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(These are slides from a session given at Math in Action 2012 on the campus of Grand Valley State University, Allendale, MI on February 25, 2012.)

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- 1. Classroom Response Systems in MathematicsLearning Math Better Through Voting Robert Talbert, GVSU / Feb 25, 2012 1
- 2. Robert Talbert, Ph.D.Associate Professor of Mathematics Grand Valley State University 2
- 3. Think of ONE CLASS you are teaching right now, or will beteaching soon, in which your students would beneﬁt from an increased focus on conceptual understanding. What class are you thinking of? (A) Pre-algebra (B) Algebra I (C) Algebra II (D) Geometry (E) Trigonometry (F) Calculus (G) Statistics (H) Other (specify) 3
- 4. Learners in every class canbenefit from improvedconceptual understandingthrough pedagogies that useactive student choice. 4
- 5. Agenda 5
- 6. Agenda✤ Good reasons for using clickers 5
- 7. Agenda✤ Good reasons for using clickers✤ Simple ways to use clickers and voting 5
- 8. Agenda✤ Good reasons for using clickers✤ Simple ways to use clickers and voting✤ Peer instruction design activity 5
- 9. Agenda✤ Good reasons for using clickers✤ Simple ways to use clickers and voting✤ Peer instruction design activity✤ ≥ 5min at the end for technology issues. 5
- 10. Agenda✤ Good reasons for using clickers✤ Simple ways to use clickers and voting✤ Peer instruction design activity✤ ≥ 5min at the end for technology issues.✤ QUESTIONS welcome throughout 5
- 11. Why use voting? 6
- 12. Why use voting? Inclusivity 6
- 13. Why use voting? Inclusivity Data http://www.ﬂickr.com/photos/mcclanahoochie/ 6
- 14. Why use voting? Inclusivity Data Engagement http://www.ﬂickr.com/photos/mcclanahoochie/ 6
- 15. http://www.ﬂickr.com/photos/unav/ Why use clickers?7
- 16. http://www.ﬂickr.com/photos/unav/ Simplicity Why use clickers?7
- 17. Why use clickers? http://www.ﬂickr.com/photos/unav/ Simplicity Ease of use 7
- 18. Why use clickers? http://www.ﬂickr.com/photos/unav/ Simplicity Ease of use Anonymity 7
- 19. Ways to use clickers 8
- 20. Demographics/Information GatheringOn a scale of 1 to 5, rate your familiarity with the Bubble Sort and InsertionSort algorithms.(a) 1 (= Never heard of these)(b) 2(c) 3(d) 4(e) 5 (= Very familiar with these) What could you do with this information? Why might this be better than a show of hands? 9
- 21. Polling (not related to course material)The Math Department is considering adding a course fee to MTH 201, 202, and203 to help cover the licensing fee for Mathematica. If you were taking one ofthese courses, what is the maximum amount of money you’d be willing to payfor this fee?(a) $0 (= I don’t want a fee)(b) $5(c) $10(d) $25(e) $50 10
- 22. Polling (not related to course material)The Math Department is considering adding a course fee to MTH 201, 202, and203 to help cover the licensing fee for Mathematica. If you were taking one ofthese courses, what is the maximum amount of money you’d be willing to payfor this fee?(a) $0 (= I don’t want a fee)(b) $5 6(c) $10 6 6 5(d) $25 4 4(e) $50 3 2 0 $0 $5 $10 $20 $50 10
- 23. (c) Must diverge Gathering basic formative assessment dataSection 9.2 1. Which of the following is/are geometric series? 1 1 1 (a) 1 + 2 + 4 + 8 + ··· 4 8 16 (b) 2 − 3 + 9 − 27 + · · · (c) 3 + 6 + 12 + 24 + · · · 1 1 1 (d) 1 + 2 + 3 + 4 + ··· (e) (a) and (b) only (f) (a),(b), and (c) only (g) All of the above 8 16 32 2. −6 + 4 − + − = 3 9 27 266 (a) − 81 11
- 24. Focus questioning11.6: Directional Derivatives and the Gradient Vector 4 6 8 10 12 14 2.4 2 2.2 15 2.0 13 11 9 1.8 7 5 3 1.6 2 0 2 1 1 1 0.0 0.5 1.0 1.5 2.0 1. Consider the contour map of the function z = f (x, y) above. Which of the following has the greatest value? (a) fx (1, 2) (b) fy (1, 2) (c) The rate of ascent if we started at (1, 2) and traveled northeast (d) The rate of ascent if we started at (1, 2) and traveled west 12
- 25. Motivator/discussion catalyst for group work ∞ 1 5. The series nen n=1 (a) Converges (b) Diverges ∞ (n − 1)! Put students into working groups to ﬁnd the answer. 6. The series 5nDiscuss not only the answer but also the methods used to get it. n=1 (a) Converges 13
