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Session 10, Part A:
Statistics as a Problem-Solving Process (30 minutes)
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A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After the children have gathered and organized their data, they should analyze and interpret the data by relating the data back to the real-world context and the question that motivated the investigation in the first place. Too often, classrooms focus on the techniques of making data displays without engaging children in the process. However, it is important to include children in all aspects of the process for solving statistical problems. The process studied in this course consisted of four components:
Children often talk about numbers out of context and lose the connection between the numbers and the real-world situation. During all steps of the statistical process, it is critical that students not lose sight of the questions they are pursuing and of the real-world contexts from which the data were collected.
When viewing the video segment, keep the following questions in mind:
• | How do the students in this classroom apply the first two components of the statistical process? What statistical question are the students trying to answer? How were the data collected? |
• | As the fifth graders move onto the next two components of the statistical process -- analysis and interpretation -- what issues do you think will come up? |
• | Thinking back to the big ideas of this course, what are some statistical ideas these students are likely to encounter through their investigation of this situation? |
Note 2
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Problem A1 |  |
Answer the questions you reflected on as you watched the video:
• | How do the students in this classroom apply the first two components of the statistical process? |
• | What statistical question are the students trying to answer? |
• | How did the students collect their data? |
• | As the students move on to analysis and interpretation of their data, what issues do you think will come up? |
• | What statistical ideas are students likely to encounter as they investigate this situation? |
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Problem A2 | |
In this video, Ms. L'Esperance establishes a rich and elaborate real-world context to situate the students' investigation of family size. How do you think the class would have responded if she had not constructed a context for the investigation and instead had simply said, "Today we are going to investigate family size; how many people are in your family?" What is the impact on the students' level of engagement?
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Problem A3 | |
Too often, students lose the connection between the numbers and the real-world situation once they have gathered their data. How might the richer context provided by Ms. L'Esperance reinforce the connection between the data and the real-world phenomenon being studied, and prevent students from working with mere numbers out of context? |
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Problem A4 | |
What are some ways in which this richer context will support students' reasoning as they "interpret the results"? |
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Problem A5 | |
Why do you think Ms. L'Esperance phrased the question about family size as "How many people live in the house that you slept in last night," as opposed to simply "How many people are in your family?" With your own students, how would you define "family"? Note 3 |
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When engaging students in the process of statistical problem solving, students must consider what to measure and how to measure it to ensure accuracy in collecting their data. In this lesson, Ms. L'Esperance defined "family" for her students. But, it is also important to give students a chance to form -- or to help form -- their own definitions for the purpose of their investigations.
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Problem A6 | |
How would you facilitate a discussion with your students on what constitutes a "family"? Describe some of the sensitive issues that might arise and how you would handle them. |
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