Teaching Difficult Topics in Statistics THE STATWAY LEARNING MODEL Rachel Mudge – Statway Writer, Math Prof. at Foothill College, Los Altos Hills, CA Andre Freeman – Statway Writer, Math Prof. at Capital Comm. Coll.,Hartford, CT Scott Guth – Statway Writer, Math Prof. at Mt. San Antonio College, Walnut, CA

Overview In our presentation, we will discuss the following: How Statway introduces difficult statistics topics. What we know about how students learn statistics. The Statistical Reasoning Learning Environment. Two Statway activities that apply this environment. 2

A Difficult Topic: Sampling Distributions 3 To understand sampling distributions, students need to understand, integrate, and apply prior studied statistics topics: The idea of variability The idea of a distribution The idea of sampling Students must also understand how to apply the Central Limit Theorem to applied contexts. (Chance et al, 2004)

The M&M Lesson 4 As you participate in this lesson, think about how the lesson implements: A focus on ideas – not procedures Real and motivating data that engage students A classroom activity that supports student reasoning Appropriate technology (not for just getting answers) Meaningful classroom discourse

Summary: The M&M Lesson Let’s ponder a few questions about this lesson. Is the lesson accessible to students? How are the central ideas demonstrated? Real and interesting data set? Supports development of student reasoning? Integrates appropriate technology? Promote classroom discourse? Achieves desired outcomes? 5

Statistical Reasoning Learning Environment The Statway Learning Model is an example of the Statistical Reasoning Learning Environment. Developed by Garfield and Ben-Zvi Based on six principles of instructional design described by Cobb and McClain (2004) 6

Statistical Reasoning Learning Environment The statistical reasoning learning environment has six basic elements. 1.Focus on developing central statistical ideas rather than on presenting a set of tools and procedures. 2.Use real and motivating data sets to engage students in making and testing conjectures. 3.Use classroom activities to support the development of students' reasoning. 7

Statistical Reasoning Learning Environment 4.Integrate the use of appropriate technological tools that allow students to test their conjectures, explore and analyze data, and develop their statistical reasoning. 5.Promote classroom discourse that includes statistical arguments and sustained exchanges that focus on significant statistical ideas. 6.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. 8

A Difficult Topic: Hypothesis Testing To understand the concept and process of hypothesis testing, students should understand: The underlying logic. The idea of a P-value. Sampling distributions. 9

Hypothesis Testing in Statway 10 I.Determine the Hypotheses II.Collect Data III.Assess the Evidence IV.State a Conclusion To see how these are developed, let’s look at the next lesson. At this point in Statway students have thought about sampling distributions of sample proportions for as long as two weeks. The goal of the following lesson is to introduce hypothesis testing in a way that is natural and meaningful. Statway sees hypothesis tests as having four basic elements.

Summary: A Game of Cards In this lesson, students conduct an informal statistical investigation. What assumption is made about the population proportion of all cards that are red? (What is H 0 ?) What data are gathered? Do they represent a random sample? How do we assess the evidence gathered? What sort of conclusion is drawn? Do students express this with plain language? 11

Thinking about the Statistical Reasoning Learning Environment Does this introduction to the four elements of the hypothesis testing process violate the first principle of the statistical reasoning learning environment, Focus on developing central statistical ideas rather than on presenting a set of tools and procedures. 12

Thinking about the Statistical Reasoning Learning Environment Think about the six basic elements of the Statistical Reasoning Learning Environment. Can you think of ways that you could supplement these lessons to better align with these recommendations? Please explain your ideas. 13

Thank You … Questions 14