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
Armando Madrigal: "Using Cumulative Frequency Models: Is our data normally
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
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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.