Why I chose to teach with simulation-based methods

Josh Tabor, Canyon del Oro High School

Tabor

Short answer: I teach with simulation-based methods because I believe they make it easier for students to understand the logic of inference and see statistics as a complete investigative process from asking questions to drawing conclusions.

I settled on two guiding principles that would inform the way I designed the course:

  1. Emphasize that Statistics is an investigative process, not a set of isolated skills.
  2. Stay focused on the logic of inference.

The long answer begins in the spring of 2009, when our high school was looking to create new 4th-year math courses to satisfy revised graduation requirements in the state of Arizona.  As a long-time teacher of AP Statistics, and an even longer-time fan of sports, I proposed a course called  “Statistical Reasoning in Sports.”  The course would be primarily about statistical reasoning, with the motivational hook of using sports contexts throughout.

Because there was no existing curriculum or standards that I needed to cover, I could teach the course in the best way I saw fit.  I could use as much or as little technology as I wanted to.  I could teach the course in the traditional order or mix it up.  Having so many options is great—but also a challenge.  To know how to build the course, I had to identify the principles that I valued most.

I settled on two guiding principles that would inform the way I designed the course:

  1. Emphasize that Statistics is an investigative process, not a set of isolated skills.
  2. Stay focused on the logic of inference.

Using randomization-based methods allowed me to stay true to both of these guiding principles.

Historically in K-12 education, Statistics has been presented to students as an unconnected set of skills—if Statistics has been taught at all.  In one course, students might learn how to calculate means and medians.  In another course, they might learn how to make a box-and-whisker plot and a stem-and-leaf plot.  But these graphs are typically an end in themselves.  Because they aren’t used to help answer interesting statistical questions, students write them off as tedious and useless.

To counter this perception, every unit in my course starts with a question (e.g., Is there a home-field advantage in the NFL?) and we spend the rest of the chapter learning the skills necessary to answer this question.  We learn how to collect the relevant data, how to analyze the data, and how to make inferential conclusions using the data.

Yes, we are making inferential conclusions starting in the first week of school!  Randomization-based methods allow us to estimate p-values and make inferential conclusions without having to know anything about Normal (or t) distributions.  Because the inferential piece fits so naturally as the last step in the statistical process, students never wonder “why are we doing inference so early?”  In fact, they find it strange when I tell them that my AP students won’t be learning about p-values for five months!*

*Actually, I use randomization-based methods in my AP class as well, even though the AP curriculum is much more traditional; I have discussed my experiences with the simulation-based methods in AP Statistics classes here.  During the first semester, we do several activities that conclude with what is essentially a randomization test.  During the second semester, I try to introduce each major inference procedure (e.g., test for a difference in proportions, test for slope) with the equivalent randomization test. 

The second guiding principle for my course was to stay focused on the logic of inference.  I want students to leave knowing that all tests of significance are essentially the same: comparing the observed result with what might happen by chance alone.  Using randomization tests helps students keep their eyes on the bigger picture by avoiding the specific technical details that accompany each of the different traditional tests.

This makes my course much more accessible to students—once they learn how to do a test comparing two proportions, they can easily extend the same logic to a test comparing two means, or a test comparing two standard deviations.  In a traditional course, these are three very different tests that use three different distributions.  In a course that uses randomization-based methods, they are essentially the same test.

Randomization-based methods also make it easy to utilize hands-on activities that better facilitate student understanding.  And the development of easy to use applets** makes it easy to automate the simulation process once students understand what is going on.

**Applets for the randomization tests we use in Statistical Reasoning in Sports can be found at www.whfreeman.com/SRIS

The accessibility of randomization-based methods has made it much easier for me to expose a wide audience to the power of the statistical investigative process.

That’s the long answer.

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