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

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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

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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

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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/educat
  ion/gaise/)
• Build materials on important instructional design
  principles

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Materials Developed

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

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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)

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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.

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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.

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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)

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Examine an Activity

• Sampling Reeses Pieces
• Adapted from great activity by Rossman and Chance
  (Workshop Statistics)
• Adapted lesson to align with the six
  instructional design principles

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AIMS Reeses 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 Reeses Pieces
  candies.
• Take a sample of candies and see the proportion
  of orange candies, make a second conjecture

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AIMS Reeses Pieces Activity

• If you took a sample of 25 Reeses 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

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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.

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Use Real and Motivating Data Sets

• Students take physical samples of Reeses Pieces
  candies and construct distributions of sample
  proportions.
• Students simulate data based on population
  estimates.

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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.

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

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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?

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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?
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• Sams large family size bag.
• Kerrys small fun size bag.
• Both bags are equally likely to have more than
  70 brown candies.
•  
• Explain.

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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)

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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)

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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

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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.

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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_at_umn.edu
• Bob delMas delma001_at_umn.edu
• Andy Zieffler zief0002_at_umn.edu