An Introduction to Clickers" (actually, Peer Instruction)

Transcription

1 An Introduction to Clickers" (actually, Peer Instruction) College of St. Benedict/St. John s University Department of Mathematics

2 Today s lesson Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes of Syracuse

3 Today s lesson Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. Archimedes of Syracuse A boat is drifting in the middle of the ocean. If someone throws the anchor into the water, what happens to the sea level? 1 The sea level rises (a tiny bit). 2 The sea level sinks (a tiny bit). 3 The sea level does not change.

4 Benefits of Peer Instruction 1 100% student participation

5 Benefits of Peer Instruction 1 100% student participation 2 Immediate feedback to teacher

6 Benefits of Peer Instruction 1 100% student participation 2 Immediate feedback to teacher 3 Immediate feedback to students

7 Benefits of Peer Instruction 1 100% student participation 2 Immediate feedback to teacher 3 Immediate feedback to students 4 Improved learning ( 1 2 of a grade, p = , according to Maria Terrell)

8 Benefits of Peer Instruction 1 100% student participation 2 Immediate feedback to teacher 3 Immediate feedback to students 4 Improved learning ( 1 2 of a grade, p = , according to Maria Terrell) 5 Fun

9 More Evidence SupportingPeer Instruction

10 Even More Evidence SupportingPeer Instruction

11 Even More Evidence SupportingPeer Instruction

12 Types of Questions 1 Computational 2 Conceptual

13 Types of Questions 1 Computational 2 Conceptual ( Misconception eliminators")

14 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct

15 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video

16 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video 3 Clear" video students: 6.2/26 on exact same post-test.

17 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video 3 Clear" video students: 6.2/26 on exact same post-test. They were also more confident in their answers.

18 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video 3 Clear" video students: 6.2/26 on exact same post-test. They were also more confident in their answers. 4 Confusing" video students: 13/26 on exact same post-test.

19 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video 3 Clear" video students: 6.2/26 on exact same post-test. They were also more confident in their answers. 4 Confusing" video students: 13/26 on exact same post-test. They were also less confident in their answers.

20 Misconceptions are Stubborn 1 Take pre-test, averege 6/26 correct 2 Watch one of two videos: clear" lecture, or confusing" video 3 Clear" video students: 6.2/26 on exact same post-test. They were also more confident in their answers. 4 Confusing" video students: 13/26 on exact same post-test. They were also less confident in their answers. Clickers help to create these confusing," yet helpful environments.

21 Math 119 Computational Example What is the derivative of f (x) = 2 x 3? 1 f (x) = 2x 2 2 f (x) = 2x 3 3 f (x) = 2x 4 4 f (x) = 6 x 2 5 f (x) = 6 x 3 6 f (x) = 6 x 4 7 f (x) = 6 x 2 8 f (x) = 6 x 3 9 f (x) = 6 x 4

22 Math 124 Computational Example To construct a 92% confidence interval, the correct z to use is

23 Math 119 Definition/Conceptual Example If a function f is not defined at x = a, then 1 lim x a f (x) cannot exist 2 lim x a f (x) could be 0 3 lim x a f (x) must be 4 None of the above

24 Math 119 Definition/Conceptual Example You decide to estimate e 2 by squaring longer decimal approximations of e = [Terrell, et al] 1 This is a good idea because e is a rational number 2 This is a bad idea because e is an irrational number 3 This is a good idea because y = x 2 is a continuous function 4 This is a good idea because y = e x is a continuous function

25 Math 119 Definition/Conceptual Example True or false: You were once exactly 3 feet tall. [Terrell, et al] 1 True, and I am confident 2 True, and I am not confident 3 False, and I am not confident 4 False, and I am confident

26 Math 119 Definition/Conceptual Example Below is a graph of the function f Let g(x) = x 0 f (t) dt. Then 1 g(0) = 0, g (0) = 0, and g (2) = 0 2 g(0) = 0, g (0) = 4, and g (2) = 0 3 g(0) = 1, g (0) = 0, and g (2) = 1 4 g(0) = 0, g (0) = 0, and g (2) = 1

27 Math 124 Definition/Conceptual Example We would like to construct a confidence interval to estimate the population mean µ of some random variable X. For a given sample size, which confidence level will produce the shortest interval? 1 90% confidence 2 95% confidence 3 99% confidence 4 These three will all have the same size interval

28 Math 124 Definition/Conceptual Example Suppose an experiment finds that more women prefer Toyotas than men. If the p-value is 0.14, then... 1 The results are wrong 2 There is a 14% chance of getting similar results (or stronger) if men and women actually like Toyotas equally. 3 It is only true of 14% of the women. 4 Only 14% of men prefer Toyotas. 5 There is a 14% chance that this study is wrong. 6 There is a 14% chance that this study is right.

