Upload
statisfactions
View
1.304
Download
0
Tags:
Embed Size (px)
DESCRIPTION
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.
Citation preview
A flavor of the CATALST Course:
Using randomization-based methods in an introductory
statistics course
Elizabeth Fry and Laura ZieglerCATALST 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
Outline of Presentation• Introduction to CATALST course• Radical content• Radical pedagogy• Radical technology• Student assessment• What we learned• Publications and references
"I argue that despite broad acceptance and rapid growth in enrollments, the consensus curriculum is still an unwitting prisoner of history. What we teach is largely the technical machinery of numerical approximations based on the normal distribution and its many subsidiary cogs. This machinery was once necessary, because the conceptually simpler alternative based on permutations was computationally beyond our reach. Before computers statisticians had no choice. These days we have no excuse. Randomization-based inference makes a direct connection between data production and the logic of inference that deserves to be at the core of every introductory course."
Inspiration for CATALST George Cobb (2005, 2007)
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: From cookbook procedures to really cooking. In J. G. Greeno & S. Golman (Eds.), Thinking practices: A symposium on mathematics and science learning (pp. 299-319). Hillsdale, NJ: Lawrence Erlbaum Associates.
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
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
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
• 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 discussion
Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2),129- 184.
Example from a Non-Randomization-Based CourseA student takes a 50 question multiple choice test with four options per question. She has not studied for the test, but she gets a score of 54%. Is her performance on this test better than what would be expected if she was blindly guessing on each question?
Example from a Non-Randomization-Based Course• Approach: Hypothesis testing
– H0: p = 0.25
– Ha: p > 0.25
• Check assumptions: np0 > 10 and n(1-p0) > 10
• Test statistic = = 4.75• Calculate p-value < 0.001• Conclude: Yes, the student is doing better
than random guessing.
CATALST Example: Matching Dogs to Owners
• Do dogs resemble their owners?• Research Question:
1. _____ 1)
2)2. _____
3. _____
4. _____
5. _____5)
4)
3)
6)6. _____
1. _____
2. _____
3. _____
4. _____
5. _____
6. _____
1
3
6
5
2
4
Non-Randomization-Based CourseTechnology• Students use technology (e.g. StatCrunch, Minitab, graphing calculator) to compute p-value
• The main purpose of technology is to help with calculations.
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 statistics
Konold, C., & Miller, C.D. (2005). TinkerPlots: Dynamic data exploration. [Computer software] Emeryville, CA: Key Curriculum Press.
Matching Dogs to OwnersBuilding the Model & Simulation
Radical Assessment
• Frequent and varied assessment• Assess students’ ability to reason and
think statistically • Focus less on computation and more on
understanding of concepts
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)
Non-Randomization-Based CourseExample 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.
Assessments to Evaluate the CATALST 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
Advantages of Randomization-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
Disadvantages of Randomization-Based Curriculum• Technology must be readily available in
the classroom• Students may still want or need to
learn z- and t-procedures However…• Many of our students bring laptops to
class• Our students come from fields where
they will not need to use z- and t- procedures
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.
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.
Contact Information
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 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
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 Using Randomization
Mixer Stacks Spinner Bars Curve Counter
Fastest Options
Draw1
Repeat50
Question
Right
0.2500
Wrong
0.7500
Results of Sampl... Options
Question <new>
2
3
4
5
6
7
8
Right
Right
Wrong
Wrong
Wrong
Wrong
Wrong
Results of Sampler 1 Options
Wrong Right
70% 30%
Question
Circle IconHistory of Results of Sampler 1 Options
0 5 10 15 20 25 30 35 40 45 50 55 60
100% 0% 0%
percent_Question_Right
Circle Icon
p < 0.001
(Using 1,000 trials)