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A flavor of the CATALST Course:Using randomization-based methods in an introductory statistics course              Elizabe...
Outline of Presentation•   Introduction to CATALST course•   Radical content•   Radical pedagogy•   Radical technology•   ...
Inspiration for CATALST   George Cobb (2005, 2007)"I argue that despite broad acceptance and rapid growth inenrollments, t...
Cooking in Introductory Statistics                         • CATALST teaches students to cook                           (i...
Radical Content• New sequence of topics; building ideas of inference  from first day• No t-tests; use of probability for s...
Randomization-Based curriculum• No z-tests or t-testsInstead, students:• Specify a model   – Random chance, or “no differe...
3 CATALST Units• Chance Models and Simulation• Models for Comparing Groups• Estimating Models Using Data
Radical Pedagogy• Student-centered approach based on research in  cognition and learning, instructional design principles•...
Example from aNon-Randomization-Based CourseA student takes a 50 question multiple choicetest with four options per questi...
Example from aNon-Randomization-Based Course
CATALST Example: Matching Dogsto Owners• Do dogs resemble their owners?• Research Question:
1. _____   1)2. _____   2)3. _____   3)           4)4. _____           5)5. _____6. _____   6)
1. _____     12. _____     33. _____     64. _____     55. _____     26. _____     4
Non-Randomization-Based Course Technology• Students use technology (e.g. StatCrunch, Minitab, graphing  calculator) to com...
Radical Technology• Focus of the course is simulation• TinkerPlots™ software is used• Unique visual (graphical interface) ...
Matching Dogs to OwnersBuilding the Model & Simulation
Radical Assessment• Frequent and varied assessment• Assess students’ ability to reason and think  statistically• Focus les...
CATALST Student Assessments• Homework  – Approximately 1 per in-class activity (15 in total)  – Reinforces ideas from the ...
Non-Randomization-Based Course Example Assessment Item• In order to set rates, an insurance company is trying to  estimate...
Assessments to Evaluate theCATALST Curriculum• GOALS (Goals and Outcomes Associated with  Learning Statistics)   – 27 forc...
Advantages ofRandomization-Based Curriculum• Does not require much math background• You can look at messier problems like ...
Disadvantages ofRandomization-Based Curriculum• Technology must be readily available in the  classroom• Students may still...
What We Have Learned• We can teach students to “cook”.• Based on interview and assessment data,  students seem to be think...
CATALST PublicationsGarfield, J., delMas, R. & Zieffler, A. (2012). Developing statistical   modelers and thinkers in an i...
Contact Information            jbg@umn.edu            Joan Garfield            http://www.tc.umn.edu/~catalst/
References• Cobb, G. (2005). The introductory statistics course: A saber tooth  curriculum? After dinner talk given at the...
Matching Dogs to OwnersBuilding the Model & Simulation
Matching Dogs to OwnersBuilding the Model & Simulation
Matching Dogs to OwnersBuilding the Model & Simulation
Matching Dogs to OwnersBuilding the Model & Simulation
Multiple Choice Example UsingRandomization                                                                                ...
CATALST intro stats course presentation at JMM 2013 (Elizabeth Fry, Laura Ziegler)
CATALST intro stats course presentation at JMM 2013 (Elizabeth Fry, Laura Ziegler)
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CATALST intro stats course presentation at JMM 2013 (Elizabeth Fry, Laura Ziegler)

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CATALST, an introductory statistics course, represents a sharp break from many statistics education traditions. Elizabeth Fry and Laura Ziegler describe its radical content, pedagogy, technology, and assessments as part of a panel discussion on randomization methods in the introductory course.

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CATALST intro stats course presentation at JMM 2013 (Elizabeth Fry, Laura Ziegler)

  1. 1. A flavor of the CATALST Course:Using randomization-based methods in an introductory statistics course Elizabeth Fry and Laura Ziegler CATALST Team: Joan Garfield, Andrew Zieffler, Robert delMas, Allan Rossman, Beth Chance, John Holcomb, George Cobb, Michelle Everson, Rebekah Isaak, & Laura Le Funded by NSF DUE-0814433
  2. 2. Outline of Presentation• Introduction to CATALST course• Radical content• Radical pedagogy• Radical technology• Student assessment• What we learned• Publications and references
  3. 3. Inspiration for CATALST George Cobb (2005, 2007)"I argue that despite broad acceptance and rapid growth inenrollments, the consensus curriculum is still an unwittingprisoner of history. What we teach is largely the technicalmachinery of numerical approximations based on the normaldistribution and its many subsidiary cogs. This machinery wasonce necessary, because the conceptually simpler alternativebased on permutations was computationally beyond our reach.Before computers statisticians had no choice. These days wehave no excuse. Randomization-based inference makes a directconnection between data production and the logic of inferencethat deserves to be at the core of every introductory course."
