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Overview. GoalsStimulate thought and discussionFive propositions as to what the next BIG thing isAbout undergraduate, introductory statisticsSet stage for breakout sessions, other plenariesInspiration
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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. The next BIG thing in teaching statistics will be Removing the letters z and t from introductory courses
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. The next BIG thing in teaching statistics will be Students entering introductory college courses with considerable knowledge of statistics
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 next BIG thing in teaching statistics will be The disappearance of print textbooks
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. The next BIG thing in teaching statistics will be Online and hybrid courses replacing face-to-face interactions among students/students and instructor
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 …
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)
51. BUT 50 years ago… “It's very likely that a course taught on television, because of the careful preparation, will be better organized lecture by lecture than the usual lecture in class, but it does have a lack of flexibility…. The idea that certain materials can be expressed better in a tv session seemed to me to be right, and still can be right. I think that the expanded ability to produce material that has more visual content than anything we were able to put together adds a lot more interest to the course.” -- Fred Mosteller (1993)
52. Granted … Online courses have great potential for interactivity that televised courses do not
But in some (many?) online courses the instructor merely delivers information passively to students
53. BUT … “Social interaction plays a fundamental role in the process of cognitive development” (Vygotsky)
Granted, today’s students are very comfortable with socializing online
But our sense, and our own experience, is that (synchronous) face-to-face discussions can be much more efficient and productive than working (asynchronously) online
Is there something special about face-to-face social interaction with regard to learning?
54. Compromise? Different model for face-to-face classes
Students complete background reading/ podcast with guided questions, drill and practice prior to attending class (literacy)
Class time is spent working examples, presenting solutions, asking questions (of other students and instructor), teamwork, peer instruction
Examples
“Inverted Classroom” (e.g., Mazur; Lage, Platt, Treglia)
“Statistical Reasoning Learning Environment” (e.g., Garfield & Ben-Zvi, 2008)
55. More Discussion: Online Teaching Breakouts
11am today (Fairborn and Zeitler: Transition to Online Teaching)
11am tomorrow (Everson and Miller: Social Media)
56. The next BIG thing in teaching statistics will be Curriculum and pedagogy decisions will be grounded in educational research
57. Statistics Education Research May still be in its infancy as a discipline
But has enjoyed a tremendous growth spurt!
Journal of Statistics Education
Founded at N.C. State in 1993
Nearing its 20th anniversary
Publishing high-quality, rigorously refereed scholarship
Including more and more research articles
58. More statistics education research Statistics Education Research Journal
Nearing its 10th anniversary (launched 2002)
Publishing exclusively research articles in statistics education
Ph.D. Dissertations
IASE website lists 70 Ph.D. dissertations in statistics education since 2000
Including many from researchers here today
Probably many more not listed there
U of Minnesota Ph.D. program in Statistics Education (8 students in fall)
Ph.D. program to be developed at U of Georgia
59. More statistics education research Models of Qualitative and Quantitative methods
Using statistics effectively in mathematics education research (ASA, 2007)
SRTL Research forums
SERJ special issue (Nov, 2010)
Second Handbook of Research on Mathematics Teaching and Learning (Lester, 2007)
60. More statistics education research CAUSE
Research Advisory Board
Led by Joan Garfield since inception of CAUSE
Research Clusters
2007-09: 3 clusters with 11 participants
2009-11: 3 clusters with 12 participants
Grant proposals, journal articles and presentations at national and international conferences
61. Connecting Research to Practice? JSE has a new feature titled “From Research to Practice”
Garfield and Ben-Zvi, Developing Students’ Statistical Reasoning: Connecting Research to Practice, Springer, 2008.
62. Example – The Statistics Pathway (Carnegie Foundation, Dana Center) Development of one-year curriculum in statistics, data analysis and quantitative reasoning for developmental math students equivalent to one-semester college course
Collaboration of representatives of several professional organizations, statistics educators (2 and 4 year), developmental mathematics educators (2 year), researchers, and designers, access to policy makers
63. Design of Statway curriculum, materials, teaching routines is evidence-driven
Based on hypotheses grounded in ed, math ed and stat ed research, practitioner experience
Hypotheses tested and refined as Statway is implemented by community college faculty
Revisions guided by evidence of student learning, experiences of faculty implementers
Eliciting diverse sources of expertise
Building on open source materials
64. BUT… Statistics education research can provide sound principles, but think about how many decisions instructors make on a daily basis
Example: Statistical significance for 2×2 tables
Learning Goals:
Understand concept
Apply relevant procedure to real data
Interpret results
Draw appropriate scope of conclusions
Explain impact of various factors such as group sizes
65. BUT I have to decide… Which method to present first? Which to present at all?
Simulate randomization test, Fisher’s exact test, Two-proportion z-test, Chi-square test
Describe method first, or try to ask questions to lead students to suggest method?
Present example through lecture, or guided activity, or on-their-own activity or …?
66. OK, simulation. So now have to decide: Start with tactile simulation or technology?
Which technology to use?
Should students design own simulations or press buttons?
Choice of dataset
Real or realistic? Randomized experiment or independent random samples or neither? Significant difference or non-significant?
Choice of test statistic
Difference in success proportions or number of successes in group A or relative risk or odds ratio or …?
67. Still more decisions How many examples to present? With what characteristics?
How to assess student learning to guide learning?
Group quiz, individual quiz, homework assignment, mini-project, multiple choice questions, …?
68. BUT … Not many research studies in statistics education compare several options and try to identify the most effective
With sufficient replication for results to be generalizable
Not feasible to ask for research studies in such a young field to address all of these small decisions
Decisions instructors make every single day
69. BUT … Another big hurdle College faculty members as a group are very resistant to change
Yes, we’ve said this before
College faculty members as a group do not like to be told what to do
Even when that advice is based on rigorous educational research
College faculty members are often skeptical of education research
Especially qualitative research
70. Compromise? Research can continue to establish general principles
For example, active is better than passive learning
Instructors can be trained to use their judgment on how to apply them in their particular setting
And given the freedom to do so
Develop and support more teacher-scholars in statistics education
71. More Discussion: Statistics Education Research Statway: Kristen Bishop, Dana Center
Plenary: Bob delMas
Breakouts:
11am today (Zieffler & Mvududu: Qualitative methods)
3pm today (Lovett: Qualitative data)
11am tomorrow (Hilton and Enders: Conceptual framework)
72. Let’s Review Eliminating z and t has potential
But not a magic bullet
Future students will know more statistics before college
So we need to get prepared
Textbooks aren’t going away
But instructors need better access to plethora of open-source, collaborative resources
73. Let’s Review Online learning, multimedia resources will continue to gain in popularity & accessibility
Opportunity to change classroom experience
Research can lead to more effective curriculum and pedagogy
Needs to be closely tied to teaching practice
For more debate
Breakout 11am today (Peck)
74. So… Focus more logic of inference
Students will come in knowing statistics
Textbooks need to change
Have more interactive class sessions
Learn from the research
75. Why BIG now and not before? Improved technology and understanding of how to use technology for good
More availability and appreciation of data
Students are changing
Better understanding of student learning
Including specific to statistics
More buy in, alignment of stars
More insights: Pearl dinner presentation
76. Take Home Message Engage students
Persist in face of resistance
Break shackles
Enjoy the conference!
77. Thanks very much! arossman@calpoly.edu
bchance@calpoly.edu