Engaging Students Through Classroom Voting in Introductory Statistics
Classroom voting is a dynamic teaching approach where students actively participate by voting on multiple-choice questions, fostering discussions, and challenging misconceptions in introductory statistics. This method enhances student engagement, promotes peer learning, and positively impacts learning outcomes. By incorporating activity periods, voting periods, and setting rules for participation, instructors can create an interactive and stimulating learning environment in the classroom.
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Clicker questions that stimulate discussions and provoke misconceptions in introductory statistics Kelly Cline Carroll College Helena, Montana
What is classroom voting? 1. The instructor presents a multiple-choice question to the class. 2. Students are given a few minutes to consider the question and to discuss it with their peers. 3. Each student votes on the answer thus requiring every student to form an opinion. 4. The instructor leads a class-wide discussion, asking individual students to explain and defend their vote. Each question usually takes 3-5 minutes.
How do students vote? Clickers Student phones or laptops Students may vote by holding up colored cards. Some systems allow for students to submit sketches, equations, and numbers too. Questions and votes can be interspersed into a lecture, or might occupy a full period in a flipped classroom.
Results of Classroom Voting: Students Get Engaged Each student must take an active role, thinking and participating in the class period. Research shows classroom voting can have positive impacts on student learning, especially when the emphasis is on creating peer learning through the pre- vote small group discussions. Student surveys tell us that they enjoy the class more when classroom voting is used regularly because they are actively involved. Many report that attendance improves and attrition drops.
Activity periods & Voting periods In some of my class periods, students will spend most of the time working independently (usually in pairs), to run simulations in TinkerPlots, gather and analyze data, or to study a real world data set on their computers. In other periods, I will alternate between a few minutes of lecture, and voting questions, using these questions to lead the students through lesson. My preference is to ask the clicker question first, challenging students to figure out the scenario based on logic and the reading assignment, then to follow with a lecture segment clarifying and generalizing the ideas.
The Rules 1. All students must vote. 2. All students must talk with at least one other student before voting. 3. After the vote, students will be called on to explain their votes, and in this discussion the only unacceptable response is, I just guessed. I do not count clicker questions toward student grades nor use clickers to take attendance. Clickers are used purely to enhance the classroom experience and promote student learning.
Let the votes trickle in It is hard to predict how much time the class will need with any given question. Tell the students to vote when they re ready, after some discussion. When about 60 75% of the class has voted, we call for the rest to finish up. Make a headcount, and require everyone to participate before closing the vote.
Conducting the Post-Vote Class-Wide Discussion 1. Ask a student: What did you vote for, and why? 2. Initially, give no feedback as to whether this was right or wrong, and ask the same question of another student, encouraging the students to figure out the correct answer for themselves. 3. If students express contradictory arguments, ask them to respond to each other. 4. If possible, confirm the correct answer after most have already figured it out.
Getting student buy-in I vote several questions in almost every class period. Questions are usually interspersed throughout the class. Students must see that questions form a vital part of the lesson, rather than being an optional add-on to be squeezed in if time permits. Students must see that essential ideas are taught through the questions and resulting discussion. The questions must be directly relevant and help prepare students for the assignments and tests which follow.
The Key: Good Questions Some questions regularly generate rich discussions and strong engagement, with students energetically debating important ideas. Some questions generate almost no discussion at all. It is surprisingly difficult to anticipate the quality of discussion that will result from a given question. Some questions look straight forward, but bring up a kaleidoscope of important issues. Other questions look like they will create good discussions, but quickly fall flat.
Strategy: Record Voting Results Keep records of the class percentage voting for each option, every time a question is voted. After several votes have been recorded on a question over several semesters, the data becomes useful. We recorded the percentage of the class voting on every question used in 19 sections of introductory statistics courses, taught by 3 instructors (Kelly Cline, Holly Zullo, David Huckaby), at 2 institutions (Carroll College & Angelo State), over the course of 9 years, a total of 971 class votes on a set of 206 questions.
78 questions had at least 5 votes 45 40 STD Percentage Correct 35 30 25 20 15 10 5 0 0 10 20 30 Mean Percentage Correct 40 50 60 70 80 90 100
Learning from voting results Evaluation of discussions was qualitative. Many questions regularly caused a strong majority to vote correctly: We found that these questions rarely produced much discussion. We found other voting patterns that indicate questions tend to stimulate good discussions: Misconception/Common Error questions. These are questions where a large majority regularly vote for a specific wrong answer. Students expect the majority to be correct, and are surprised and intrigued to find out that they were wrong.
Misconception/Common Error Questions These questions usually generate very rich, high energy post-vote discussions. Small group peer instruction is important: Sometimes small group discussions can be created by simply telling the class that the majority is wrong and calling for another round of voting. For each of the 78 questions with at least five votes, we identify the most popular incorrect answer, and find the average percentage voting for this answer. We rank the questions based on this number to find the best misconception/common error questions.
