# 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. [pullquote]…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.[/pullquote] Continue reading

# Making the Most of Simulation-Based Inference in an AP Statistics Class

Catherine Case, University of Florida

My first experience teaching statistics was at the college level, so for my first few years of teaching, I never heard the infamous question, “Can we have a free day?” Now that I teach AP Statistics at a high school, I do hear that question from time-to-time (somewhere between 1 and 1 million times per day), and I need to be prepared with a good answer! Why should they care about what we’re doing in class today? My first goal for each class is to get buy-in from my students, to convince them that statistics is relevant to their lives and we have important, interesting things to accomplish. Simulation-based inference helps me do that. We’re able to draw inferences from real-world data starting on the first day of class, and breaking out spinners, dice, and coins never hurts! [pullquote]Incorporating simulation-based inference in a high school statistics class presents… opportunities for students to make connections and gain experience with statistical inference throughout the course.[/pullquote]

# Getting Started with a Simulation-based Curriculum

Kathryn Dobeck – Lorain County Community College, Ohio

In 2012, I had a simple goal for my first sabbatical project: to revise the course materials for my Introduction to Statistics course in order to make them more accessible and relevant to my students. I had long been bothered by the presentation of statistical concepts that our textbook used, due to its overuse of flowcharts and “cookbook-style” explanations where logical justification should have been. With this approach, students were hung up on basic ideas such as arithmetic, rounding issues, and determining which formula to use, but never reached the higher orders of statistical thinking. My quintessential statistics course would convey the power of analyzing data, present motives for inferential statistical methods, and demonstrate the ubiquitous nature of the discipline. Unfortunately, at that time, the specific details of how I was going to solve these problems and realize my ideal course were yet to be determined (and hence the need for a sabbatical!). [pullquote]I’d be lying if I said that changing to a simulation-based curriculum wasn’t a lot of work. It definitely was. However, the work load was manageable over the course of a year and was worth every bit of it. Now, student success rates and attitudes have improved and the course is an absolute joy to teach.[/pullquote]

# Finding the Right Balance

For me, the hardest part about getting started was finding the right balance in my classroom – the right balance between lecture and activities; the right balance between in-class and out-of-class learning; the right balance between student accountability and student responsibility. None of this, however, really had much at all to do with the randomization-based curriculum. I had taught courses for pre-service and in-service K-12 teachers that focused on simulation-based methods . . . I knew it was effective pedagogically. The hard part came when a colleague and I decided that we would try to flip our classrooms the same semester we implemented the randomization-based curriculum. And, that too in a classroom with 2-3 times as many students as a “typical” intro class in our department. [pullquote]… the right balance between lecture and activities; the right balance between in-class and out-of-class learning; the right balance between student accountability and student responsibility.[/pullquote]

# Moving from a traditional curriculum to a simulation/randomization-based curriculum

My move from the traditional curriculum to the simulation/randomization-based curriculum was confounded with the simultaneous move of inference to the beginning of the course. Not only was I going to dive in to simulation/randomization as the primary mode by which to develop student understanding of statistical significance, but I was going to try it while completely turning the traditional ordering on its head.[pullquote] But moving inference to week 2 means my students immediately experience statistics as a science, and they get this experience repeatedly throughout the course, and in the end showing them what statisticians do and how statisticians think is more important than my struggle with where to put the definitions of parameter and statistic.[/pullquote] Continue reading

# Using Simulation-Based Inference in AP Statistics

Josh Tabor, Canyon del Oro High School

The AP Statistics course is designed to mimic a traditional college-level introductory statistics class. Students are expected to use z-tests for proportions, t-tests for means and slopes, and chi-square tests for distributions of categorical data. There are at least three good reasons to incorporate simulation-based inference methods in the AP course, however.[pullquote]Doing these simulations takes time up-front, but helping students understand the logic of inference through simulation saves time in the long-run.[/pullquote]

# Highlighting real statistical studies

Kevin Ross – Cal Poly, San Luis Obispo

One of the recommendations of the GAISE report is to “use real data where possible.” While this is great advice, perhaps an even better recommendation is to “always use real statistical studies.” This post describes some ways I highlight real studies in my courses. While my approach might not be novel, I hope you find some of these ideas useful. [pullquote]Highlighting real data in our teaching is extremely important.   However, perhaps a better goal is to highlight real statistical studies…[/pullquote]