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Aiming to Improve Students' Statistical Reasoning: An Introduction to AIMS Materials

Bob delMas, Joan Garfield, and Andy Zieffler University of Minnesota. Aiming to Improve Students' Statistical Reasoning: An Introduction to AIMS Materials. Overview of Webinar. Goals of AIMS: Joan Materials developed: Joan Research foundations and design principles: Bob

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Aiming to Improve Students' Statistical Reasoning: An Introduction to AIMS Materials

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  1. Bob delMas, Joan Garfield, and Andy Zieffler University of Minnesota Aiming to Improve Students' Statistical Reasoning: An Introduction to AIMS Materials

  2. Overview of Webinar • Goals of AIMS: Joan • Materials developed: Joan • Research foundations and design principles: Bob • AIMS Pedagogy: Bob • Examine an activity: Andy • AIMS Resources: Andy • Evaluation: Bob

  3. Goals of AIMS • Integrate and adapt innovative materials developed for introductory statistics • Develop lesson plans and activities for important topics • Focus on developing statistical literacy and reasoning (see GAISE; http://www.amstat.org/education/gaise/) • Build materials on important instructional design principles

  4. Materials Developed • AIMS website (http://www.tc.umn.edu/~aims/) • Lesson plans (28) • Activities • Suggested sequences of activities • Compilation of research (DSSR book)

  5. Research Foundations • Research related to important statistical ideas (e.g., distribution, variability) • Research on use of technology, cooperative learning, assessment • Pedagogy implied by Instructional Design Principles (Cobb and McClain, 2004)

  6. Instructional Design Principles • Focus on developing central statistical ideas rather than on presenting set of tools and procedures. • Use real and motivating data sets to engage students in making and testing conjectures. • Use classroom activities to support the development of students’ reasoning.

  7. Instructional Design Principles • Integrate the use of appropriate technological tools that allow students to test their conjectures, explore and analyze data, and develop their statistical reasoning. • Promote classroom discourse that includes statistical arguments and sustained exchanges that focus on significant statistical ideas. • Use assessment to learn what students know and to monitor the development of their statistical learning as well as to evaluate instructional plans and progress.

  8. AIMS Pedagogy • Student centered • Emphasis on discussion (small and large group) • Discovery of concepts through activities • Use of technology throughout class (Fathom, web applets, Sampling Sim) • Simulation, data analysis, modeling • Use of student data (first day survey; body measurement data)

  9. Examine an Activity • Sampling Reese’s Pieces • Adapted from great activity by Rossman and Chance (Workshop Statistics) • Adapted lesson to align with the six instructional design principles

  10. AIMS Reese’s Pieces Activity • Guess the proportion of each color in a bag: • Make a conjecture: Pretend data for 10 students if each took samples of 25 Reese’s Pieces candies. • Take a sample of candies and see the proportion of orange candies, make a second conjecture

  11. AIMS Reese’s Pieces Activity • If you took a sample of 25 Reese’s Pieces candies and found that you had only 5 orange candies, would you be surprised? Is 5 an unusual value? • Discussion of class data • Simulation, using web applet at http://www.rossmanchance.com • Discussion of results

  12. Focus on Developing Central Statistical Ideas Student Goals for the Lesson: • Understand variability between samples (how samples vary). • Build and describe distributions of sample statistics (in this case, proportions). • Understand the effect of sample size on how well a sample resembles a population, and the variability of the distribution of sample statistics. • Understand what changes (samples and sample statistics) and what stays the same (population and parameters). • Understand and distinguish between the population, the samples, and the distribution of sample statistics.

  13. Use Real and Motivating Data Sets • Students take physical samples of Reese’s Pieces candies and construct distributions of sample proportions. • Students simulate data based on population estimates.

  14. Use Activities to Support Development of Reasoning • Simulation helps students reason about sampling variability and factors affecting variability. (e.g., What happens if sample size is 10? 100?) • Helps develop informal reasoning about p-value and statistical inference.

  15. Integrate Appropriate Technological Tools to Test Conjectures, Explore and Analyze Data Simulation

  16. Promote Classroom Discourse • Students compare and explain their conjectures • Students argue for different interpretations of a surprising value (for a sample statistic) • Students describe the predictable patterns they see as simulations are repeated with larger sample sizes

  17. Use Assessment to Monitor Development of Statistical Learning • Discuss the use of a model to simulate data, and the value of simulation in allowing us to determine if a sample value is surprising (e.g., 5 orange candies in a cup of 25 candies). So, should I complain if I get a bag with only 20% orange? How would I give evidence to support this answer?

  18. Use Assessment to Monitor Development of Statistical Learning • A certain manufacturer claims that they produce 50% brown candies. Sam plans to buy a large family size bag of these candies and Kerry plans to buy a small fun size bag. Which bag is more likely to have more than 70% brown candies? • Sam’s large family size bag. • Kerry’s small fun size bag. • Both bags are equally likely to have more than 70% brown candies. • Explain.

  19. AIMS Resources • AIMS website (http://www.tc.umn.edu/~aims/) • Lesson and lesson plans • Sequences of ideas and activities • Technology tools used • The new book by Garfield and Ben-Zvi (provides research foundations for lessons)

  20. AIMS Evaluation • Student evaluations (midterm feedback, end of course surveys) • AIMS student survey (Rob) • Class observations (Rob) • Instructor interviews (Rob) • Student Assessments (midterm, final, START)

  21. Evaluation Results • Student responses to the activities • Overall student performance • Instructor advice to teachers

  22. Advice From AIMS Instructors • Trust the Structure. Don't give the students everything – facilitate! • Don't be afraid! Trust the students to explore. Force them to work together. Have fun. • Don't guide too much or give direct answers. Expect the students to say off-the-wall things, but trust that the conversation will lead to the desired conclusion.

  23. Thank You! • Please check out and use our materials. AIMS website (http://www.tc.umn.edu/~aims/) • Please send us your feedback. Joan Garfield: jbg@umn.edu Bob delMas: delma001@umn.edu Andy Zieffler: zief0002@umn.edu

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