron because, unlike cubes, which play a starring role in high school math lessons, icosahedra are not as common in core curricula. Learners usually explore icosahedra using a real model (out of wood or wire) or a virtual model on a computer display. Continuous, fluid mental movements such as morphing are not specifically called for in the task, even though students will construct such mental images, and they may even prove to be productive. The intended mental images are all of a visual nature; however, the first contact with the construction material might be accompanied with tactile mental images of moist or cool clay.