- 26. 1. If an bn for all n and bn converges, then (a) an converges (b) an diverges “Best answer” questions (c) Not enough information to determine convergence or divergence of an ∞ ln n2. The best way to test the series for convergence or divergence is n n=1 (a) Looking at the sequence of partial sums (b) Using rules for geometric series (c) The Integral Test (d) Using rules for p-series (e) The Comparison Test (f) The Limit Comparison Test ∞ cos2 n3. The series n2 + 1 n=1 (a) Converges (b) Diverges 14
- 27. Break into pairs or threes. Come up with a single clicker question tomeasure something of interest in the class you identiﬁed at the beginning of the talk.Write it on the paper provided and we’ll share on the document camera. 15
- 28. 16
- 29. Peer Instruction Students teach each other concepts using multiple choice questions designed to expose common misconceptions.Eric Mazur, Harvard University 17
- 30. 5n + 11. The sequence sn = n (a) Converges, and the limit is 1 (b) Converges, and the limit is 5 (c) Converges, and the limit is 6 (d) Diverges2. The sequence sn = (−1)n (a) Converges, and the limit is 1 (b) Converges, and the limit is −1 (c) Converges, and the limit is 0 (d) Diverges3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · · Data from MTH 202, Sec 03, Fall 2011 at GVSU (a) Converges 18
- 31. 5n + 1 1. The sequence sn = n (a) Converges, and the limit is 1 (b) Converges, and the limit is 5 (c) Converges, and the limit is 6 (d) Diverges 2. The sequence sn = (−1)n FIRST VOTE (after 1min individual reflection)2418 (a) Converges, and the limit is 1 1412 (b) Converges, and the limit is −1 6 (c) Converges, and the limit is 0 6 2 2 0 (d) Diverges Converges to 1 Converges to 5 Converges to 6 Diverges 3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · · Data from MTH 202, Sec 03, Fall 2011 at GVSU (a) Converges 18
- 32. 5n + 1 1. The sequence sn = n (a) Converges, and the limit is 1 (b) Converges, and the limit is 5 (c) Converges, and the limit is 6 (d) Diverges 2. The sequence sn = (−1)n VOTE (after 2min peer instruction) SECOND FIRST VOTE (after 1min individual reflection)24 24 2118 (a) Converges, and the limit is 1 18 1412 (b) Converges, and the limit is −1 12 6 (c) Converges, and6 the limit is 0 6 2 2 2 1 0 (d) Diverges 0 0 Converges to 1 Converges to 5 Converges to 6 Diverges Converges to 1 Converges to 5 Converges to 6 Diverges 3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · · Data from MTH 202, Sec 03, Fall 2011 at GVSU (a) Converges 18
- 33. Peer instruction leads to signiﬁcant gains in student learning on essential conceptual knowledge E. Mazur, Peer Instruction: A User’s Manual 19
- 34. But: Focusing on conceptual learning alsoimproves problem-solving skill even though less time in class is spent on examples! E. Mazur, Peer Instruction: A User’s Manual 20
- 35. Let’s design a Peer Instruction-oriented Calculus class session. Which topic would you like? (A) The deﬁnition of the derivative (B) The Product and Quotient Rules (C) Optimization problems (D) The deﬁnition of the deﬁnite integral 21
- 36. Working in pairs or threes:What are the 3--4 most fundamental points from our topic? (If students can’t demonstrate understanding of ______, then they can’t master the topic.) Make a brief outline for a 5-8 minute minilecture around each fundamental point. THEN: Write a ConcepTest question for each point. Focus on a single concept Not solvable by relying on equations Adequate number of multiple-choice answers Unambiguously worded Neither too easy nor too difﬁcult 22
- 37. DEBRIEF What’s good? What are the challenges?How does this compare to the way you or a colleague teach this material now?What are the potential costs/beneﬁts for students, teachers, schools, administrators, etc.? 23
- 38. Standard GVSU clicker setup TurningPoint TurningPoint Anywhere ResponseCard RF LCD software (free download)(≈ $30 at GVSU bookstore; http://www.turningtechnologies.com/ receiver ≈ $100) responsesystemsupport/downloads/ 24
- 39. AlternativesiClicker TurningPoint ResponseWare PollEverywhere Index cards Little whiteboards 25
- 40. Email: talbertr@gvsu.edu Blog: http://chronicle.com/ blognetwork/castingoutnines Twitter: @RobertTalbertGoogle+: http://gplus.to/rtalbert 26

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