How to Teach using Data Simulations

Research that examines the use of simulations on student outcomes suggests that even 'well-designed' simulations are unlikely to be effective if the interaction with the student isn't carefully structured (Lane & Peres, 2006). Consequently, how simulations are used is of great importance.

Simulations can involve physical materials (drawing items from a bag, tossing coins, sampling candies) or they can involve generating data on the computer (drawing samples from a population or generating data based on a probability model). Even when using computer simulations, Rossman and Chance (2006) suggest always beginning with a concrete simulation (e.g., having students take random samples of words from the Gettysburg address before taking simulated samples using their Sampling Words applet, or having students take physical samples of Reese's Pieces candies before using a web applet to simulate samples of candies).

Effective Ways to Use Simulations

Regardless of whether the simulation is based on concrete materials, a computer program, or a web applet there are some suggested ways to use simulations to enhance students learning. These include:

Cautions about Using Simulations with Students

Here are some practical considerations to keep in mind when designing or using activities involving simulations.

Using a Visual Model to Illustrate the Simulation Process

Keeping track of populations (or random variables), samples, and sample statistics can be confusing to students when running certain simulations. It can be useful to use a graphical diagram to illustrate what is happening when simulating data, helping students to distinguish between population, samples, and distributions of sample statistics. The Simulation Process Model (Lane-Getaz, 2006b) can be used for this purpose.

The Simulation Process Model (Microsoft Word 64kB Oct15 06) provides a framework for students to develop a deeper understanding of the simulation process through visualization. The first tier of the model represents the population and its associated parameter. The second tier of the model represents a given number of samples drawn from the population and their associated statistics. The third tier of the model represents the distribution of sample statistics (i.e., the sampling distribution).

The Sampling Reese's Piece activity provides a good example of how the Simulation Process Model might be used. In this activity students use an applet to simulate samples of candies, while a graph of the distribution of orange candies is dynamically generated. The population of candies (shown in a candy machine) would be the first tier of the model. Multiple random samples of 25 candies and the proportion of orange candies in each sample make up the second tier of the model. Finally, the distribution of the sample proportions of oranges candies make up the third (and bottom) tier of the model. Sharing this model with students after they complete the simulation activity can help them better understand the simulation and distinguish between the different levels of data.

Examples of Simulation Activities

Generating Data by Specifying a Probability Model

In the One Son Policy simulation students are first presented with a research question about the consequences of the one son policy, where families continue to have children until they have one boy, then they stop. Students are then asked to make conjectures about the average family size and ratio of boys to girls under this policy. Then students simulate this policy, with coins and a computer applet. Students then compare their conjectures to their observed results. Through this simulation students gain a deeper understanding of the processes associated with probability models.

Hypothesis Testing and Inference

In the Coke vs. Pepsi Taste Test Challenge students first design and conduct an experiment where students participate in a blind taste test. Students collect and analyze data on whether their peers can detect the difference in colas, using simulation to generate data to compare their results to.

Sampling from a Population

In the Reese's Pieces Activity students first make a prediction about the proportion of orange Reese's Pieces in the population of Reese's Pieces candy, then randomly sample 25 candies and record the proportion of oranges candies, then simulate data using an applet.

Assessment of Learning after a Simulation Activity

There are different ways student learning can be assessed after using a simulation activity. These include:

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