Birth of an activity

1. Birth of an activity Beth Chance Department of Statistics Cal Poly – San Luis Obispo bchance@calpoly.edu

2. Overview • Common Visionproject (PI: Karen Saxe, Macalester College) • AMATYC, AMS, ASA, MAA, SIAM • Freeman report (2014): Active learning increases student performance in science, engineering, and mathematics • Failure rates under traditional lecturing are 55 percent higher than the rates observed under active learning • When Monica asked me about this session, I was just finishing up creating a new activity • Did I have any “strategies” that might be useful to other teachers? • What does a “good” activity look like?

3. Step One: Pick a topic • Identify an area in which students consistently struggle • e.g. conceptual vs. procedural understanding • Write out learning goals • Make explicit what you want students to be able to do, remember afterwards • What is your motivation for the activity?

4. Step One: Pick a topic • Context: • In both my “Stat 101” and “Stat 201” courses, we have centered on randomization-based inference from the very beginning of the course • Example: Fourteen of 16 infants choose to play with a “helping” toy rather than a “hindering” toy indicating social evaluation (6 mos) • Is that convincing evidence or could this have happened just by chance? • Chance model: toss 16 coins, is 14 an unusual outcome? • Where does 14 fall on the “null” distribution? • Binomial model • Normal approximation/z-statistic: more than 2SD away? • So what conclusions can we draw from this study?

5. Step One: Pick a topic • More Context: • What is probability? • Descriptive statistics and inference for one proportion • Two proportions (conditional proportions, bar graphs, randomization tests, normal approximation) • 2nd midterm (week 7 of 10-week quarter)

6. So what’s the problem? • Quantitative data • How do I introduce importance and measures of variability with categorical data? • Distributional thinking is difficult for many students • How do I show them the richness of “big data”? • Motivation • Do more with quantitative data earlier in the course • “Catch up” those who haven’t seen standard deviation before with straight forward example • Use interesting data where students will be motivated to think about shape, center, variability

7. Step Two: Find interesting data • Better yet: find interesting research question • Need to assess what your students are interested in (e.g., initial course survey) • Use existing resources as much as possible • Data and Stories Library, STEW websites • Collect data on your students (anonymously) • Listen to TV, NPR, news websites • Set a time limit to how long you will spend tracking down the article • Recent examples: Early exposure to peanuts, Using lotteries to promote safe sex, Experiment investigating effectiveness of programs for the poor, Tylenol also dulls emotional pain

8. Step Two: Find interesting data • Also wanted to give students a sense of the richness of data on the web • “Impacts of raising speed limits on driver safety” • FARS Encyclopedia

9. Step Two: Find interesting research question • 2009 study:

10. Step three: Context • Summarizing background, motivation for the study, authenticity • Students can be asked to read this outside of class • Students can be asked to relate to the study personally • Students can be asked to generate their own research questions • Focus on restrictions, exclusion criteria (e.g., rural vs. urban highways) • Wikipedia page

11. Step four: Context

12. Step four: Classroom context • Classroom layout, Class size • Discussion among students? • Lecture or Guided exploration or Open ended • Access to technology • Individually or in teams • Expectation for participation from day one • Student products/incentive system • What do/should/might students know about this topic coming into class? (Stat 201) • Watch for sensitive topics

13. Step four: Classroom context • Computer classroom • First day of class • Didn’t want to overwhelm them with technology • Didn’t want to assume any prior knowledge • Mostly interested in ‘exposure’ • Data • Variability • Modern data science • (a couple others along the way)

14. Step five: Scaffolding • “Hook” students into the activity • Start with learning goals • Start with definitions, new terms? • Start to build cognitive dissonance • Get them to ask the next question? • “Habits of mind” • Surprise students!

15. Step five: Scaffolding • From the table do you see any patterns or trends? • What additional information is important to consider? • What can you learn from the following plot?

16. Step five: Scaffolding • Absolute difference vs. percentage change • 1974: -17.14% Where is 1974? Why does it start in 1900? What do you learn from the graph?

17. Step five: Scaffolding • Other ways to compare 1974 to the other years? • Dotplot: • How does this graph compare to the timeplot? • How might you judge whether 1974 is unusual?

18. Step five: Scaffolding • Introduce descriptors: shape, center, variability • Introduce formulas for mean, standard deviation • Quick check of understanding • Use technology to create own graph • Dotplot vs. histogram • 1994-1995 data (1.74%) • Extension/Application • Investigate California, what year did CA repeal? • Causation? • Explore FARS website

19. Role of technology • Try to minimize unhelpful by-hand calculations • Standard deviation once? • Focus on comparing SD across distributions • Be very conscious of learning curve of technology • Added timeplot feature • Use technology to explore • Make more than one graph • Histogram bin width • Slider • Critique, Don’t use default settings • Discuss limitations (e.g., axis labels)

20. Step six: Test the activity! • Play the role of student • Read the questions fresh • Write out the answers (spacing, enough information, sequencing of ideas, reference) • Ask another faculty member to review • Ask a student to review • Use R readHTMLtable to scrape data from Wikipedia page

21. Step seven: Use the activity • Cross your fingers • Advance planning • Contingency plans • Be proactive in monitoring student progress • Make sure students realize what they are responsible for having learned from the activity • Not only fun and games • Resist repeating the lessons of the activity in lecture • Get students to tell you the big idea • Make sure students don’t miss the gorilla

22. Step eight: Make notes • Take 5-10 minutes to jot down notes to yourself (others?) on how the activity went • Where did students get stuck • Were students engaged in the context • How was the timing • What were the common questions • How does this tie into previous/upcoming content • What “props” do you need to remember to bring next time?

23. One of my favorite activities • Give students a copy of the Gettysburg Address and ask them to quickly circle 10 representative words • Sample vs. Population • Have students calculate the average length of their sample (statistic) • Pool student results together to create a dotplot of averages (sampling distribution) • Compare to the population mean (parameter) • Repeat with random samples of 5 words and compare the results

24. One of my favorite activities • Compare distributions • Move to technology, tweak inputs

25. One of my favorite activities • Common misconception: Role of population size

26. Evolution of the activity • Activity-Based Statistics (1996)

27. Workshop Statistics

29. Measurement: tip to tail

31. Statistical concepts • Population vs. sample, parameter vs. statistic • Bias, variability, precision • Random sampling, effect of sample size • Effect of population size • Sampling variability, sampling distribution, Central Limit Theorem (consequences and applicability)

32. Critiquing the activity • Did it make the best use of within vs. outside of class time? • Multi-tasking, prepared ways to collect data • Did it use real data? • Real scientific question? • Did it hook students? • Were students actively involved? • Were important statistical lessons clear? • Does it connect to other parts of the course? • Did it make effective use of technology? • Tactile simulation vs. black box • Learning curve • Is there a clear way of determining whether students ‘got it’?

33. Reminders • Active learning  Free-for-all • Find engaging contexts (e.g., data on students) • Elicit participation, prediction from students • Promote collaborative learning • Association  Causation • Get students to tell you the point • Provide lots of feedback • Follow-up with related assessments • Inter-mix with lecture, as needed • Do not underestimate the ability of activities to “teach” • Have fun!