29 Math 239 Definition/Conceptual Example Let A be a matrix. If A 2 is the zero matrix, then A must be the zero matrix. 1 True, and I am confident 2 True, and I am not confident 3 False, and I am not confident 4 False, and I am confident

30 Math 239 Definition/Conceptual Example If all entries of a square matrix A are 0 or 1, then det(a) must be 1, 0, or 1. 1 True, and I am confident 2 True, and I am not confident 3 False, and I am not confident 4 False, and I am confident

31 Math 305 Definition/Conceptual Example For which of the paths is the line integral positive? 1 None are positive 2 Only C 1 3 Only C 2 4 Only C 3 5 Only C 4 6 Exactly two line integrals are positive 7 Exactly three line integrals are positive 8 All line integrals are positive

32 Math 305 Definition/Conceptual Example Choose the vector field with the largest flux through the surface below. 1 F1 = 2 i 3 j 4 k 2 F2 = i 2 j + 7 k 3 F3 = 7 i + 5 j + 6 k 4 F4 = 11 i + 4 j 5 k 5 F5 = 5 i + 3 j + 5 k

33 Math 343 Definition/Conceptual Example THERE EXISTS an ɛ > 0 such that FOR ALL N N THERE EXISTS an n N such that a n a < ɛ means: 1 (a n ) is bounded 2 (a n ) has a bounded subsequence 3 (a n ) has a convergent subsequence 4 (a n ) is constant 5 (a n ) could be anything 6 Either a (a n ) or (a n ) has a convergent subsequence

34 Math 348 Definition/Conceptual Example What are we integrating over" when we compute γ f dz? 1 Only the inside of the curve γ (not the boundary of γ) 2 Only the outside of the curve γ (not the boundary of γ) 3 The inside of the curve and the boundary of γ 4 The outside of the curve and the boundary of γ 5 Only the boundary of γ

35 You have 5 minutes Now it is your turn: write a question based on a common student misconception.

36 How to write good slides 1 Identify an important idea or misconception.

37 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it.

38 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it. 3 Be sure to write good distractor" choices.

39 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it. 3 Be sure to write good distractor" choices. 4 Force students to think.

40 Student s don t have to think What causes the seasons? 1 The change in the earth s distance from the sun during the year 2 The tilt of the earth s axis 3 Changes in the sun s brightness 4 Changes in clouds 5 None of the above

41 Students have to think What would happen to the seasons if the earth s orbit around the sun was made a perfect circle (but nothing else changed)? 1 There would be no seasons 2 The seasons would remain pretty much as they are today 3 Winter to spring would differ much less than now 4 Winter to spring would differ much more than now (Question courtesy of Stephanie Chasteen)

42 Students don t have to think If a function is differentiable at a point, then the function is positive at that point. 2...the function is negative at that point. 3...the function is concave up at that point. 4...the function is concave down at that point. 5...the function is continuous at that point.

43 Students don t have to think If a function is differentiable at a point, then the function is positive at that point. 2...the function is negative at that point. 3...the function is concave up at that point. 4...the function is concave down at that point. 5...the function is continuous at that point. Now see if you can write a better question that tests differentiability implies continuity."

44 Math 119 Definition/Conceptual Example If f (a) exists, then lim x a f (x)... 1 Equals f (a) 2 Equals f (a) 3 Must exist, but there is not enough information to determine it exactly 4 Might not exist

45 How to write good slides 1 Identify an important idea or misconception.

46 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it.

47 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it. 3 Be sure to write good distractor" choices.

48 How to write good slides 1 Identify an important idea or misconception. 2 Write a multiple choice question about it. 3 Be sure to write good distractor" choices. 4 Force students to think. Now revise the original question you wrote:.