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# Chapter

• ### "We were nicer, but we weren't fairer!" Mathematical modeling exploring "fairness" in data management.

This article describes a teaching study with fifth- and sixth-grade students in which they explored some of issues involved in critically examining data such as questioning the underlying assumptions. Students generated their own mathematical models as a way of understanding a real-life situation.

• ### Using real data and technology to develop statistical thinking.

This article describes some internet-based projects using real data produced and collected from students in the United Kingdom and elsewhere. We believe that these projects enable students to understand better the reasons for data collection and ad a dimension to their learning.

• ### Using regression to connect algebra to the real world.

This article describes the use of regression in middle school grades and Algebra 1 settings to connect algebraic functions to real-world contexts. It is suggested that using data sets will intrigue and motivate students.

• ### Using data to enhance the understanding of functions: Data analysis in the precalculus curriculum.

This article examines two essential questions in making a good model from data - describing the pattern of variation and explaining the proportion of the variation by using functions.

• ### Changing the face of statistical data analysis in the middle grades: Learning by doing.

The purpose of this article is to document the efforts of an ongoing collaboration between a cohort of middle school mathematics teachers and a university professor in defining statistics instruction for students. In the process, our goals for statistics instruction changed from that of creating the correct graph or calculation of measures of center to that of answering the meaningful questions on the basis of the exploration of trends and patterns in data.

• ### Understanding data through new software representations.

In this article, we describe how middle and high school teachers and students analyze data using TinkerPlots, especially in how they express and support their analyses, and the conceptual issues about data and distributions that their explorations illuminate.

• ### Using graphing calculator simulations in teaching statistics.

This article describes how graphing calculators can help make statistical concepts more accessible and understandable through the use of simulations. Examples of simulations are given on the Law of Large Numbers, Normal Probability Plots, Central Limit Theorem, Confidence Intervals, and Significance Testing.

• ### What is statistical thinking, and how is it developed?

This article describes a learning environment used in a college preparatory high school class which incorporated investigative lab activities.

• ### Using graphing calculators to redress beliefs in the "Law of Small Numbers".

This article presents several activities and programs for a graphing calculator that can help students deal with misconceptions about expecting short runs to reflect closely the theoretical probability or the long-term behavior.

• ### Statistics and mathematics: On making a happy marriage.

This article explores the complementarity of statistical reasoning and mathematical thinking in the mathematical sciences. The difference between the two is illustrated by critically examining some items used to test students' understanding in data analysis and statistics.