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

2. 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.

3. 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

4. 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!

5. 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!!!

6. The Cycle of Learning
Setup
Implement
Closure

7. 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.

8. 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!

9. Implement
Physical
Simulation
Theory

10. 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!

11. 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

12. 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

13. 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?

14. 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)

15. Go to Rossman Chance Applet Site (Free, works on Smart Phones)
Look for:

16. 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.

17. 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.

18. 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

19. 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!

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

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

22. This can lead to Inference!
P-value!

23. Showing HOW we sample matters

24. Reese’s Pieces Activity – By Hand

25. 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

26. Free resources for simulation applets:
Rossman Chance Applet Collection
StatKey (Locks)
Utilizes Bootstrapping
OnlineStatBook for Central Limit Theorem
…and many more! These are ones that we regularly use for sampling distribution, hypothesis testing, and confidence intervals.

27. 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

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