MIT BLOSSOMS Project-Based Learning Units: Flaws of Averages

MIT BLOSSOMS Project-Based Learning Units: Flaws of Averages

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MIT BLOSSOMS has a Project-Based Learning site with six in-depth lessons designed for high school teachers who want to give PBL a try, but are not sure just how to get started. Each BLOSSOMS PBL unit is developed to provide a teacher with all the resources and scaffolding needed to conduct a three to five-week classroom project. Every BLOSSOMS unit kicks off with a BLOSSOMS video lesson, thus providing the anchoring content and direction for a follow-on project. Teachers new to PBL will also find on this site many answers to questions they may have, as well as invaluable advice on how to successfully lead a PBL unit. While we understand that most teachers won’t be able to devote three weeks completely to a Project-Based Learning unit, the units provided here can be presented on non-consecutive days, for example, two days per week. It is our hope that these units will be valuable stepping stones as teachers grow in confidence about developing their own PBL units! We encourage teachers new to PBL to visit the following resource on this site: Teacher Questions on PBL. To take a Video Tour of this BLOSSOMS PBL site, click here.

Flaws of Averages: Driving Question
How to better understand Averages: what information are they giving us and in what ways may they be misleading us?

Flaws of Averages: Big Idea
The “Tyranny of Averages” refers to the idea that group averages fail to impart the whole story of data because averaging flattens otherwise jagged information to a single point, thus leaving out important details and variations within the data. In this PBL, student teams will collect data from their communities, create a histogram and distribution of that data, analyze the mean, median and mode and report their findings to a relevant community official, with suggestions for ameliorative actions. One important goal of this project is to make students more knowledgeable and skeptical consumers of statistics.

During this one month project:

Students will learn:

• About many situations in which focusing only on the average of a data set can distort the reality of that data
• About Histograms and how to construct them
• About Distributions and what they tell us
• The definitions of the mean, median and mode
• About the role of data outliers
• Clarifying data collection goals and validating a measurement system for data collection
• About safety issues in their own communities

Students will be able to:

• Distinguish between situations where the use of averages is effective and those where one needs to think in terms of displayed distributions, not only averages
• Collaborate with team members to design and implement an effective data collection strategy on an important safety issue in their community
• Analyze that data by constructing and displaying a Histogram of it
• Integrate the data, compute mean, median, and mode, and ultimately make inferences from the data that could benefit the community
• Write up a report on the findings and present that report to relevant community officials
• Prepare and present a presentation on their findings to a large audience

For all project materials, visit: https://blossoms.mit.edu/projects/flaws_averages

Resources

External resources
Videos
Flaws of Averages
Remote video URL

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