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:
1. 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.
2. 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.
3. 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.
4. A Post-Test, also drawn from prior years' AMC contest problem sets, is completed.