Classroom response systems in mathematics: Learning math better through voting

Classroom Response Systems in Mathematics

Learning Math Better Through Voting

Robert Talbert, GVSU / Feb 25, 20121

Robert Talbert, Ph.D.Associate Professor of Mathematics

Grand Valley State University

2

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

Learners in every class can benefit from improved conceptual understanding through pedagogies that use active student choice.

4

Agenda

5

Agenda

✤ Good reasons for using clickers

5

Agenda


✤ Simple ways to use clickers and voting

5

Agenda



✤ Peer instruction design activity

5

Agenda




✤ ≥ 5min at the end for technology issues.

5

Agenda




✤ ≥ 5min at the end for technology issues.

✤ QUESTIONS welcome throughout

5

Why use voting?

6

Why use voting?

Inclusivity

6

Why use voting?

Inclusivity

Data

http://www.flickr.com/photos/mcclanahoochie/

6



Why use voting?

Inclusivity

Data


Engagement

6



Why use clickers? ht

tp:/

/ww

w.fl

ickr

.com

/pho

tos/

unav

/

7

http://www.flickr.com/photos/unav/


Why use clickers?

Simplicity

http

://w

ww

.flic

kr.co

m/p

hoto

s/un

av/

7



Why use clickers?

Simplicity Ease of use

http

://w

ww

.flic

kr.co

m/p

hoto

s/un

av/

7



Why use clickers?

Simplicity Ease of use

http

://w

ww

.flic

kr.co

m/p

hoto

s/un

av/

Anonymity

7



Ways to use clickers

8

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

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

Polling (not related to course material)

10

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

Polling (not related to course material)

0

2

4

6

$0 $5 $10 $20 $50

3

566

4

10

Classroom Voting Questions: Calculus IISection 9.1

1. The sequence sn =5n+ 1

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


(b) Converges, and the limit is −1


(d) Diverges

3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · ·

(a) Converges

(b) Diverges

4. A sequence that is not bounded

(a) Must converge

(b) Might converge

(c) Must diverge

Section 9.2

1. Which of the following is/are geometric series?

(a) 1 + 12 + 1

4 + 18 + · · ·

(b) 2− 43 + 8

9 − 1627 + · · ·

(c) 3 + 6 + 12 + 24 + · · ·(d) 1 + 1

2 + 13 + 1

4 + · · ·(e) (a) and (b) only

(f) (a),(b), and (c) only

(g) All of the above

2. −6 + 4− 8

3+

16

9− 32

27=

(a) −266

81

(b) −422

27

(c) −110

27

(d)110

27

1

Gathering basic formative assessment data

11

Focus questioning

11.5: The Chain Rule

1. Suppose that y = u2 and u = sin x. Thendy

dx

(a) Equals 2u

(b) Equals 2x

(c) Equals cos x

(d) Equals 2 cos x

(e) Equals 2 sin x cos x

(f) Equals cos(x2)

(g) Equals 2 cos(x2)

(h) None of the above

11.6: Directional Derivatives and the Gradient Vector

�15

�14

�13

�12

�11

�10

�9

�8

�7

�6

�5

�4

�3

�2

�2

�1 �1

0

12

0.0 0.5 1.0 1.5 2.0

1.6

1.8

2.0

2.2

2.4

1. Consider the contour map of the function z = f(x, y) above. Which of the followinghas 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

2

12

Motivator/discussion catalyst for group work

5. The series∞�

n=1

1

nen

(a) Converges

(b) Diverges

6. The series∞�

n=1

(n− 1)!

5n

(a) Converges

(b) Diverges

4

Put students into working groups to find the answer. Discuss not only the answer but also the methods used to get it.

