Teaching Statistics with Simulation Dustin Silva and Ambika Silva College of the Canyons, Santa Clarita, CA

Why use simulation? What is Simulation? Simulation is a way to model random events, such that simulated outcomes closely match real-world outcomes. It can involve randomly sampling from: theoretical population(s) based off assumption(s) probability distribution(s) obtaining repeated observations of the outcome of a random experiment  Why use simulation? By observing simulated outcomes, students can visually see and gain insight into sampling variability.

Why Teach with Simulation? Conceptual Understanding (Deep Learning) Instructional Simulations have the potential to engage learners and empowers understanding as opposed to surface learning that requires only memorization Actively Engages Simulation isn’t passive

Why Teach with Simulation? Allows Students to Refine their own thought processes Instructional Simulations allow students to think about what happened during their simulation and why the simulation behaved the way it did Gives Students a Way to Visualize!! Students seeing what a p-value is or how sampling distributions play a role is so powerful!

The Verdict? You be the judge! The good news: Instructional Simulations can be very effective in student learning The bad news: Sometimes requires a lot of preparations for the activities Instructor Preparation is Crucial!!!

The Cycle of Learning Setup Implement Closure

Analogy of “Cycle of Learning” - Backwards Design Setup is like…. Packing up your car for the trip. Implementation is like… The journey to get to your destination. Closure is like. …. The destination.

Setup: Include a Bridge in Can be as simple as posing a question “…..” Video clips Entices the students Set up does NOT mean what you’re doing as an instructor, that’s all the pre-set up stuff!

Implement Physical Simulation Theory

Closure: Post Simulation Discussion is crucial! Closure is so important, but often the first to be rushed/skipped Be sure to allow time for students to reflect on and discuss what they learned from the simulation Show students how the simulation/activity is fitting with the lesson objectives for the day Check for understanding Ask for student feedback!

Let’s do a lesson: PENNIES! This experiment can be used in a variety of ways! Shape, center (Done on Day 1 or 2 of an intro class!) Spread, Empirical rule, sampling variability Probability Sampling Distributions P-value, Inference

Pre-Set up for instructor Instructor needs a roll of pennies (enough for a class), this is an affordable investment! Print out handouts for students

Set – up in class You’re talking to a friend and they say that flipping 9 or 10 heads out of 10 flips is no big deal. Do you agree? Disagree? https://www.youtube.com/watch?v=U8nSrlhxX7s

The Experiment: You are being given a penny, please flip it ten times and record the number of HEADS You will be asked to come up and record your results Our class this semester, day ONE of class (intro Statistics course)

Go to Rossman Chance Applet Site (Free, works on Smart Phones) http://www.rossmanchance.com/applets/index.html Look for:

Try One at a time! Doing one sample at a time helps students see that the dot that pops up is THEIR result, or what their result could have been! Do this a few times, one at a time, and show them it’s like them coming up to the board/poster and putting their dot up.

Do the class size! Doing your “Class Size”, whatever it is, shows them how your class may look similar or very different. Great way to show sampling variability! Show students that they need to RESET or it will keep adding to the dots. (Which is fine if you want to just keep doing more to add to it.) Even now, we still don’t have any 10’s or 0’s for the number of heads.

Go Big or Go Home! Now you can show students as if we had MANY students doing the experiment, or if we just keep doing it over and over Try clicking on Summary Stats to see the mean and SD

Our original question: Is 9 or 10 out of 10 flips a big deal? Based on the simulation of our class size, it’s impossible But that’s not right!?!? Solution: Do more experiments!

Our original question: Is 9 or 10 out of 10 flips a big deal? Doing more experiments!

Our original question: Is 9 or 10 out of 10 flips a big deal? Compare to the theoretical! It’s very close 

This can lead to Inference! P-value!

Showing HOW we sample matters

Reese’s Pieces Activity – By Hand

Other Ideas… Up/Down Activity (credit: Beth Flynn) – modeling sampling distributions What’s in your Bag – Using vase gems to do a goodness of fit test Modeling Scientific Research – Using playing cards/index cards to simulate results from real experiments. Using Reese's Pieces to learn Confidence intervals

Free resources for simulation applets: Rossman Chance Applet Collection http://www.rossmanchance.com/applets/index.html StatKey (Locks) Utilizes Bootstrapping http://www.lock5stat.com/StatKey/ OnlineStatBook for Central Limit Theorem http://onlinestatbook.com/stat_sim/sampling_dist/ …and many more! These are ones that we regularly use for sampling distribution, hypothesis testing, and confidence intervals.

Closure: Whip Around! Complete this Sentence: I think simulation is . . . For students we would have their whip around to be: What I learned today is. .. ..

Questions? Comments? Feel free to email us at Ambika.Silva@Canyons.edu Dustin.Silva@canyons.edu