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# Chapter

• ### What does it mean that "5 has a lot"? From the world to data and back.

The article focuses on how elementary school students engage with developing a statistical question (how students learn about developing and refining a question for data collection) and the analysis part of the data. For the analytic part, how students make sense of their data once they are collected, e.g. how they relate graphs, numbers, and statistics back to their original question, is addressed in this article.

• ### Learning to talk back to a statistic.

This article contains stories from several grades K-5 classrooms used to illustrate the importance of children assuming a critical orientation toward data displays. Some of these critical attitudes stem from students questioning the question, examining what the data do not say, analyzing the categories for the data, and identifying the background knowledge and experience of the sample population.

• ### Engaging students in authentic data analysis.

This article will address some issues involved in shifting away from teaching statistics as a collection of techniques and tools toward what can be called a more authentic approach that involves genuine problem solving and reasoning with data.

• ### Students' probabilistic thinking revealed: The case of coin tosses.

This article reports on a subset of a larger study that addresses students' probabilistic thinking; the focus here is on students' thinking to three tasks involving coins. As well there are also highlights of the associated interview dialogues between the teacher-researcher and the students.

• ### Assessing the development of important concepts in statistics and probability.

This article is based on research with students in grades 3 to 9 and is concerned with a model that tracks the steps in the development of students' understandings of probabilistic and statistical concepts over time.

• ### Research on students' understanding of some big concepts in statistics.

This article highlights some research on several big ideas in statistics that seem particularly pertinent to school mathematics. A discussion of the notion of statistical thinking lays the foundation for discussing students' understanding of average, concept of variability and some important connections between proportional reasoning and statistical reasoning. In conclusion, some suggestions for teaching are offered from the research literature on the teaching and learning statistics.

• ### A statistical study of generations.

This article describes the project "A Statistical Study of Generations" that attempts to engage high school students and also teach sound mathematical and statistical reasoning. Some evidence is presented that students' were disposed to view mathematics as "sensible, useful, and doable".

• ### More than "meanmedianandmode" and a bar graph: What's needed to have a statistical conversation?

This article focuses on the ideas on what it means to "do statistics", and the important ideas used for data analysis, namely characterizing the shape of data distributions and their variability and center.

• ### When data and chance collide: Drawing inferences from empirical data.

The purpose of this article is to share the insights gained from implementing a task using Probability Explorer with sixth-grade students as they learned to draw inferences form empirical data. Features of the task that elicit and extend students' reasoning are described and evidence is provided on what exemplifies the notion of "compelling evidence" amongst middle grade students.

• ### Experimental design: Learning to manage variability.

This article considers some of the methods the experimenter has for managing planned, systematic variability, chance like variability and unplanned, systematic variability in the context of an example. The methods used are control, randomization, replication, and blocking.