What Clicks in the ClassroomWhat Clicks in the Classroom:: The The Power of ClickersPower of ClickersPower of ClickersPower of Clickers

Kari Lock and Xiao-Li Mengd i i i iHarvard University Statistics Department

lock@stat.harvard.edu

International Conference on Technology in Collegiate MathematicsInternational Conference on Technology in Collegiate Mathematics3/13/10

Have you used clickers in your classroom?

62%1. Yes

No38%

2. No

1 2

My Clicker DetailsMy Clicker DetailsModule-Based Undergraduate Statistics Course

Turning Technologies clickers

Clicker responses make up 15% of gradeClicker responses make up 15% of gradeAt least 50% credit for simply clicking inSometimes, 50% depends on correct answers, 5 p

All multiple choice

Usually conceptual questions (no calculations)

About 3 questions per lecture

The formula for a 95% CI uses 1.96 as a multiplier of the SE. If we instead wanted a 99% CI, would we use a number higher or l th 6?lower than 1.96?

100%?X SE± × 100%?X SE± ×

2.61. Higher2. Lower

0%0%0%

3. The Same4. No Clue

 High

er

 Lowe

r

 The S

ame

 No C

lue

The following graph is a i f hi h representation of which

of the following functions?functions?

(a)y = 6x + 6

80%

(a)y = 6x + 6(b) y = 3x + 6(c) y = 3x + 6(c) y = -3x + 6(d) y = 6x – 2( ) 3 + 2

13%

7%

(e) y = 3x + 2(f) y = -3x + 2

 y = 6

x + 6

  y = 

3x + 

6  y

 = ‐3

x + 6

  y = 

6x – 

2  y

 = 3x

 + 2

  y = 

‐3x +

 2

0% 0%0%

In the graph shown, at x = 0 h i f h f i d the signs of the function and

the first and second derivatives in order are:derivatives, in order, are:

(a) –, –, – 67%(b) –, –, +

(c) –, +, –(d) –, +, +(e) +, –, –

7%

20%

7%

(f) +, –, +(g) +, +, –

  –, –

, –

  –, –

, +

  –, +

, –

  –, +

,  +

  +, –

, –

  +, –

, +

  +, +

, –

  +, +

, +

7%

0% 0%0%0%

7%

(h) +, +, +

Assume A = ( – ∞, 3) and B = [2, 5].Wh t i A B ?What is A ∩ B ?

69%(a) ( – ∞, 2) 69%(a) ( , 2)(b) ( – ∞, 2](c) ( – ∞ 5)(c) ( ∞, 5)(d) ( – ∞, 5](e) ( 2 3)

6%

19%

6%

(e) ( 2, 3)(f) [2, 3)(g) ( 2 3]

  ( 2, 

3)

  [2, 3

)

  ( 2, 

3]

  [ 2,3

]

0%

6%

0% 0%0%

6%(g) ( 2, 3](h) [ 2,3]

“If A ⊆ B, then A ∪ C ⊆ B ∪ C.” What is the best first sentence of a formal What is the best first sentence of a formal direct proof?

50%

(1) Assume A ∪ C.

( ) A A B

19%

(2) Assume A ⊆ B.(3) Let x ∈ B ∪ C .

6% 6%

13%

6%

(4) Let x ∈ A.(5) Let x ∈ A ⊆ B .

  Let

 A = 

{1, 2

...(6) Let A = {1, 2, 3, 4} and B = {2, 4, 6}

“Easy” Questions“Easy” QuestionsStraightforward, relatively quickStudents should be able to get the answerStudents should be able to get the answer

Purpose: Purpose: INVOLVE the students! Gauge student understandingGauge student understandingSolidify concepts and definitions

Review/recap materialQuick assessmentQuick assessment

What’s the expected return of this pportfolio?

Total Shares Expected ReturnpGOOGLE 500 8%

MICROSOFT 500 4%

88%1. 4%2 6%2. 6%3. 8%

% % % %

0%

12%

0%0%

4. 12%5. I need more

4% 6% 8% 12%

 I nee

d mor

e in.

..

information

What’s the expected return of this tf li ?portfolio?

