Reasoning and Data and Chance Summary

Monday - Friday, July 3 - 7, 2006

Members of the Reasoning with Data/Chance group continued their work to create lessons that emphasize statistical reasoning in the mathematics classroom. We asked 52 participants from PCMI to guess the weight of their book bag/backpack We then weighed their backpacks.

The data was collected, and entered into a Fathom data file. Group members analyzed the data, and began creating lessons that help illustrate ways to help students develop statistical reasoning in four major areas: asking good questions, collecting data, analyzing data, and making conclusions from data. Descriptions of these lessons follow.

Kathleen Tuers, Gina Barnes: "How Much Does Your Backpack Weigh?"
A comprehensive introduction to the four major tasks of statistical reasoning: Creating a question, collecting data to answer our question, Analyzing Data, and Making conclusions based on data. (Level A - asking questions, collecting data, analyzing data, making conclusions)

Sue Antonsen: "Introducing Bias and Variability with Backpack Data."
This activity investigates the usefulness of different data displays in answering questions about our backpack wearers. Students use scatter plots and side-by-side box plots to determine whether the group of PCMI participants are good guessers of their backpack weights. The later stages of the activity push students towards creating their own numerical summaries to answer a question. Further discussions can lead to an introduction to the ideas of bias and variability. (Level B - analyzing data, making conclusions from data)

Tim Fritz: "Understanding Measures of Center and Spread"
For 9th grade students: apply knowledge of central tendencies quartiles, to develop a greater understanding of numerical summaries, appropriate uses of summaries, making appropriate claims about a population. (Level B - analyzing data)

Armando Madrigal: "Using Cumulative Frequency Models: Is our data normally distributed?"
Students investigate the normal cumulative distribution function from graphical and analytic perspectives. They will use the backpack data and compare the distribution of backpack weights and differences and compare them to what the normalcdf model predicts. (Level C - analyzing data)

Bill Thill: "Matching Graphs to Questions"
This group activity requires students to look at 8 different visual displays, and five different questions that we can use our data to answer. Many of the questions can be answered by looking at traditional displays in creative or unconventional ways. By sharing and justifying their conclusions in a group setting, students will refine their ability to choose appropriate ways of choosing questions, conveying messages with graphs, and justifying their conclusions with specific evidence from their displays.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.