Experiencing mathematics through problem solving tasks

Learning through problem solving is an old concept that has been redeveloped as a valuable strategy to teach mathematics. Many teachers feel a tension between the value of teaching through problem solving and the necessity of teaching a prescribed curriculum , often resulting in minimizing the time students spend on genuine problem solving. The purpose of this thesis was to investigate the extent that a mathematics student encounters curriculum while working freely on problem solving tasks. A student in a Pre Calculus and Foundations Math 10 course, which already had a culture of thinking and problem solving, was observed for a 1-month period to see what mathematical content they engaged with through problem solving. Observations, photographs, and notes were taken about the tasks and the mathematics that the student encountered during problem solving each day. The variety of tasks was very broad to prevent students from assuming a problem solving strategy based a current unit of study. Through analysis of the content one student engaged with, it was found that almost the entirety of the Pre Calculus and Foundations 10 prescribed learning outcomes was encountered in addition to both a review of some curricular content from Math 6 through Math 9, as well as exposure to curricular content from Math 11 and 12.