Critical Thinking and Problem Solving in Mathematics

Date of Completion


Document Type

Open Access Capstone

Degree Name

Master of Arts (MA)

First Advisor

Patricia S. Davidson


Alternative courses in mathematics for low-ability students which provide success in the use of critical thinking activities and problem solving strategies are needed. To this end, the author wrote a course called Critical Thinking and Problem Solving for the Boston Public Schools, designed to emphasize real-life application, a multi-sensual approach and problem solving strategies. The goals of this course were to provide successful leaning situations in which students critically examined information for problem solving. In so doing, the students reinforced and expanded their ability to do mathematics. This thesis attempts to demonstrate how critical thinking and problem solving can be infused with meaningful mathematics application. Critical thinking serves as a vehicle for students to connect information within mathematics and to apply it to other subject areas. A selection of problem solving strategies generates a variety of heuristics. Choosing appropriate strategies is important for students to achieve understanding and success within their individual leaning styles. Three unit lessons from the course on Critical Thinking and Problem Solving are discussed in this thesis. These are Comparison and Contrast, Classification, and Finding Reasons and Uncovering Assumptions, skills chosen for their familiarity and widespread use. Each unit begins with a real-life application of a critical thinking skill, followed by applications to language, number theory, and geometry. The author reflects on the development of the course and on its implementation during the first year. Students' reactions and suggestions for future course content are also included. By understanding how to apply critical thinking skills and how to infuse them into mathematics, students can evaluate their reasoning more effectively and approach mathematics more successfully.


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