Integrating undergraduate mathematics concepts into secondary mathematics lessons to promote advanced mathematical thinking

Research has documented that there are many ways to support students’ conceptual learning of mathematics. As Peter Liljedahl described in his book, Building Thinking Classrooms, mathematical learning is achieved by creating a “thinking classroom.” The process by which a thinking classroom is established is based on years of research by Liljedahl and his colleagues. These scholars have identified the characteristics of the optimal environment to promote students’ mathematical learning. One of these characteristics is the availability of high quality instructional and curricular resources. Currently there is a deficit of such resources in secondary mathematics classrooms. The central focus of this thesis is to address this need by presenting a series of mathematical tasks designed to engage secondary students in advanced mathematical thinking. For each task I (1) discuss the principles that informed its design, (2) present the task and its solution, (3) describe my expectations for how the task might support students’ learning, and (4) reflect on my implementation of the task in a classroom setting if applicable.