Identifying False Intuitions in Probability and Laying a Foundation for Teaching It

Abstract

Intuition is something we rely on in our daily lives as pure, untaught truths that guide and direct us. Simple statements like “the shortest distance between two points is a straight line” are common and self-explanatory. While this simple statement can be proved mathematically, it is instinctive to easily understand this notion and accept its entrance into one's cognitive intuition. However, there are other parts of mathematics that are not intuitive and require thought and proofs to explain their existence. The question then is: how does the mind distinguish between what is intuitive and what is in need of a solid explanation? Current research studies, on the psychological effects of incorrect intuitions on learning, state that false intuitions can cause misconceptions in every mathematics classroom. In particular, these false intuitions can be a detriment to students in the beginning stages of learning the basics of probability. The purpose of this thesis project is twofold - understand and examine current literature on the different intuitions brought by students into the classroom, and develop and present a curriculum unit plan that can avoid student’s false intuitions with regard to learning about probabilities in mathematics. The literature review section discusses the different ways people perceive the subject of probability while acknowledging its complexity. Discussion highlights different faulty approaches to learning probabilities with regard to heuristic methods – outcome, representative, and personal. Through a thorough examination of both heuristics and maxim beliefs it is noted that common misconceptions and intuitions are learned before students begin their secondary education. It is further suggested that probability and statistics be taught at the elementary level to avoid this trend. The curriculum section includes a unit plan on probability that meets the New York State Standards at the Integrated Algebra level. This incorporates a pre-assessment, daily lesson plan, daily classwork activities, daily formative assessments, and a unit test.