In these materials, teachers are engaged as learners of statistics with larger multivariate data sets (e.g., national school data, vehicle fuel economy, birth data). Using such contexts promotes the practice of posing meaningful questions and interpreting results within a context, and the dynamic statistics technology (TinkerPlots and Fathom) facilitates using representations to analyze data in novel ways. Tasks are designed to simultaneously develop deeper understanding of statistical ideas, technology skills, and pedagogical strategies for enhancing students’ understanding of statistics. Findings from research on students’ understandings of statistics are used to make points, raise issues, and pose questions. One chapter includes an extensive video case of students’ work with multivariate data using TinkerPlots.

**Overview Materials**

**Choose a Chapter Below**

**1. Center, Spread, and Comparing Data Sets**

Teachers engage in exploratory data analysis to examine national school expenditure data using TinkerPlots to create graphical displays of qualitative and quantitative data, explore measures of center and spread, and compare sets of data. Teachers consider how the use of a technology tool affects the teaching and learning of data analysis techniques.

**2. Analyzing Students’ Comparison of Two Distributions Using TinkerPlots**

Teachers engage in a task comparing distributions using TinkerPlots, anticipate how middle school students might think about the problem with the software, view a video case of students working with TinkerPlots on the task, and analyze students’ work and interactions with the software.

**3. Analyzing Data with Fathom**

Teachers analyze automobile data using Fathom to describe center and spread using dot plots, box plots, histograms. They will examine distributions of univariate data of a quantitative attribute as well as comparison of distributions when a qualitative attribute is added to separate distributions by categories. They will consider pedagogical issues related to use of graphical representations, measures of center and spread, and dynamic statistical software.

**4. Analyzing Bivariate Data with Fathom**

Building from ideas in Chapter 3, teachers continue to analyze automobile data using Fathom for describing relationships in bivariate data and developing a linear model for making predictions. The concept of variation and deviations from the mean is used to help conceptualize correlation and least squares regression. Teachers consider difficulties students may have in analyzing bivariate data and how to help students ask their own questions and collect data through techniques such as importing data from the internet or developing a survey.

**5. Designing and Using Probability Simulations**

Teachers learn how computing tools can be used to simulate random events and how simulations can be used to make informed estimates. The context concerns the retention rate of college freshmen. The text includes attention to an empirical approach to probability that can be used to foster understanding of the effect of sample size and variability when comparing empirical data to an expected outcome based on a theoretical estimate of probability. In addition, teachers are exposed to the usefulness of using intervals as estimates in probabilistic situations rather than single value estimates.

**6. Using Data and Simulations to Motivate Empirical Sampling Distributions**

Teachers examine whether similar male birth ratios are equally likely to occur. They use an estimated probability of a male birth based on data to create simulations for a sample of births using two different sample sizes. Simulation techniques are used to create an empirical sampling

distribution of the proportion of males born. Teachers consider pedagogical issues concerning use of real data as a springboard for probability lessons, the use of repeated samples in simulations to conceptualize effects of sample size, and ways in which simulations can support understanding sampling distributions and computation of theoretical probabilities using the binomial formula.