Aiming to Improve Students' Statistical Reasoning: An

Introduction to AIMS Materials

Bob delMas, Joan Garfield, and Andy Zieffler

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?  

a) Sam’s large family size bag.b) Kerry’s small fun size bag.c) 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

Explanation (N = 111) 1 2 3 4 5 6 7 8 9 10

Complete 76% 76% 60% 70% 49% 57% 47% 73% 85% 69%

Adequate or Complete 86% 87% 92% 88% 67% 85% 80% 87% 88% 88%

• Instructor advice to teachers

• Overall student performance

ActivitiesHelped

DiscussionHelped

Motivated to Participate

Statistics is Useful

Recommend to a Friend

Fall 07 (N = 92) 94% 83% 67% 76% 88%

Spring 08 (N = 74) 86% 89% 58% 81% 88%

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: jbg@umn.edu

Bob delMas: delma001@umn.edu

Andy Zieffler: zief0002@umn.edu