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Www.artofmathematics.org Inquiry-Based Learning in General Education Mathematics Christine von Renesse Julian Fleron Westfield State University.

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1 Inquiry-Based Learning in General Education Mathematics Christine von Renesse Julian Fleron Westfield State University

2 You are a student in our class. Here are your first tasks: Solve the first four puzzles on your handout. Compare your solution with your neighbors. Compare your strategies. Rules for RK Puzzles: Fill in all squares with whole numbers between 1 and 9. The rows, columns and diagonals have to add up to the indicated aggregates.

3 Puzzle 1:

4 Puzzle 2:

5 Puzzle 3:

6 Puzzle 4:

7 Strategies Uniqueness Solvability Whole Group Mathematical Discussion Pedagogy Tasks - Talk in your group about the following prompts: How did it feel to be a student? Do you think a lecture would have been better? Why or why not?

8 Now you are observing us as teachers while you: Solve the next three puzzles on your handout. Compare your solution with your neighbors. Compare your strategies. Rules for RK Puzzles: Fill in all squares with whole numbers between 1 and 9. The rows, columns and diagonals have to add up to the indicated aggregates.

9 Puzzle 7:

10 Puzzle 9:

11 Puzzle 11:

12 1) a + x = 15 so a = 15 - x 2) b + x + 2 = 14 so b = 12 - x 3) 7 + c + a = 27 so c + a = 9 so c + (15 - x) = 9 or c = x - 6 4) 7 = c + d + b = (x - 6) + d + (12 - x) so 7 = 6 + d and d = 1. Algebra Connection:

13 What did we do to facilitate the learning? (or not do?) Why do you think we did that? Pedagogy Tasks - Talk in your group about the following prompts:

14 3-4 students at a table, in assigned groups (name tags, may change day to day) Students work through a series of investigations (some small - some large) from our project Discovering the Art of Mathematics Whole class discussions are used to spread ideas, clear up misconceptions and contradicting ideas. Groups present their ideas during discussions (informal, maybe at board). Different Assessment Strategies, all honoring the process of inquiry, with written solutions and participation making up as much as 75% of the final grade. Elements of Our Inquiry-Based Classroom:

15 What is a CAT scan? How does it work? CAT Scans and Sliceforms

16 Here are examples of sliceforms our students made: TASKS: How are CAT scans and sliceforms related? How are CAT scans and the RK Puzzles related? CAT Scans and Sliceforms

17

18 Discovering the Art of Mathematics Project Julian Fleron, Phil Hotchkiss, Volker Ecke, Christine von Renesse, Westfield State University, Massachusetts This project is based upon work currently supported by the National Science Foundation under NSF (TUES) and previously supported by NSF (CCLI) and a gift from Mr. Harry Lucas.

19 Vision: Mathematics for Liberal Arts students will be actively involved in authentic mathematical experiences that are both challenging and intellectually stimulating, provide meaningful cognitive and metacognitive gains, and, nurture healthy and informed perceptions of mathematics, mathematical ways of thinking, and the ongoing impact of mathematics not only on STEM fields but also on the liberal arts and humanities.

20 Resources/Opportunities 11 free books for MLA: Art & Sculpture, Calculus, Dance, Games & Puzzles, Geometry, Knot Theory, Music, Number Theory, Patterns, The Infinite, Reasoning & Proof Topic Index (other math classes) Individual mentoring or collaboration (stipend) Beta-test/review (stipend) Traveling workshops


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