Bridging Between Mathematics and Education Courses: Strategy Games as Generators of Problem Solving and Proving Tasks

Abstract

Mathematics courses—pure or applied—and education courses, with pedagogical, didactic, and psychological contents are two groups of courses of which programs for training prospective high-school mathematics teachers commonly consist. They often are given in separate departments, with very little, if any, coordination among the instructors. Four independent problem solving centered bridging courses are described. They differ in the context which gives rise to the problems: (1) Mathematics problems that arise in the context of (strategy) games; (2) Mathematics problems that raise cognitive conflicts (paradoxes); (3) Mathematics problems that had a significant impact on the development of mathematics throughout its history; (4) Mathematics problems related to applications of mathematics and mathematical modeling. Ambiguity, contradictions, surprise, and paradoxes are the common thread of all the activities in these courses. This chapter focuses on the details of the first course, illustrating it by two sample tasks: (1) “Who gets first to 100?”, and (2) “Checker Board Jumps”. Emerging problem-solving activities are described and analyzed. The ultimate goal of the four-course series is to provide for a rich context in which prospective teachers can grasp the wide-scope nature of mathematics as a problem-posing/conjecturing and problem-solving/proving discipline, as well as the culture, beauty, and intellectual fulfillment of mathematics, so that they develop an enthusiastic attitude towards communicating these values to high-school students.