- Количество слайдов: 77
Debating the next BIG thing in teaching statistics Allan Rossman, Beth Chance Cal Poly – San Luis Obispo
Overview n Goals q Stimulate thought and discussion n n q n Five propositions as to what the next BIG thing is About undergraduate, introductory statistics Set stage for breakout sessions, other plenaries Inspiration q “Nothing tunes the neurons like disagreement. ” -- David Moore
Overview (cont. ) n Disclaimers: q q 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
THE NEXT BIG THING IN TEACHING STATISTICS WILL BE Removing the letters z and t from introductory courses
Elimination of letters z and t n Not literally! We can’t advertise our discipline as S_A_IS_ICS n We mean the elimination of normal-based (zand t-) significance tests and confidence intervals from the introductory course
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)
Arguments for such a curriculum n n n 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
Many have taken up Cobb’s challenge n NSF-funded curriculum development projects q q Rossman, Chance, Holcomb, Cobb (CSI) West and Woodard Gould et al (UCLA) Garfield, del. Mas, Zieffler, et al (CATALST)
More have taken up Cobb’s challenge n Full implementations q Tintle et al (Hope College) n n q Hamrick et al (Rhodes College) n q q March 2011 JSE article Textbook project 2011 JSM panel discussion Lock 5 textbook project Tabor and Franklin, Statistical Reasoning in Sports
BUT … Simple and easily grasped? !? n n Our assessment results have been mixed Many students struggle with reasoning process even after multiple activities q Pre-requisite knowledge? n q Model, distribution, “random, ” simulation Biggest sticking points n n n Seeing the big picture of why doing this Realizing/appreciating that simulation assumes null model to be true Understanding why look beyond observed result
Granted … n Student performance may improve with full integration throughout curriculum, complete materials/textbook
BUT… This has been tried before … n Wardrop, Statistics: Learning in the Presence of Variation (1994) q q q n Simulation based Early exposure to inference Normal based methods don’t appear until last 1/3 This approach did not catch on q q Ahead of its time? Not viable for publishers?
BUT… n Students still want to learn z- and tprocedures q n Many find comfort, familiarity in the (apparent) exactness of normal probability calculations Students still need to learn z- and tprocedures q q Those procedures still dominate statistical practice in other fields And will continue to do so?
Although… n Randomization methods are become more widely used and accepted not only in statistics but also in client disciplines q Manly, Randomization, Bootstrap, and Monte Carlo Methods in Biology, 3 rd ed. , 2006
More discussion: Randomization curriculum n Breakout sessions q q q n 11 am today (panel discussion on implementation) 3 pm today (Lock and Lock: bootstrapping and randomization) 11 am tomorrow (Lock, and Lock: technology demonstrations) Technology demo q 4: 30 pm today (West, Stat. Crunch)
THE NEXT BIG THING IN TEACHING STATISTICS WILL BE Students entering introductory college courses with considerable knowledge of statistics
Students will know lots of statistics n Common Core State Standards Initiative q q q 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
Common Core – Mathematical Practice Standards n Foster reasoning and sense-making in mathematics Reason abstractly and quantitatively q Construct viable arguments and critique the reasoning of others q Model with mathematics q Use appropriate tools strategically [technology] q
Common Core – Statistical Concepts n 6 th grade: q q n 7 th grade: q n Develop understanding of statistical variability Summarize and describe distributions Investigate chance processes and develop, use, and evaluate probability models High school: q q Using probability to make decisions Making inferences and justifying conclusions
Can you imagine students who? n Have already mastered q q n Variability Distribution Sampling, Experimentation Statistical Inference Have been consistently asked to q q Critique Reason Model Use technology
Jerry Moreno’s perfect world n “In 7 years or so, STATS 101 has been revised so to excite the CC student by: q q 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
What could we do with such students? n n 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) n Bayesian methods, decision theory (e. g. , Stewart plenary talk) n Computing, visualization tools (e. g. , Nolan and Lang, 2010) n Data dialogues (e. g. , Pfannkuch et al, 2010)
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
BUT … Alternative standards n n n Design and conduct statistical experiment, interpret and communicate outcomes Construct and draw inferences from graphs Understand apply measures of center, variability, association Use curve fitting for predictions Apply transformations of data
BUT … Alternative standards (cont. ) n n 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
BUT … What’s the point? n These alternative standards are modest than Common Core q q n 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 q Have we substantially changed content of Stat 101 in past 22 years based on students’ achieving these standards?
