First Year Seminar
Problem Solving Through Recreational Mathematics
Writing Assignments
The writing assignments should be type written, double-spaced, and between 250 and 500 words in length (about 1 to 2 pages). The assignments will be graded according to the rubric that you received on the first day of class.
  1. Writing Assignment #1 Polya considered his four steps to problem solving "just plain common sense...they suggest a certain conduct which comes naturally to any person who is seriously concerned with his problem and has some common sense." (Polya, p. 3) Show how Polya's four steps can be applied in a non-mathematical setting. Consider a scenario where there is some problem to be solved and show how the four steps apply. As an example, you might want to read the story of Aron Ralston who found himself pinned by a boulder while hiking in Utah. Read about the problem he faced and his solution to that problem.
  2. Writing Assignment #2 Polya discusses intuition and formal reasoning (pp. 68-72). Compare "intuitive insight" and "formal proof". How do they differ? How do they work together? Be explicit; use an example or examples from mathematics or otherwise.
  3. Writing Assignment #3 Write a Villanelle, a type of rhymed poem. Having written your poem, write an essay comparing and contrasting writing poetry with solving mathematics problems. How are they similar? How are they different?
  4. Writing Assignment #4 Write an essay comparing and contrasting Problem-Based Learning and Worked-Example Learning. Before you write your essay, read these short articles on Problem-Based Learning and Worked-Example Learning. By now you have experienced both types of learning. What are the strengths and weaknesses of each type? Which type works best for you? Why?
  5. Writing Assignment #5 Analysis and synthesis are two important components of problem solving. Write a short paper briefly describing each of analysis and synthesis. Choose one of the problems that you have worked this semester and show how analysis and synthesis are used in its solution. Before you write your paper, read Polya's account of Pappus' approach to analysis and synthesis (pages 141-148 of Polya) and Gregory McColm's discussion of analysis and synthesis.