Wednesday, May 25, 2011

A Project per Unit: Understanding By Design in AP

Some project ideas for AP Statistics that are unit specific.  I'd begin each unit by asking these questions and having kids consider just what data they'll collect and how they'll answer these questions.  Then build all the statistics concepts around them as they come up, not as a series of "concepts".

Unit I: Displaying and Describing Data
1.  Market Research: design a product, determine the market for it, determine how much you should charge for it
  • Create a coffee stand for your school building
  • Pillow-pack: A backpack with a pillow built in to it
2.  Consumer Education: Choose a series of similar products and determine which one is the best for consumers
  • I have a number of kids working on an end of the year project comparing all types of smartphones
  • Mac vs PC?
  • Tablet PC's
3.  What makes a song popular?

Unit II: Displaying and Describing Bivariate Data (probably my weakest ideas)
1.  Have them collect data that makes them think about what a correlation actually shows (not causation, only a relationship between two variables, etc)
  • Caloric Intake vs Weight 
  • Grams of Fat vs Grams of Protein consumed daily
  • Income Level vs Achievement Level in Standardized tests (state tests, SAT's, AP, etc.)
Unit III: Collecting Data
1.  What's the best sample we can get to investigate one of these questions?  I want them to see just how poorly they collected data in Unit I and II
  • What proportion of the school district has internet access?
  • Revise their sampling methods from previous units
Unit IV: Probability
1.  Design a game of chance that is profitable (run them all together on a casino day complete with fake money to see how profitable it is in the short-run)

Unit V: Inference for Proportions
1.  Continue any of the data collections that were done in the beginning of the year, looking for significant differences (consumer education, market research) - introduces significance, might be boring.
2.  Is there equality that exists between schools/institutions?  What do "richer" schools have that "poorer" schools do not?  Why?
3.  Tell a joke and determine whether or not it is funny.  Possibly look at a comedian's standup routine to determine if they are funny
4.  Type I and Type II Error: Explore wrongful convictions.  Have them explore some court cases that are under contention (OJ Simpson, Mumia, etc) and some court cases that are open and shut (Bernie Madoff).

Unit VI: Inference for Means
1.  Is there an advantage to eating a raw vegan diet vs the traditional "Western" diet? Inspired by recent events as we have recently started a Raw Vegan diet (and have never felt better)
2.  Is there equality between schools/institutions?

Unit VII: Inference when Variables are Related (T-tests for Slope and Chi-Squared Tests)
1.  Should you choose one letter over another when taking a multiple choice test? (sorry for so many testing heavy examples)
2.  Do a t-test for slope on any of the bi-variate data collected in Unit II

Most of the inferential statistics can be applied to enhance the projects and work done in the beginning of the year.  See my post on Inferential Statistics Data Collection for others, and of course feel free to lend me your ideas.

3 comments:

Frank Noschese said...

I love it! I'm think hard about designing projects in physics, but I'm debating the frequency -- every unit or every quarter?

Christiansen said...

I think I'd want to assign all the projects (every unit) at the beginning of the year. Let them investigate as they see fit throughout the year, use what they learn as they go along.

AroniStat said...

Collecting and analyzing field data may help students to get the basics in practical ways and the application of the concepts learned in classes. Statistics students, especially in non-statistics/math majors, we interacted with found statistics manuals included in syllabi to be very helpful. However, to better help students, books and manuals usually need computer application companions (and of course professionals in offices, homes, schools or on the go).
For example, AroniStat is a Statistics application that may be used as an education tool to complement statistics manuals and teachers'presentations. Developed for Mac users, it may be found in Apple App Store, Education section. For more information visit: http://aroni.us/aroni/why-aronistat/