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

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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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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
• AIMS Pedagogy: Bob
• Examine an activity: Andy
• AIMS Resources: Andy
• Evaluation: Bob
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
Materials Developed
• AIMS website (http://www.tc.umn.edu/~aims/)
• Lesson plans (28)
• Activities
• Suggested sequences of activities
• Compilation of research (DSSR book)
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)
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.
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.
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)
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
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
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
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.
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.
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.
Integrate Appropriate Technological Tools to Test Conjectures, Explore and Analyze Data

Simulation

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
• 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?
• 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.
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)
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)
Evaluation Results
• Student responses to the activities
• Overall student performance
• 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.
Thank You!
• Please check out and use our materials.

AIMS website (http://www.tc.umn.edu/~aims/)