Transcript AIMS Workshop - CAUSEweb.org

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
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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
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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
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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
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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
Activities
Helped
Discussion
Helped
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%
• Overall student performance
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
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]