Friday, August 31, 2012

A First Day Statistics Activity

I have the honor of again teaching our undergraduate statistics course in the School of Education, better known here as EDUC 4716 Basic Statistical Methods. Perhaps the most interesting thing about the course is that it's not required for any education programs, minors, or certificates. Instead, the course attracts students largely from the Department of Speech, Language, and Hearing Sciences (who don't need it to graduate, but do need it to apply to grad school or, more recently, to get certified) and sociology majors. So how does this course end up in the School of Ed? Probably due to the legacy we have in quantitative methods, thanks to people like Robert Linn, Gene Glass, Lorrie Shepard, and now faculty like Derek Briggs and Greg Camilli. Somehow all of their hard work and success filters down and gives a relative stats-hack like me a chance to teach undergrads.

Many of my students are upperclassmen and have spent much of their college experience avoiding math courses. In fact, on last year's FCQ (Faculty Course Questionnaire) my students' average rating for the item "Personal interest in this subject prior to enrollment" was a 1.8 out of 6 -- a response the university tells me is at the 0th percentile across campus. I like to think of this as a great opportunity in a "nowhere to go but up" kind of way, a chance for me to change the way students think of mathematics and see themselves as mathematical beings. Then again, it's hard to make big changes in only 15 class meetings of 2.5 hours each. If I'm going to make a difference, class has to get off to a solid start.

My opening activity this year started with the preparation of four simple index cards with different distribution shapes:
Four common distributions, clockwise from top left: normal, left skewed, right skewed, and normal.

I have the benefit of a small class of 14 students. So I cut my graphs into a total of 14 pieces:

14 pieces for 14 students. Note on the bottom I've provided the hints A, B, C, and D.

When class started, I mixed up the graph pieces and handed one to each student. Then I told the class to find the other people in class who had the graph pieces that aligned with theirs. Once they had a completed graph, form a group at one of the tables and discuss which of the following they thought their group's graph might describe:
  • People born each month of the year
  • Student GPAs at this university
  • Student heights at this university
  • Starting salaries of new graduates from this university
It took my class less than 3-4 minutes to find their groups and then I gave them another 3-4 minutes to discuss what their graph shape might describe. As a class, I had each group share their ideas and then we discussed them. Not everybody agreed initially about which shape matched which description, which led into important comments about how we might think about unbiased sampling of students and imagining different scales and labels along the horizontal axes.

So in less than 15 minutes I combined group-making, statistics, and active, student-centered problem solving into one activity. This activity also gets students thinking about distribution shapes, which I sometimes worry we ignore in the rush to calculate centers and spreads. If you're wondering how to adapt this for your classroom, I offer these suggestions:
  • If you have a few more students, cut more slices.
  • If you have twice as many students, consider making two of each distribution shape and scaling the x-axis to match one of 8 potential descriptions. (i.e., a normal distribution scaled for heights in inches could be distinguished from one scaled for SAT scores.)
  • If you want to use this for Algebra 1, you can make graphs that describe things like, "Toni walked to the bus stop at 2 mph, rode the bus at 30 mph to the bike shop, then rode a bike back home at 12 mph." Such an activity begins CPM's Algebra Connections and was the inspiration for my activity.
  • If you want to use this for Algebra 2 or higher, you can use graphs of functions that students will become familiar with (parabolas, cubics, hyperbolas, etc.). I don't think it's worth fretting over vocabulary at this point -- just give students an opportunity to think about how the functions behave and what phenomena they could possibly model.