Granted… n Common Core has a lot more political might, buy-in from important stakeholders q Much higher probability of impact
BUT … Another big concern n Preparing current and future teachers to implement such a curriculum is a big challenge q q Need considerable professional development for current teachers Need to substantially re-think teacher preparation for prospective teachers
More discussion: Common Core n Breakouts q q 11 am today (Starnes: AP Stats, Nspire CX, and Common Core) 11 am tomorrow (Scheaffer and Franklin: K-16 Common Core)
THE NEXT BIG THING IN TEACHING STATISTICS WILL BE The disappearance of print textbooks
Let’s acknowledge n Students don’t read textbooks q q q n 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” q Very comfortable looking to internet, Wikipedia as reference
Example data n Students more highly value instructors’ notes, instructor-driven decisions q 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
More importantly n Print textbooks aren’t dynamic enough to support learning q Can’t evaluate a student response and provide guiding comments q Not conducive to allowing students to work non-linearly n Can’t easily jump around to what they need Examples can become outdated very quickly q Can’t adapt to student interests on the fly q
Instead? n n n n 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
Some examples n n Activ. Stats, Cyber. Stats, SOCR, Hyper. Stat Carnegie Mellon’s Open Learning Initiative The Open University (U. K. ) Publisher learning systems q Stats. Portal (Exhibitor Test-Drive), Wiley. Plus, …
BUT … n What technology innovation has had the greatest impact on education? q Printing press!
BUT … n n n 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 q n n 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!
Compromise? n What’s needed is access to plethora of resources for instructor/student to pick and choose from q n Not one (extra large) size (print textbook) fits all And then q q q Server-side database maintaining individualized interactive student texts Add notes to e. Book in class Submission of work for instructor-embedded feedback
THE NEXT BIG THING IN TEACHING STATISTICS WILL BE Online and hybrid courses replacing face-to-face interactions among students/students and instructor
No more face-to-face classes n With all of these multimedia materials, why do we require students to q q q n 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? q Students at Cal Poly typically avoid Friday classes
More interaction? n n Some students interact better online, overcome reluctance to participate in person On-line office hours, whiteboards q n e. g. , elluminate Calibrated-peer-review model
Growing popularity and importance n Class Differences: Online Education in the United States 2010 (Sloan Consortium) q q q 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.
Economics! n n 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) q q 438, 000 students in 2010 Largest private university in U. S.
Comparison of student performance n “On average, students in online learning conditions performed better than those receiving face-to-face instruction. ” q Evaluation of Evidence-Based Practices in Online Learning: A Meta-Analysis and Review of Online Learning Studies, U. S. Department of Education, September 2010
BUT 50 years ago … n n 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!
BUT 50 years ago… “In the early and mid 1960 s, 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)
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)
Granted … n n 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
BUT … n “Social interaction plays a fundamental role in the process of cognitive development” (Vygotsky) q q q 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?
