Debating the next BIG thing in teaching statistics

1. Debating the next BIG thing in teaching statistics Allan Rossman, Beth Chance Cal Poly – San Luis Obispo

2. Overview • Goals • Stimulate thought and discussion • Five propositions as to what the next BIG thing is • About undergraduate, introductory statistics • Set stage for breakout sessions, other plenaries • Inspiration • “Nothing tunes the neurons like disagreement.” -- David Moore

3. Overview (cont.) • Disclaimers: • We’re not experts on any of these topics • We don’t have sufficient time to do justice to any of these propositions • We’ll give some unsubstantiated opinions • We don’t even necessarily agree with some of the positions we’ll espouse

4. Removing the letters z and t from introductory courses The next BIG thing in teaching statistics will be

5. Elimination of letters z and t • Not literally! We can’t advertise our discipline as S_A_IS_ICS • We mean the elimination of normal-based (z- and t-) significance tests and confidence intervals from the introductory course

6. Motivation “Ptolemy’s cosmology was needlessly complicated, because he put the earth at the center of his system, instead of putting the sun at the center. Our curriculum is needlessly complicated because we put the normal distribution, as an approximate sampling distribution for the mean, at the center of our curriculum, instead of putting the core logic of inference at the center.” – George Cobb (TISE, 2007)

7. Arguments for such a curriculum • Randomization model is simple and easily grasped • Randomization model ties data collection process to inference technique to scope of conclusion • Easily generalizeable to other statistics, other designs • Takes advantage of modern computing • Truer to Fisher’s vision of inference

8. Many have taken up Cobb’s challenge • NSF-funded curriculum development projects • Rossman, Chance, Holcomb, Cobb (CSI) • West and Woodard • Gould et al (UCLA) • Garfield, delMas, Zieffler, et al (CATALST)

9. More have taken up Cobb’s challenge • Full implementations • Tintle et al (Hope College) • March 2011 JSE article • Textbook project • Hamrick et al (Rhodes College) • 2011 JSM panel discussion • Lock5 textbook project • Tabor and Franklin, Statistical Reasoning in Sports

10. BUT …

11. BUT … Simple and easily grasped?!? • Our assessment results have been mixed • Many students struggle with reasoning process even after multiple activities • Pre-requisite knowledge? • Model, distribution, “random,” simulation • Biggest sticking points • Seeing the big picture of why doing this • Realizing/appreciating that simulation assumes null model to be true • Understanding why look beyond observed result

12. Granted … • Student performance may improve with full integration throughout curriculum, complete materials/textbook

13. BUT… This has been tried before … • Wardrop, Statistics: Learning in the Presence of Variation (1994) • Simulation based • Early exposure to inference • Normal based methods don’t appear until last 1/3 • This approach did not catch on • Ahead of its time? • Not viable for publishers?

14. BUT… • Students still want to learn z- and t-procedures • Many find comfort, familiarity in the (apparent) exactness of normal probability calculations • Students still need to learn z- and t-procedures • Those procedures still dominate statistical practice in other fields • And will continue to do so?

15. Although… • Randomization methods are become more widely used and accepted not only in statistics but also in client disciplines • Manly, Randomization, Bootstrap, and Monte Carlo Methods in Biology, 3rd ed., 2006

16. More discussion: Randomization curriculum • Breakout sessions • 11am today (panel discussion on implementation) • 3pm today (Lock and Lock: bootstrapping and randomization) • 11am tomorrow (Lock, Lock, and Lock: technology demonstrations) • Technology demo • 4:30pm today (West, StatCrunch)

17. Students entering introductory college courses with considerable knowledge of statistics The next BIG thing in teaching statistics will be

18. Students will know lots of statistics Common Core State Standards Initiative State-led effort coordinated by National Governors Association and Council of Chief State School Officers, released 6/2/2010 Standards define the knowledge and skills students should have within their K-12 education careers Currently adopted by 42 states Two assessment consortia (testing in 2014-15) www.corestandards.org

19. Common Core – Mathematical Practice Standards • Foster reasoning and sense-making in mathematics • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically [technology]

20. Common Core – Statistical Concepts • 6th grade: • Develop understanding of statistical variability • Summarize and describe distributions • 7th grade: • Investigate chance processes and develop, use, and evaluate probability models • High school: • Using probability to make decisions • Making inferences and justifying conclusions

21. Can you imagine students who? • Have already mastered • Variability • Distribution • Sampling, Experimentation • Statistical Inference • Have been consistently asked to • Critique • Reason • Model • Use technology

22. Jerry Moreno’s perfect world • “In 7 years or so, STATS 101 has been revised so to excite the CC student by: • Beginning the course with several real world projects/case studies that review/address/ challenge the content and mathematical practice base of CC statistically literate students; • Continuing the course with topics such as: Normal theory inference; risk analysis; design of experiments/clinical trials; anova;….” -- CAUSE webinar, May 2011

23. What could we do with such students? Mean vs. median? Risk analysis (e.g., Utts, 2010) Multivariate modeling (e.g., Kaplan, 2009) Large, complex data sets, data mining (e.g., Gould plenary talk) Bayesian methods, decision theory (e.g., Stewart plenary talk) Computing, visualization tools (e.g., Nolan and Lang, 2010) Data dialogues (e.g., Pfannkuch et al, 2010)

