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

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Bob delMas, Joan Garfield, and Andy Zieffler### Aiming to Improve Students\' Statistical Reasoning: An Introduction to AIMS Materials

University of Minnesota

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

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?

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.

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

- Instructor advice to teachers

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.

Thank You!

- Please check out and use our materials.

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

- Please send us your feedback.

Joan Garfield: [email protected]

Bob delMas: [email protected]

Andy Zieffler: [email protected]

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