Compromise? q Different model for face-to-face classes n n q 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 n n “Inverted Classroom” (e. g. , Mazur; Lage, Platt, Treglia) “Statistical Reasoning Learning Environment” (e. g. , Garfield & Ben-Zvi, 2008)
More Discussion: Online Teaching n Breakouts q q 11 am today (Fairborn and Zeitler: Transition to Online Teaching) 11 am tomorrow (Everson and Miller: Social Media)
THE NEXT BIG THING IN TEACHING STATISTICS WILL BE Curriculum and pedagogy decisions will be grounded in educational research
Statistics Education Research n May still be in its infancy as a discipline q n But has enjoyed a tremendous growth spurt! Journal of Statistics Education q q Founded at N. C. State in 1993 Nearing its 20 th anniversary Publishing high-quality, rigorously refereed scholarship Including more and more research articles
More statistics education research n Statistics Education Research Journal q q n Nearing its 10 th anniversary (launched 2002) Publishing exclusively research articles in statistics education Ph. D. Dissertations q IASE website lists 70 Ph. D. dissertations in statistics education since 2000 n n q q 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
More statistics education research n Models of Qualitative and Quantitative methods q q 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)
More statistics education research n CAUSE q Research Advisory Board n q Led by Joan Garfield sinception of CAUSE Research Clusters n n n 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
Connecting Research to Practice? n JSE has a new feature titled “From Research to Practice” n Garfield and Ben-Zvi, Developing Students’ Statistical Reasoning: Connecting Research to Practice, Springer, 2008.
Example – The Statistics Pathway (Carnegie Foundation, Dana Center) n n 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
n Design of Statway curriculum, materials, teaching routines is evidence-driven Based on hypotheses grounded in ed, math ed and stat ed research, practitioner experience q Hypotheses tested and refined as Statway is implemented by community college faculty q Revisions guided by evidence of student learning, experiences of faculty implementers q Eliciting diverse sources of expertise n Building on open source materials n
BUT… n n 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: q q q Understand concept Apply relevant procedure to real data Interpret results Draw appropriate scope of conclusions Explain impact of various factors such as group sizes
BUT I have to decide… n Which method to present first? Which to present at all? q n n 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 …?
OK, simulation. So now have to decide: n Start with tactile simulation or technology? q q n Choice of dataset q n Which technology to use? Should students design own simulations or press buttons? Real or realistic? Randomized experiment or independent random samples or neither? Significant difference or non-significant? Choice of test statistic q Difference in success proportions or number of successes in group A or relative risk or odds ratio or …?
Still more decisions n n How many examples to present? With what characteristics? How to assess student learning to guide learning? q Group quiz, individual quiz, homework assignment, mini-project, multiple choice questions, …?
BUT … n Not many research studies in statistics education compare several options and try to identify the most effective q n 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 q Decisions instructors make every single day
BUT … Another big hurdle n College faculty members as a group are very resistant to change q n College faculty members as a group do not like to be told what to do q n Yes, we’ve said this before Even when that advice is based on rigorous educational research College faculty members are often skeptical of education research q Especially qualitative research
Compromise? n Research can continue to establish general principles q n Instructors can be trained to use their judgment on how to apply them in their particular setting q n For example, active is better than passive learning And given the freedom to do so Develop and support more teacher-scholars in statistics education
More Discussion: Statistics Education Research n n n Statway: Kristen Bishop, Dana Center Plenary: Bob del. Mas Breakouts: q q q 11 am today (Zieffler & Mvududu: Qualitative methods) 3 pm today (Lovett: Qualitative data) 11 am tomorrow (Hilton and Enders: Conceptual framework)
Let’s Review n Eliminating z and t has potential q n Future students will know more statistics before college q n But not a magic bullet So we need to get prepared Textbooks aren’t going away q But instructors need better access to plethora of open-source, collaborative resources
Let’s Review n Online learning, multimedia resources will continue to gain in popularity & accessibility q n Research can lead to more effective curriculum and pedagogy q n Opportunity to change classroom experience Needs to be closely tied to teaching practice For more debate q Breakout 11 am today (Peck)
So… n n n Focus more logic of inference Students will come in knowing statistics Textbooks need to change Have more interactive class sessions Learn from the research Many of these ideas are not so new…
Why BIG now and not before? n n 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 q n n Including specific to statistics More buy in, alignment of stars More insights: Pearl dinner presentation
Take Home Message n Engage students n Persist in face of resistance n Break shackles n Enjoy the conference!