  4. 4. Cooking in Introductory Statistics • CATALST teaches students to cook (i.e., do statistics and think statistically) • The general “cooking” method is the exclusive use of simulation to carry out inferential analyses • Problems and activities require students to develop and apply this type of “cooking”Schoenfeld, A. H. (1998). Making mathematics and making pasta: Fromcookbook procedures to really cooking. In J. G. Greeno & S. Golman(Eds.), Thinking practices: A symposium on mathematics and sciencelearning (pp. 299-319). Hillsdale, NJ: Lawrence Erlbaum Associates.
  5. 5. Radical Content• New sequence of topics; building ideas of inference from first day• No t-tests; use of probability for simulation and modeling (TinkerPlots™)• A coherent curriculum that builds ideas of models, chance, simulated data• Immersion in statistical thinking• Textbook (Statistical Thinking: A Simulation Approach to Modeling Uncertainty) written for this course includes examples using real data
  6. 6. Randomization-Based curriculum• No z-tests or t-testsInstead, students:• Specify a model – Random chance, or “no difference” model• Randomize and Repeat – Simulate what would happen under the model and repeat many trials• Evaluate – Compare observed result to what is expected under the model
  7. 7. 3 CATALST Units• Chance Models and Simulation• Models for Comparing Groups• Estimating Models Using Data
  8. 8. Radical Pedagogy• Student-centered approach based on research in cognition and learning, instructional design principles• Minimal lectures, just-in-time as needed• Cooperative groups to solve problems• “Invention to learn” and “test and conjecture” activities (develop reasoning; promote transfer)• Writing; present reports; whole class discussionSchwartz, D. L., & Martin, T. (2004). Inventing to prepare for futurelearning: The hidden efficiency of encouraging original student productionin statistics instruction. Cognition and Instruction, 22(2),129- 184.
  9. 9. Example from aNon-Randomization-Based CourseA student takes a 50 question multiple choicetest with four options per question. She has notstudied for the test, but she gets a score of 54%.Is her performance on this test better than whatwould be expected if she was blindly guessing oneach question?
  10. 10. Example from aNon-Randomization-Based Course
  11. 11. CATALST Example: Matching Dogsto Owners• Do dogs resemble their owners?• Research Question:
  12. 12. 1. _____ 1)2. _____ 2)3. _____ 3) 4)4. _____ 5)5. _____6. _____ 6)
  13. 13. 1. _____ 12. _____ 33. _____ 64. _____ 55. _____ 26. _____ 4
  14. 14. Non-Randomization-Based Course Technology• Students use technology (e.g. StatCrunch, Minitab, graphing calculator) to compute p-value• The main purpose of technology is to help with calculations.
  15. 15. Radical Technology• Focus of the course is simulation• TinkerPlots™ software is used• Unique visual (graphical interface) capabilities – Allows students to see the devices they select (e.g., mixer, spinner) – Easily use these models to simulate and collect data – Allows students to visually examine and evaluate distributions of statisticsKonold, C., & Miller, C.D. (2005). TinkerPlots: Dynamic data exploration.[Computer software] Emeryville, CA: Key Curriculum Press.
  16. 16. Matching Dogs to OwnersBuilding the Model & Simulation
  17. 17. Radical Assessment• Frequent and varied assessment• Assess students’ ability to reason and think statistically• Focus less on computation and more on understanding of concepts
  18. 18. CATALST Student Assessments• Homework – Approximately 1 per in-class activity (15 in total) – Reinforces ideas from the in-class activities• Exams – 3 group exams – 2 individual exams• Final Exam – Basic knowledge: GOALS assessment (Goals and Outcomes Associated with Learning Statistics) – Statistical thinking: MOST assessment (Models of Statistical Thinking)
  19. 19. Non-Randomization-Based Course Example Assessment Item• In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at a large company take per year. A sample of 50 workers is randomly selected and the sample mean number of sick days is 4 days per year, with a sample standard deviation of 1.4 days. – Find a 95% confidence interval for the population mean number of sick days for full time workers at this company.• Students will compute a t-interval to answer this question.• One problem: We are estimating the average – but this may not be the best measure of center if distribution is skewed.
