# Probability teaching ideas using simulation

This post provides some teaching examples for using an online probability simulation tool. It’s a supplement to the workshop I offered for the NZAMT 2015 conference.

**Probability simulation tool**

I recently developed a very basic online probability simulation tool . I wanted a simulation tool that would run online without using applets or flash (tablet compatible). I also wanted to be able to animate repeated simulations in a loop – in the past to get this effect, I had to either make animated GIFs or set up slides in Powerpoint to transition automatically. I did a quick search for online simulation tools and couldn’t find what I wanted so I adapted some code I had written previously to get what I wanted.

*An example of an animated looped simulation from the probability simulation tool*

It’s very much designed “fit for a specific purpose” (more about that in the part 2) so I know it has lots of limitations 🙂 But what I like about the feature being demonstrated above is that it will keep running automatically, freeing me up to ask the students questions about what they are seeing and why they are seeing this.

**Small samples – lots of variation**

One of the activities I presented in the workshop involved teachers trying to work out who my siblings were based on photos. I presented five sets of four photos. Within each set, one photo was of one of my siblings, the rest were photos of other non-related people. In the workshop there around 30 teachers present. The basic idea (with lots of assumptions) is that distribution for the number of correct selections IF teachers were guessing can be modelled by a binomial distribution with n = 5 and p = 0.25.

After “marking” the teachers selections of my siblings, I created a dot plot of the 30 individual results. One of the questions put to the teachers at the workshop was “Do these results look like what we’d see if each of you was guessing which person was my sibling?”‘

To build up a simulated distribution based on guessing, each teacher then used five different hands-on simulations to make new sibling selections for each set of photos (see the resources link at the end of this post). I then created another dot plot from these simulated selections and asked teachers to compare the features of the two plots e.g. centre, spread, shape, unusual.

For this workshop, the two distributions actually came out to look pretty similar. But this won’t necessary happen. To demonstrate the amount of variation between repeated simulations (of 30 students guessing across five sets of possible siblings), I set up the probability simulation tool with the options shown in the screen grab below:

So that the axis does not resize for each simulation, I fixed the axis between 0 and 5. To stop the dots from automatically resizing, I fixed the dot size to the smallest option. I then pressed “Start animation” and let the simulations run over and over again. This gives the following animation:

This animation could then be used to ask questions like:

- “What would be an unlikely number of correct siblings if someone was guessing?”
- “How many correct siblings would you expect to see if someone was guessing – between where and where?”
- “What looks similar for each animation?”- “What looks different?”
- “What variation are we seeing?” – “Why are we seeing it?”
- “What does one dot on the graph represent?”
- “How is the simulated data being generated?”

**Want to read/see more?**

Wild, C. Animations of sampling variation

Wild, C. VIT – Visual inference tools

NZ Senior secondary guide – Lateness: Choice or chance

**Resources**