Challenging Mathematics with Multiple Solution Tasks and Mathematical Investigations in Geometry

In this chapter, I analyze multiple solution tasks (MSTs) and mathematical investigations (MIs) and the interplay between them. I argue that MSTs and MIs are effective instructional tools for balancing the level of mathematical challenge in the mathematics classroom and, thus, for realizing students’ mathematical potential at different levels. Additionally, these tasks lead to the development of mathematical knowledge, mental flexibility, and critical thinking. They also deepen mathematical understanding since they promote the design of mathematical connections of different types. I present several examples of MSTs and MIs and analyze these mathematical tasks from the perspective of their conventionality, the mathematical connections embedded in the tasks, and their potential for developing learners’ mathematical creativity. MIs will be presented in this paper in connection to MSTs. Particular emphasis is placed on analyzing the relationships between production of multiple solutions, mathematical investigations, and varying levels of mathematical challenge.