  20. 20. Assessments to Evaluate theCATALST Curriculum• GOALS (Goals and Outcomes Associated with Learning Statistics) – 27 forced-choice items – Items assess statistical reasoning in a first course in statistics• MOST (Models of Statistical Thinking) – 4 open-ended items that ask students to explain how they would set up and solve a statistical problem – 7 forced-choice follow-up items
  21. 21. Advantages ofRandomization-Based Curriculum• Does not require much math background• You can look at messier problems like Matching Dogs to Owners• Can make inferences about any statistic (e.g. median), not just limited to means and proportions• Fewer assumptions are required• Focus is on inference• Takes advantage of modern technology
  22. 22. Disadvantages ofRandomization-Based Curriculum• Technology must be readily available in the classroom• Students may still want or need to learn z- and t-proceduresHowever…• Many of our students bring laptops to class• Our students come from fields where they will not need to use z- and t- procedures
  23. 23. What We Have Learned• We can teach students to “cook”.• Based on interview and assessment data, students seem to be thinking statistically (even after only 6 class periods!)• We can change the content/pedagogy of the introductory college course.• We can use software at this level that is rooted in how students learn rather than purely analytical.
  24. 24. CATALST PublicationsGarfield, J., delMas, R. & Zieffler, A. (2012). Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course. ZDM: The International Journal on Mathematics Education.Ziegler, L. and Garfield, J. (in press) Exploring student understanding of randomness with an iPod shuffle activity. Teaching Statistics.Isaak, R., Garfield, J. and Zieffler, A. (in press). The Course as Textbook. Technology Innovations in Statistics Education.Garfield, J., Zieffler, A., delMas, R. & Ziegler, L. (under review). A New Role for Probability in the Introductory College Statistics Course. Journal of Statistics Education.delMas, R. , Zieffler, A. & Garfield, J. (under review). Tertiary Students Reasoning about Samples and Sampling Variation in the Context of a Modeling and Simulation Approach to Inference. Educational Studies in Mathematics.
  25. 25. Contact Information jbg@umn.edu Joan Garfield http://www.tc.umn.edu/~catalst/
  26. 26. References• Cobb, G. (2005). The introductory statistics course: A saber tooth curriculum? After dinner talk given at the United States Conference on Teaching Statistics.• Cobb, G. (2007). The introductory statistics course: A ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1). http://escholarship.org/uc/item/6hb3k0nz#page-1• Roy, M.M. & Christenfeld, N.J.S. (2004). Do dogs resemble their owners? Psychological Science, 15(5), 361-363.• Schoenfeld, A. H. (1998). Making mathematics and making pasta: From cookbook procedures to really cooking. In J. G. Greeno and S. V. Goldman (Eds.), Thinking practices in mathematics and science learning (pp. 299–319). Mahwah, NJ: Lawrence Erlbaum
  27. 27. Matching Dogs to OwnersBuilding the Model & Simulation
  28. 28. Matching Dogs to OwnersBuilding the Model & Simulation
  29. 29. Matching Dogs to OwnersBuilding the Model & Simulation
  30. 30. Matching Dogs to OwnersBuilding the Model & Simulation
  31. 31. Multiple Choice Example UsingRandomization Results of Sampler 1 Options Options Fastest Results of Sampl... Options Repeat Question Question <new> 70% 30% 50 0.2500 2 Right Right 3 Right Draw 1 4 Wrong Wrong 5 Wrong 0.7500 6 Wrong 7 Wrong Wrong Right Mixer Stacks Spinner Bars Curve Counter 8 Wrong QuestionHistory of Results of Sampler 1 Circle Icon Options 100% 0% 0% p < 0.001 (Using 1,000 trials) 0 5 10 15 20 25 30 35 40 45 50 55 60 percent_Question_Right Circle Icon

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