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# Aiming to Improve Students Statistical Reasoning: An Introduction to AIMS Materials - PowerPoint PPT Presentation

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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University of Minnesota

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

• 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

• 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

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

• Lesson plans (28)

• Activities

• Suggested sequences of activities

• Compilation of research (DSSR book)

• 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)

• 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.

• 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.

• 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)

• Sampling Reese’s Pieces

• Adapted from great activity by Rossman and Chance (Workshop Statistics)

• Adapted lesson to align with the six instructional design principles

• 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

• 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

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.

• Students take physical samples of Reese’s Pieces candies and construct distributions of sample proportions.

• Students simulate data based on population estimates.

• 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 Conjectures, Explore and Analyze Data

• 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 Learning

• 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 Learning

• 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 Learning

• 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! Learning

• Please check out and use our materials.

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