Park City Mathematics Institute
Reasoning and Data and Chance
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Members of the Reasoning and Data and Chance group created a series of lessons that emphasize statistical reasoning in the mathematics classroom.
To provide ways of meeting guidelines set by the American Statistical Association Framework for introducing statistical concepts in grades K-12. These guidelines are set at three levels:
- A (grades 6-9)
- B (grades 10-12)
- C (grades 12-college/AP Stats)
To use a common data set. By doing this, teachers across grades will share labor, ideas, and understand how their lesson will fit into the different levels. By collaborating, everybody benefits.
Because nearly all students carry a book bag or backpack to school, we decided that nearly all schools could collect data about backpack weights. In addition, members were interested in how well people could guess their backpack weights. We collected a sample of 52 adults from the PCMI 2006 summer program, asked them to estimate their backpack weight, and then found its actual weight with a common bathroom scale. This data collection can easily be repeated in most schools at low cost, with little time commitment.
- How Much Does Your Backpack Weigh?
- Kathleen Tuers, Gina Barnes
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: formulating questions, collecting data, analyzing data, interpretation
- Graphic Differences
- Tim Fritz
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
- Data Analysis with our Backpack Data
- Sue Antonsen
This activity investigates the usefulness of different data displays in answering questions about our backpack wearers. Students use scatterplots and side-by-side box plots to determine whether the group of PCMI participants are good guessers of their backpack weights. Association is also studies, as gender is incorporated into the analysis. The later stages of the activity push students towards creating their own numerical summaries to answer a question.
Level B: analyzing data, interpretation
- Using cumulative frequency models: Is our data normally distributed?
- Armando Madrigal
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 normal cumulative distribution function predicts.
Level C: analyzing data
- Making Conclusions from Graphs
- Bill Thill
This group activity requires students to look at 8 different visual displays, and five different questions that we can use our graphs 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.
Level C: question formulation, analyzing data, interpretation
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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.