I’ve been teaching AP Statistics since the 1996-1997 school year, the first year the exam was offered by the College Board. If you’ve never seen / experienced the course as a teacher or student, check it out. I had always enjoyed statistics in college, but this course was designed with a very different set of goals than my year-long mathematical statistics course had. In particular, the AP Statistics course wants students to become skilled in four main themes:
* Exploring data (choosing / interpreting appropriate numerical summaries and visual displays to describe patterns in data)
* Sampling/ Experimentation (designing / implementing studies effectively)
* Anticipating Patterns (the mathematics of randomness, probability, sampling distributions)
* Statistical Inference (making conclusions about populations from samples, hypothesis tests, confidence intervals)
While College Board’s course description claims it’s equivalent to a one-semester introductory statistics course, many of my returning students reveal that they go much more deeply than what they saw in a university-level course. As a teacher, the integration of activities, mathematics and writing in the same course has been challenging and exhilarating.
As I’ve grown in my teaching, I now find myself wishing I could do more with my students than what is done in the course. Furthermore, our school has been embarking on some cool initiatives: a Department of Independent Studies and Individual Research , and an Institute for Sports Medicine and Science .
Here’s what it means:
- The school is encouraging (and supporting) teachers to design courses that help students “go beyond the curriculum,” and
- The school is working professional-level researchers to find ways to educate, support, and study our student-athletes. Some of the work that’s already been done is found here.
So I’m jumping in the mix. My course proposal will be entitled “Statistics, Sports, and School.” My goals:
- Create and answer a substantive, interesting research question related to sports or sports medicine.
- Students will study related topics in library research, sports data, sports medicine, statistics, and writing that will support and inform their work throughout the year.
- Students will develop their understanding of statistical reasoning by using randomization tests and bootstrap intervals.
My hope is that the course helps our kids practice some independent research techniques and learn important skills in writing, research and statistics along the way. Additionally, I see great potential for students to work with professional researchers to produce studies that help them progress as student-athletes. Serious symbiosis, folks.
To prepare for this course, I’m “wearing my student hat” and learning deeply about some of the studies that are currently being done with our students by a team of accomplished UCLA researchers. They are currently working on a study to answer the following question:
How can an extensive nutrition program on a group of high-school athletes impact athletes’ performance, injury risk/recovery, and nutrition knowledge?
I have been very impressed with the degree of preparation, planning, and effort by everybody involved with the study. Plus, it includes collecting data with really cool machines like this one over here. It’s Called a BOD POD. It’s measures lean body mass and a ton of other cool stuff without dunking you into a pool of water.
Does anybody have experience / advice with a year-long course in student research?
Does anybody have advice/ experience with teaching bootstrap intervals or randomization tests? I’d love feedback like the kind Tim Erickson gives at his blog.
This sounds so cool! One person I would want advice from is Jeff Adkins, who at least used to be at Deer Valley High in Antioch, CA, teaching physics, astronomy, and research methods. A quick check on old URLs I have for him—and not that old—didn’t come up with a link. Maybe one of your readers knows where he is (or how I missed him!)
Thanks, Tim: I may be picking your brain as I get into the the “grunt work” of planning activities for students to do along the year as they simultaneously start working on their year-long investigation.
I’m no expert, but I did write a paper for NCSSM on randomization methods, and why the same formulas work for experiments as for samples, even though the conditions for samples are badly violated in the case of experiments. No heavy theory, but a bit of an explanation as informed by Dick Scheaffer. I can provide a link if you want.
Also, if you haven’t seen it, Josh Tabor and Chris Franklin have their Statistical Reasoning in Sports. It’s a non-AP book, full of simulations and randomization methods.
I definitely would love a link to the paper Corey… Plus, I’m thinking that we’ve talked before about the fact that it’s more challenging for students to grasp the idea of randomization tests and bootstrapping than the more traditional stuff. Is this accurate? Do you still feel that way? Is it more nuanced than that?
And yes, yes, yes! Josh & Christine’s book is probably going to be the statistics basis of my class. Here’s the link, by the way:
I think it’s not at all clear that the randomization perspective is more challenging than the traditional way. I think from my experience I’m convinced that it IS challenging. And students may THINK it’s more challenging if they see both. But I keep coming back to this: with the traditional approach, do they actually know what’s going on?
I think my students from last year mostly actually knew that they were comparing reality to the what-if, “could it be chance alone” situation when they used randomization, or that they were imagining what the variability in a stat could be when they bootstrapped.
But if I had started them with the Normal distribution and they learned how to find critical values—it might have been easier for them to come up with an answer, but I’d bet that they would not actually understand as deeply what those answers meant.
That’s what I am anticipating as well: That students might be confused at first, but at least they are thinking about the variability of the statistic, and not which magic button to press. With a less “classical approach,” students will be using a computer simulation to see how a measurement of interest (whatever it is) behaves in repeated sampling. The normal (or t, or chi-squared) model is there to “idealize” the process, but it’s also another layer of abstraction upon their thought process. Furthermore, the simulation based approach seems to model what they might encounter in 5 or 10 years…. Do modern statisticians even use “old school” tools? It seems that our computing power in our smartphones is probably powerful enough to run an appropriate simulation regardless of the scenario… It’s all in the design, I’d imagine.
which begs another question.. What is the role classical “classical stats” in the modern world?
That reassures me Tim. I feel pretty confident that i have enough activities and resources to make inference via simulation reasonable to them. To be honest the larger challenges, I think, will be in helping them through the overall process of finding a workable research question, and designing an implementable procedure to collect data. The journey from ideas to design to actual procedures is high level stuff. I wonder a lot about how to best shepherd them through this process without a lot of wasted effort or poor advice on my part. Then there’s the write up!
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