# How do I use simulation-based methods to enhance student understanding of AP Statistics

Bob Peterson, Mona Shores High School, Muskegon, Michigan

I love statistics!!  I have been teaching for 25 years, and in 2003, when I got the opportunity to develop an AP Statistics class after having been teaching AP Calculus, I jumped at the chance. At that time, I was fortunate enough to participate in a course called INSPIRE, which was run by the stats gurus Allan Rossman, Beth Chance, Roxy Peck and many others. This class was designed for the new AP Stats teacher. Since then I have tried many different ways to help my AP Statistics students gain a deeper understanding of statistics. So, when I learned about the possibility of using simulation-based methods I was immediately excited about a course that could take advantage of tangible hands-on activities, computer simulations and high levels of reasoning.

…since I have implemented more simulations within my class, students have had an easier time of understanding the hows and whys of the theory-based methods of inference that AP students must master.

I have found that when students enter my AP Statistics class, their background in mathematics consists of remembering formulas, repeating the SAME problem over and over, and unfortunately very little or no practice with communication, reasoning or explaining solutions in context.

The beauty of statistics, particularly AP Statistics, is that students are required to do all of these things. This type of thinking and communication is new to most students regardless of ability. Simulations, and simulation-based methods are great tools for students to see the big picture. I have seen many “aha” moments when students are involved in simulations.

I am sure the reasons that I use simulations are not unique:

1. Students get exposed to the big picture early in the course, and get involved in the statistical process.
2. The visual representations that simulations provide are a powerful tool for inference. The phrase that “a picture is worth a 1000 words” is clearly evident.
3. By first introducing an inference concept using simulations, followed by an introduction to the conditions and formulas of the theory-based method approach to a particular inference topic is the way to approach inference. (My opinion, of course!)
4. Simulations are a great way to answer the question “What if the conditions aren’t met”?

I usually start the year with a simulation on the first or second day of school. Students get exposure to the concept of p-values and null hypotheses, CLT, and other types of inference concepts early in the course. In essence, they are exposed to the statistical process WITHOUT getting bogged down by the formal null and alternative hypotheses forms, the different formulas or the conditions of inference that are required for the theory-based methods. I have had a few years when students are exposed to the concept of p-values and such before the formal introduction in later chapters. Much of this is to do with simulations. I use simulations as introductions to inference concepts and more importantly to reinforce “ the big picture”.

… there is a strong sense of engagement by the students.

Most of simulation activities that I use involve using applets . Two of my frequent resources are the Rossman/Chance applets applets and the Lock5 Statkey applets. But some of the most enriching simulations are those that involve good old hands-on activities that involve using cards, M&M’s, or simply drawing objects from a hat.

I have no doubt that since I have implemented more simulations within my class, students have had an easier time of understanding the hows and whys of the theory-based methods of inference that AP students must master. Most importantly, there is a strong sense of engagement by the students. This year I did a simulation with Reese’s Pieces, and then students were to answer questions using an applet from the Rossman/Chance applets. It was amazing how many 17-year olds were mesmerized by the applet!

Even though I get a kick out of using simulations, I still I consider myself to be a newbie, so I would love to dialogue with others about their experiences particularly in the AP Statistics world.

Well, this was my testimonial about my experiences and feelings about simulations in an AP statistics class. I hope that this blog will continue to grow. I would love to hear what other teachers have experienced.