This is a simulation designed to explore probabilities and convergence, specifically of the sum and product obtained when rolling two dice. Probability Histogram is about learning what a probability histogram is and how basic probabilities (rolling a die) are incorporated on a histogram. It could be used in a statistics course that has an emphasis on probability as an introduction to probability histograms. The histogram displays multiple trials of the sum of two dice as well as the product of two dice.
Type of Material:
Online simulation activity
I recommend that this tool be used in conjunction with a written activity that guides the students through specific steps of how to use it. Such an activity might include questions that prompt the students to think about what they expect to see and have them compare their intuition with what actually happens in the simulation. Could be used in-class, as part of lecture, or as an out-of-class assignment.
Identify Major Learning Goals:
Students will develop a deeper understanding about probability histograms and probabilities of rolling dice. Students will explore the sum or product when two dice are rolled and will explore the convergence of each outcome in the long run.
Target Student Population:
Introductory statistics – specifically where an intuitive understanding of probability outcomes is a learning goal. Alternatively, this could be used in a course that introduces students to probability.
Prerequisite Knowledge or Skills:
An understanding of simple probability rules and the ability to read histograms may be helpful, although not required.
Evaluation and Observation
The visual aspect is great. It clearly shows how single trials work and provides a way to collect many trials to see what happens in the long run. The explanations on the right side are short, but are helpful in understanding what is going on. The content appears to be correct.
I think the explanations could include more information in order to provide a more complete demonstration of the concept. A written activity supplementing this tool would probably be the best solution. I would have liked to see the Sum and Product tabs to be linked. If you roll the dice in one, it should do the same in the other so students can make a direct comparison. I would have also liked to see an option to roll the dice maybe 20 times. A skip from 1 to 100 is quite large.
Potential Effectiveness as a Teaching Tool
It allows the students to explore a useful probability concept at their own pace, in their own way. This can help to build strong conceptual understanding. The Probability Histogram may be effective in a statistics course that has a heavy focus on probability.
On its own, I do not see this tool as being particularly effective. It needs to be supported by an activity that guides students through the learning process. It only seems to apply to statistics courses that have a heavy emphasis on probability. Many courses are moving away from probability. However, if the course has a focus on probability, it seems that it would require work for the teacher to make an activity that would develop critical thinking skills using the simulation.
Ease of Use for Both Students and Faculty
I like the overlay of the empirical distributions on top of the simulated data – students can easily see how their data start to follow that pattern as they run more and more trials. Overall, the visual aspect of the tool is very good, and the instructions are clear.
There is no “reset” button. I think it would be helpful to have one. It might also be good to have a way to display the results of each trial (i.e. a list of the outcomes of each trial: each individual die result and the sum/product). The colors are quite bright; they could be toned down a bit. In addition, it's possible that students might get bored with the Probability Histogram. They would be done with it in less than 5 minutes. It would be helpful to see the two tabs linked and more options on the number of rolls. There should be a label on the y-axis that states it is a probability. The x-axis label is not centered. There are a couple of letters that are underlined and I am not sure of the purpose for that.
Other Issues and Comments:
There are other resources/tools available that work similarly to this, but have much more extensive functionality. For example, Tinkerplots allows students to build their own simulations to model a variety of different probabilistic situations. I question the usefulness of an applet like this because it constrains the students to a very specific simulation environment.
It might be helpful to include a statement of the purpose of Probability Histogram and what audience it is geared towards. I feel that the visual aspects would quickly turn people away before they even started. I think the most important change would be to link the two tabs. Maybe they could even be shown on the same page without having tabs if you really are interested in the product.