Total Shares Expected ReturnpGOOGLE 500 8%

MICROSOFT 500 4%

1. 4%2 6%2. 6%3. 8%4. 12%5. I need more

information Need to know the price of each share

Discussion QuestionsDiscussion QuestionsQuestions require thought and reasoningYou don’t expect all students to get the answer

Ask once, do not give the answerCall on students to defend their answersH l di i di i iHave a class discussion, or discuss in pairsAsk the same question again

Results:Students very engaged in discussionsOn the second polling, many more correct answersp g, yStudents form their own opinions with reasoningStudents hear the reasoning of their peers, helping them figure out the correct answer f gStudents have to convince others

Answers when asked the first time…Answers when asked the first time…

Answers after discussion…Answers after discussion…

Questions Preceding Material Questions Preceding Material

Have students answer a question before being f ll t ht h t itformally taught how to answer itDon’t expect students to answer correctly

Purposes:Introduce a topicIntroduce a topicStimulate independent thinkingArouse curiosityyMake students want to learn the materialDevelop intuition…Or show why intuition fails (shock value)

A 40-year old woman participates in routine screening and has a positive routine screening and has a positive mammography. What’s the probability she has cancer?she has cancer?

40%

1. 0-10% 7.8%

27%

1. 0 10%2. 10-25%3. 25-50%

50 75% 20%4. 50-75%5. 75-100%6. I have no idea.

7%

0%

7%

0-10

% 10

-25%

25-50

% 50

-75%

75-10

0% I h

ave n

o idea

.

Challenge Questions Challenge Questions

You only expect a few students to be able to figure out the answer

Purpose:Challenge even the brightest studentsg gCorrect answer not immediately obvious, so it makes everyone thinkyPerhaps leave as an open question until the next lecture, encouraging thought the next lecture, encouraging thought outside of class

A poll of 500 people was taken in Oklahoma (population ≈ 3.6 million) to predict Oklahoma in (population 3.6 million) to predict Oklahoma in the 2008 presidential election. How large a poll would you need in California (population ≈ 36 million ) to get a prediction as precise?million ) to get a prediction as precise?

69%

1. 500

15%

2. 500*√103. 5000 15%

8%8%0%

4. > 50005. I have no idea

500

5000

> 5000

I hav

e no id

ea

5

Collecting DataCollecting Data

Great for statistics classes!

Inference for proportionsp pReal class data can be generated on the spot and used to illustrate topics like p pconfidence intervals and hypothesis tests

Why Use Clickers?Why Use Clickers?Engage students!Gauge student understandingGauge student understandingStimulate active thoughtM ti t di iMotivate discussionIntroduce a topic, arouse curiosity

i i iMini-quizzesReviewSolidify a concept or definitionCollect dataAttendance (gets students to come to class!)

Why Use Clickers?Why Use Clickers?Clickers work with…

Small and large classesh d i dShy and outgoing students

Bright and struggling studentsIntro classes and upper level classesAny topicy pAny professor

Potential ConcernsPotential ConcernsClass Time

Lecture = passive learning, Clickers = active learning

Prep TimeMany text books come with pre-made clicker questionsClicker questions are available on the webqVery easy to create your own right within Powerpoint

CostClickers are about $40 each Students at many universities already own a clickerOptions for students to “click in” over the internet

Multiple Choice LimitationsMany fantastic conceptual multiple choice questionsMore advanced open-ended response clickers available

Math questions in this talk…Math questions in this talk…provided by Patti Frazer Lock

Calculus questions are from the ConcepTests(ready to go clicker questions) which accompany (ready to go clicker questions) which accompany the Hughes-Hallett et. al. Calculus books

Bridge to Higher Math, Group Theory, Graph Theory clicker questions available at http://myslu.stlawu.edu/~plock/

Clicker Questions on the WebClicker Questions on the WebClicker Questions on the WebClicker Questions on the Web

For math and stat clicker questions clicker For math and stat clicker questions, clicker papers, links to clicker companies, and more…

Math QUESTMath QUestions to Engage STudentsQ g g

http://mathquest.carroll.edu/

It’s easy!It’s easy!It s easy!It s easy!

Let’s create a clicker questionLet s create a clicker question…