Statistical Analysis of a Federal Data Set: Project Based Learning in the Introductory Statistics Classroom

Melvin J. Berman Hebrew Academy offers two statistics classes to seniors.  The first is a yearlong gently-paced class that largely focuses on descriptive rather than inferential statistics.  The other is the second semester of a yearlong Calculus/Statistics sequence, for students who do not enroll in AP Calculus due either to placement or to competing courses.

In my first year at Berman, I taught statistics traditionally, with textbook-driven exercises and frequent tests. In my second year teaching these courses, I switched to Project Based Learning in the classroom.  Students obtained their own data sets, typically from federal data agencies.  As an ongoing activity throughout the semester, they developed a paper and/or poster exploring their data.  We adopted Project Based Learning for a variety of reasons. I sought greater student engagement in their work and was eager to develop seminar-style skills of discussion and interaction among the students.  I was also frustrated with the simplicity of many textbook examples, wanted to deepen understanding of the material by according responsibility to students to fully investigate a data set, and sought new ways to engage seniors, especially in the second semester of their senior year.

Other goals were related to the ‘real-life’ nature of the Project.  Students select and analyze a federal data set, by state, so each student has 51 (states + DC) data points for analysis.  Sample data sets have included: per capita personal consumption expenditures, childhood obesity, housing characteristics, murder rates, rape rates, abortion rates, religious beliefs, distribution of federal workforce, gun ownership, identity theft, tornado incidence, % of students who receive Special Ed support, distribution of angora goat population across the US, deaths due to DUI, gun ownership, and teen pregnancy rates.  With data sets like these, I was able to pursue these outcomes:

• familiarity with the federal statistics system
• connection of data analysis to a topic of personal interest
• experience in technical writing and production of a statistical report
• participation in a national statistical poster competition sponsored by the American Statistical Association.

Here are examples of sources of their data:

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In the yearlong statistics course, the first semester runs traditionally with homework practice and tests.  Most of the second semester (which is shortened in our school due to senior internships) is devoted to the Poster Project.  I had worried about redundancies from the first semester, but students reported to me that their understanding of statistical techniques deepened when they applied first semester textbook skills to their own analyses.  In the Calculus/Statistics course, I asked students to choose a data set early in the semester.  After learning a skill (eg, histograms) from the textbook with a night of homework practice, students immediately applied the technique to their own data sets, building their statistical papers unit by unit, typically using class time rather than listening to lectures.  The frequent in-class work days allowed me to float from student to student, providing timely and direct feedback. Students responded to this ‘seminar-style’ approach with enthusiasm.  They worked together in class, critiqued one other’s work either in pairs or in presentations of student work on the Smartboard, and rejoiced in not having tests (though in fact, they were working harder on these papers than they would have studying for tests!).

One measure of success has been our achievements in the American Statistical Association poster competition.  At our chapter level (the Washington Statistical Society), we had a Berman “sweep” our first year, taking 1^st, 2^nd, 3^rd place along with two honorable mentions.  In our second year, students won 2^nd place and two honorable mentions.  This has been a particularly enjoyable outcome, as the yearlong Statistics class have typically been the weakest math students in their grade.  Last year, I was gratified watching one of our winning students explain her project to a past President of the American Statistical Association.

Here are some sample posters:

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Rachel Braun has taught Statistics and Mathematics for 20 years. She earned a BA in Mathematics and a BA/MA in Regional Science from University of Pennsylvania, and an MA in Mathematical Statistics from George Washington University. Now at Melvin J. Berman Hebrew Academy in Rockville, MD, she enjoys a school environment that strives for personal attention for each student and that values many aspects of student accomplishment. She worked as a consulting statistician in her first career, and has served on education-related committees of the American Statistical Assocation. Fun fact: Rachel is the Guinness Book of World Records holder for the largest graph paper collection in the world, with over 1300 distinct sheets of mostly vintage graph paper.