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Course 4: Experimentation, Conjecture and Reasoning
(Problem Solving for the Middle Level Mathematics Teacher)
Graduate Credit Hours: 3
Usual Delivery Format: Fall semester, distance course with initial 2-day, on-site component
Text: Starbird, M.& Burger, E. The Heart of Mathematics.
Description: This course focuses on problem solving, reasoning and proof and communicating mathematics. It utilizes the extensive resources of the American Mathematics Competition (AMC) to help middle level mathematics teachers develop problem solving skills.
Course Goals: The overall goal for this course is to bring participants to the next level in the development of their mathematical habits of mind: A person who is an effective mathematical thinker has a toolbox of skills and knowledge to experiment, conjecture, reason, and ultimately solve problems. Sound habits of mind are marked by great flexibility of thinking and the strong belief that precise exposition of solutions is important.
Topics: include the Pythagorean Theorem, golden rectangles, Platonic solids, Fibonacci numbers, the Art Gallery Theorem, Symmetry and Shifts, counting, probability and Bayes Theorem.
Instructional Style: The course is divided into four generally independent sessions based on the following topics: geometry, patterns (geometric and numeric), counting and probability, and conditional probability. Within each session are subsections in which (roughly) the following pattern of activities is completed every two to three weeks:
Relevant sections of the text are read to add items to the toolbox of skills and knowledge for reasoning, conjecturing, proving, and solving. The reading also gives precise definitions and algorithms.
A Pre-Test drawn from prior years' AMC contest problems is completed on-line. The Pre-Test is not for grading, but for individually assessing a starting point for skills in solving problems related to the topic.
Assigned problems (including a Habits of Mind problem) are completed and submitted. Emphasis is placed on identifying multiple pathways to and clear explanations of solutions.
A Post-Test, also drawn from prior years' AMC contest problem sets, is completed.
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