On linear regression A store manager conducted an experiment in which he systematically varied the width of a display for toothpaste from 3 ft. to 6 ft. and recorded the corresponding number of tubes of toothpaste sold per day. The data was used to fit a regression line, which was: 9 votes: a) b) c) tubes sold per day = 20 + 10(display width) 13 11 71 7 5 0 0 0 0 0 0 0 80 84 29 93 64 86 86 What is the predicted number of tubes sold per day for a display width of 12 feet? a) 120 b) 140 c) It would be unwise to use the regression line to make a prediction for a display width of 12 ft. (Question by Roxy Peck) 7 36 14 14 0 100 90 79.1 21.2 10 Avg. STD 19.6 21.6 1.3 2.7
On descriptive statistics Suppose your statistics instructor tells you that you scored 70 on an exam and that the class mean was 74. You should hope that the standard deviation of exam scores was. a) Small b) Large (Question by Roxy Peck) 11 votes: a) b) 43 13 65 65 35 32 54 17 75 27 27 41 21 57 87 35 35 65 68 46 83 25 73 73 59 21 On average 59% of students vote for (a) small. However, if the standard deviation is large--- much larger than four points---then these four points below average would have very little significance relative to the class distribution, making the score only slightly below average. Avg. STD
On hypothesis testing If the conclusion in a hypothesis test is to fail to reject H0, we can conclude that there is strong evidence that the null hypothesis is true. a) True b) False (Question by Roxy Peck) 12 votes: a) b) The question directly presents students with one of the most common misconceptions in statistics via a simple true/false question. Many students are confused by the double negative statement fail to reject and think that this must be equivalent to accepting the null hypothesis. 36 71 56 26 27 64 29 44 74 73 92 72 50 8 28 50 100 86 27 44 47 27 0 14 73 56 53 27 Avg. STD
Identifying Discussion Questions Questions tend to stimulate rich and engaging discussion when there are multiple options that attract significant numbers of votes. On each vote, identify the percentage voting for the plurality winner, find the mean of these percentages. Rank the questions looking for the lowest mean winning percentage.
The fundamental concept underlying statistical inference is that (a) through the use of sample data we are able to draw conclusions about a sample from which the data were drawn. (b) through the examination of sample data we can derive appropriate conclusions about a population from which the data were drawn. (c) when generalizing results to a sample we must make sure that the correct statistical procedure has been applied. (d) Two of the above are true. (e) All of the above are true. a) 0 0 7 0 0 0 0 0 0 7 11 2.3 15 4 b) 29 33 0 15 0 23 0 0 33 7 29 c) 0 8 0 8 0 4 0 0 0 0 29 4.5 8.8 d) 29 42 40 54 35 58 32 57 11 40 29 39 14 e) 41 17 53 23 65 15 68 43 56 46 4 39 21 Winner 41 (d) 42 (d) 53 (e) 54 (d) 65 (e) 58 (d) 68 (e) 57 (d) 56 (e) 46 (e) 29(bcd) 51.7 11.4 (Question by Murphy, McKnight, Richman, and Terry) Avg STD 14
A 95% confidence interval has been constructed around a sample mean of 28. The interval is (21, 35). Which of the following statement(s) is true? a) The margin of error in the interval is 7. b) 95 out of 100 confidence intervals constructed around sample means will contain the true population mean. c) The interval (21,35) contains the true population mean. d) Both (a) and (b) are true. e) (a), (b), and (c) are true. (Question by Jack Oberweiser) a) 0 77 17 33 12 0 0 46 16 6 13 31 21 23 b) 18 0 0 0 0 0 0 0 11 16 7 19 5.9 7.9 c) 0 8 25 0 6 10 0 15 0 6 0 4 6.2 7.7 d) 47 15 25 58 24 68 71 15 32 61 20 12 37 22 e) 35 0 33 8 59 23 29 23 42 11 60 35 30 19 Winner 47 (d) 77 (a) 33 (e) 58 (d) 59 (e) 68 (d) 71 (d) 46 (a) 42 (e) 61 (d) 60 (e) 35 (e) 54.8 14.1 Avg. STD
Many individuals, after the loss of a job, receive temporary pay unemployment compensation until they are re-employed. Consider the distribution of time to re- employment as obtained in an employment survey. One broadcast reporting on the survey said that the average time until re-employment was 4.5 weeks. A second broadcast reported that the average was 9.9 weeks. One of your colleagues wanted a better understanding of the situation and learned (through a Google search) that one report was referring to the mean and the other to the median and also that the standard deviation was about 14 weeks. Knowing that you are a statistically-savvy person, your colleague asked you which is most likely the mean and which is the median? a) 4.5 is the mean and 9.9 is the median. b) 4.5 is the median and 9.9 is the mean. c) Neither (A) nor (B) is possible given the SD of the data. d) I am not a statistically-savvy person, so how should I know? (Question by Murphy, McKnight, Richman, and Terry) a) 11 7 65 0 0 17 b) 35 27 12 45 45 33 14 c) 27 53 8 55 55 40 21 d) 27 13 15 0 0 11 11 Winner 35 (b) 53 (c) 65 (a) 55 (c) 55 (c) 52.6 10.9 Avg. STD 27
Identifying Checkpoint Questions Classroom voting provides instant feedback, from every student in the class, allowing the instructor to adjust and modify the lesson. If a question creates the same pattern of voting results in every class, then it is not conveying much useful information about student understanding. We seek questions on which sometimes a high percentage vote correctly and sometimes a low percentage vote correctly. We look for high STD in the percentages voting correctly between different classes.
