This document summarizes a presentation about using classroom response systems, also known as clickers, to improve student conceptual understanding in mathematics courses. The presentation discusses the benefits of clickers for inclusivity, gathering formative assessment data, and increasing student engagement. It provides examples of how clickers can be used for polling, focusing questioning, and motivating group work. A significant portion of the presentation focuses on implementing peer instruction, a pedagogical technique where students teach each other concepts through multiple choice questions designed to address common misconceptions. Attendees worked in groups to design sample peer instruction sessions for calculus topics. The presentation emphasizes that focusing on conceptual learning improves problem-solving skills even if less class time is spent

1. Classroom Response
Systems in Mathematics
Learning 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 be
teaching 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 can
benefit from improved
conceptual understanding
through pedagogies that use
active 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
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11. Why use voting?
6

12. Why use voting?
Inclusivity
6

13. Why use voting?
Inclusivity
Data
http://www.flickr.com/photos/mcclanahoochie/
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14. Why use voting?
Inclusivity
Data
Engagement
http://www.flickr.com/photos/mcclanahoochie/
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15. http://www.flickr.com/photos/unav/
Why use clickers?
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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
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20. Demographics/Information Gathering
On a scale of 1 to 5, rate your familiarity with the Bubble Sort and Insertion
Sort 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, and
203 to help cover the licensing fee for Mathematica. If you were taking one of
these courses, what is the maximum amount of money you’d be willing to pay
for 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, and
203 to help cover the licensing fee for Mathematica. If you were taking one of
these courses, what is the maximum amount of money you’d be willing to pay
for 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 data
Section 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 questioning
11.6: 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
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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
5n
Discuss not only the answer but also the methods used to get it.
n=1
(a) Converges
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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 n
2. 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 n
3. The series
n2 + 1
n=1
(a) Converges
(b) Diverges 14

27. Break into pairs or threes.
Come up with a single clicker question to
measure 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.
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28. 16

29. Peer Instruction
Students teach each
other concepts using
multiple choice
questions designed to
expose common
misconceptions.
Eric Mazur, Harvard University
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30. 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
(a) Converges, and the limit is 1
(b) Converges, and the limit is −1
(c) Converges, and the limit is 0
(d) 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

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)
24
18
(a) Converges, and the limit is 1
14
12
(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
21
18
(a) Converges, and the limit is 1
18
14
12
(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 also
improves 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
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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
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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.?
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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/
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39. Alternatives
iClicker TurningPoint
ResponseWare PollEverywhere
Index cards Little whiteboards
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40. Email: talbertr@gvsu.edu
Blog: http://chronicle.com/
blognetwork/castingoutnines
Twitter: @RobertTalbert
Google+: http://gplus.to/rtalbert
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