24. Essential (and cool!) skills … “I keep saying that the sexy job in the next 10 years will be statisticians. And I’m not kidding. Now we really do have essentially free and ubiquitous data. So the complimentary scarce factor is the ability to understand that data and extract value from it. -- Hal Varian, Chief Economist, Google

25. BUT …

26. BUT … Alternative standards Design and conduct statistical experiment, interpret and communicate outcomes Construct and draw inferences from graphs Understand and apply measures of center, variability, association Use curve fitting for predictions Apply transformations of data

27. BUT … Alternative standards (cont.) Understand sampling and recognize its role in statistical claims Use simulation to estimate probabilities Create and interpret discrete probability distributions Use properties of normal curve to answer questions about relevant data

28. BUT … What’s the point? These alternative standards are more modest than Common Core Perhaps more realistic to attain? But could still require a fundamental change in content of introductory college courses 1989 NCTM Curriculum and Evaluation Standards for School Mathematics Have we substantially changed content of Stat 101 in past 22 years based on students’ achieving these standards?

29. Granted… • Common Core has a lot more political might, buy-in from important stakeholders • Much higher probability of impact

30. BUT … Another big concern Preparing current and future teachers to implement such a curriculum is a big challenge Need considerable professional development for current teachers Need to substantially re-think teacher preparation for prospective teachers

31. More discussion: Common Core • Breakouts • 11am today (Starnes: AP Stats, Nspire CX, and Common Core) • 11am tomorrow (Scheaffer and Franklin: K-16 Common Core)

32. The disappearance of print textbooks The next BIG thing in teaching statistics will be

33. Let’s acknowledge • Students don’t read textbooks • See textbooks as a (very expensive!) repository of homework problems • Perhaps also skim examples hoping to mimic for homework problems • Students don’t keep textbooks as reference • Today’s students are “digital natives” • Very comfortable looking to internet, Wikipedia as reference

34. Example data • Students more highly value instructors’ notes, instructor-driven decisions • How useful did you find the following learning aids/materials in helping you understand statistics? (77-78 responses) 1 = Not helpful, 5 = Most helpful, skip the question if you did not use the resource consistently

35. More importantly Print textbooks aren’t dynamic enough to support learning Can’t evaluate a student response and provide guiding comments Not conducive to allowing students to work non-linearly Can’t easily jump around to what they need Examples can become outdated very quickly Can’t adapt to student interests on the fly

36. Instead? • Integration of hot-off-the-press case studies • Adaptable presentation • Interactive demonstrations • Optional drill and practice • Immediate individualized feedback • Flexibility in timing and presentation • Replayable podcasts • Interactive online surveys

37. Some examples • ActivStats, CyberStats, SOCR, HyperStat • Carnegie Mellon’s Open Learning Initiative • The Open University (U.K.) • Publisher learning systems • StatsPortal (Exhibitor Test-Drive), WileyPlus, …

38. BUT … What technology innovation has had the greatest impact on education? Printing press!

39. BUT … • Books have had huge impact on education • Textbooks maintain firm hold on U.S. higher education • College faculty members (as a group) are very resistant to change • Some of these multimedia materials have been around for a while and have not taken over the world • Even if the use of print textbooks lessens considerably in the next few years … • Print textbooks are not going away!

40. Compromise? • What’s needed is access to plethora of resources for instructor/student to pick and choose from • Not one (extra large) size (print textbook) fits all • And then • Server-side database maintaining individualized interactive student texts • Add notes to eBook in class • Submission of work for instructor-embedded feedback

41. Online and hybrid courses replacing face-to-face interactions among students/students and instructor The next BIG thing in teaching statistics will be

42. No more face-to-face classes • With all of these multimedia materials, why do we require students to • Sit in (uncomfortable) seats • At the same place at the same time • Often without access to any resources beyond paper and pencil? • Why not let students work at their own pace, using technology, when it’s convenient? • Students at Cal Poly typically avoid Friday classes

43. More interaction? • Some students interact better online, overcome reluctance to participate in person • On-line office hours, whiteboards • e.g., elluminate • Calibrated-peer-review model

44. Growing popularity and importance • Class Differences: Online Education in the United States 2010 (Sloan Consortium) • 63% of reporting institutions said online learning was a critical part of their long term strategy, compared to 59% in 2009 • Nearly 30% of U.S. higher education students took at least one online course in 2009, compared to 20% in 2006, 10% in 2002 • Many more institutions reported seeing an increase in demand for online courses and programs than for face-to-face.

45. Economics! Online courses do not compete for scarce classroom space “Across the country, traditional colleges are struggling, but for-profit schools such as the University of Phoenix are experiencing tremendous growth.” Moneywatch (2010) 438,000 students in 2010 Largest private university in U.S.

46. Comparison of student performance • “On average, students in online learning conditions performed better than those receiving face-to-face instruction.” • Evaluation of Evidence-Based Practices in Online Learning: A Meta-Analysis and Review of Online Learning Studies, U.S. Department of Education, September 2010

47. BUT

48. BUT 50 years ago … • Another exciting new technological marvel was predicted to replace face-to-face class meetings between instructor and students • Frederick Mosteller pioneered the teaching of statistics via … TELEVISION!

50. BUT 50 years ago… “In the early and mid 1960s, television was the great technological hope. Here is a quote from Time magazine: ‘Not only is a taped professor as informative as a live one, but he seldom turns sour and never grows weary of talking.’ There was actually a feeling that taped teaching by master teachers would replace live teachers on campus as well as taking advantage of the reach of broadcast television.” -- David Moore (1993)