On P-values A parachute manufacturer is concerned that the failure rate of 0.1% advertised by his company may in fact be higher. A hypothesis test was run and the result was a P-value of 0.03333. The most likely conclusion the manufacturer might make is: a) My parachutes are safer than I claim. b) My parachutes are not as safe as I claim them to be. c) I can make no assumption of safety based on a statistical test. d) The probability of a parachute failure is 0.03333. e) Both (b) and (d) are true. (Question by Jack Oberweiser) 5 votes: a) b) c) d) e) 0% 18% 19% 7% 90% 27% 36% 8% 9% 4% 3% 0% 5% 4% 15% 27% 0% 7% 10% 12% 10% 0% 9% 12% 13% 0% 7% 6% 77% 36% 65% 70% 0% 50% 32% Avg. STD
On confidence intervals Suppose you construct a 95% confidence interval from a random sample of size n = 20 with sample mean 100 taken from a population with unknown mean and known standard deviation = 10, and the interval is fairly wide. Which of the following conditions would NOT lead to a narrower confidence interval? a) If you decreased your confidence level b) If you increased your sample size c) If the sample mean were smaller d) If the population standard deviation were smaller (Question by Derek Bruff) 5 votes: b) 88% 36% 50% 5% 7% 37% 34% a) c) d) 0% 36% 50% 95% 59% 48% 35% 13% 7% 0% 0% 27% 9% 11% 0% 21% 0% 0% 7% 6% 9% Avg. STD
On outliers Suppose you take a random sample of 10 juniors who bought the same model laptop when they were freshmen. You test these 10 laptops to determine how long their batteries last before needing to be recharged, and you obtain the following data (in hours): 1.2, 1.3, 3.8, 3.9, 3.9, 4.0, 4.1, 4.1, 4.2, 4.3. What should be done with the values 1.2 and 1.3? Which of the following is the best course of action? a) Delete them from the data set since they are outliers. b) Keep them in the data set even though they are outliers. c) Determine why these values were so much lower than the rest, then delete them. d) Determine why these values were so much lower than the rest, then keep them in the data set, provided they weren t due to data entry errors. (Question by Derek Bruff) a) b) c) d) 95% 93% 21% 5% 38% 42% 79% 68% 68% 0% 0% 0% 0% 0% 0% 0% 0% 0% 5% 0% 79% 95% 58% 58% 21% 32% 32% 0% 7% 0% 0% 4% 0% 0% 0% 0% 0% 100% 0% 0% 0% 100% 0% 0% Avg. STD 64% 33% 0% 0% 35% 34% 1% 2%
Question characteristics Misconception questions, a majority votes for the a particular incorrect answer: brief and tightly focused on particular misconceptions. Discussion questions, votes are divided, broadly distributed over different options: based on general cases, often without numbers. Checkpoint questions, percentage voting correctly varies substantially from semester to semester: high-quality distractors, tapping into common student issues and confusions.
Student survey results On average: 92% agree voting makes the class more fun 89% agree voting helps you engage in the material 84% agree voting helps you learn When asked if they had to choose between a class with voting and one without, 74% would choose the one with voting.
Discussions are the key! There are many different things you can do with voting. The research and our experience indicate that deep questions and small group discussions produce excellent results. Learning to talk stats means learning to think stats. Students learn to logically defend statistical ideas! We don t give points or penalties for right or wrong answers. In our small classes, we don t even have to give participation points. The purpose of the questions is to teach, not to assess and evaluate.
http://mathquest.carroll.edu/stt.html Our website has approximately 2,300 multiple- choice questions designed for classroom voting in university mathematics, and 206 questions for introductory statistics. Past voting statistics and LaTeX files available with an e-mail request to: kcline@carroll.edu We have found classroom voting with clickers to be an effective way to promote peer instruction and active learning. Keeping records of voting results can be an effective way to identify useful clicker questions.
Thank you for your attention! Any questions?