13

“Best answer” questions

(b) Diverges

7. The series∞�

n=1

�1

2n+

1

n

�

(a) Converges

(b) Diverges

8. The series∞�

n=1

1

n(1 + lnn)

(a) Converges

(b) Diverges

9. The series∞�

n=1

�1

2n+

1

n

�

(a) Converges

(b) Diverges

Section 9.4

1. If an > bn for all n and�

bn converges, then

(a)�

an converges

(b)�

an diverges

(c) Not enough information to determine convergence or divergence of�

an

2. The best way to test the series∞�

n=1

lnn

nfor convergence or divergence is

(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

3. The series∞�

n=1

cos2 n

n2 + 1

(a) Converges

(b) Diverges

4. The series∞�

n=1

(n−1.4 + 3n−1.2)

(a) Converges

(b) Diverges

3

14

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.

15

16

Students teach each other concepts using

multiple choice questions designed to

expose common misconceptions.

Eric Mazur, Harvard University

Peer Instruction

17



n




(d) Diverges





(d) Diverges

3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · ·

(a) Converges

(b) Diverges


(a) Must converge

(b) Might converge

(c) Must diverge

Section 9.2


(a) 1 + 12 + 1

4 + 18 + · · ·

(b) 2− 43 + 8

9 − 1627 + · · ·

(c) 3 + 6 + 12 + 24 + · · ·(d) 1 + 1

2 + 13 + 1

4 + · · ·(e) (a) and (b) only



2. −6 + 4− 8

3+

16

9− 32

27=

(a) −266

81

(b) −422

27

(c) −110

27

(d)110

27

1

Data from MTH 202, Sec 03, Fall 2011 at GVSU

18



n




(d) Diverges





(d) Diverges

3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · ·

(a) Converges

(b) Diverges


(a) Must converge

(b) Might converge

(c) Must diverge

Section 9.2


(a) 1 + 12 + 1

4 + 18 + · · ·

(b) 2− 43 + 8

9 − 1627 + · · ·

(c) 3 + 6 + 12 + 24 + · · ·(d) 1 + 1

2 + 13 + 1

4 + · · ·(e) (a) and (b) only



2. −6 + 4− 8

3+

16

9− 32

27=

(a) −266

81

(b) −422

27

(c) −110

27

(d)110

27

1

0

6

12

18

24

Converges to 1 Converges to 5 Converges to 6 Diverges

6

2

14

2

FIRST VOTE (after 1min individual reflection)


18



n




(d) Diverges





(d) Diverges

3. The sequence 2, 2.1, 2.11, 2.111, 2.1111, · · ·

(a) Converges

(b) Diverges


(a) Must converge

(b) Might converge

(c) Must diverge

Section 9.2


(a) 1 + 12 + 1

4 + 18 + · · ·

(b) 2− 43 + 8

9 − 1627 + · · ·

(c) 3 + 6 + 12 + 24 + · · ·(d) 1 + 1

2 + 13 + 1

4 + · · ·(e) (a) and (b) only



2. −6 + 4− 8

3+

16

9− 32

27=

(a) −266

81

(b) −422

27

(c) −110

27

(d)110

27

1

0

6

12

18

24


6

2

14

2

FIRST VOTE (after 1min individual reflection)

0

6

12

18

24


12

21

0

SECOND VOTE (after 2min peer instruction)


18

Peer instruction leads to significant gains in student learning on essential conceptual

knowledge

E. Mazur, Peer Instruction: A User’s Manual

19

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

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

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 equationsAdequate number of multiple-choice answers

Unambiguously wordedNeither too easy nor too difficult

22

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

TurningPoint ResponseCard RF LCD

(≈ $30 at GVSU bookstore; receiver ≈ $100)

TurningPoint Anywhere software (free download)

Standard GVSU clicker setup

http://www.turningtechnologies.com/responsesystemsupport/downloads/

24





Alternatives

iClicker TurningPointResponseWare

Index cards Little whiteboards

PollEverywhere

25

Email: [email protected]

Blog: http://chronicle.com/blognetwork/castingoutnines

Twitter: @RobertTalbert

Google+: http://gplus.to/rtalbert

26

mailto:[email protected]

mailto:[email protected]

http://chronicle.com/blognetwork/castingoutnines




http://gplus.to/rtalbert

http://gplus.to/rtalbert

Education

Classroom response systems in mathematics: Learning math better through voting