I hope you’ve enjoyed the Wolfram Language in the Classroom series. Today is the fifth and final post in the series and I’ll be talking about introducing more data into civics and social studies classrooms. One of the great things about this lesson is that the data can be drawn from your location, giving it a personalized feel.

This lesson employs a computational thinking methodology by asking students to create and support claims by analyzing data.

Lesson title: Quantifying the World around You
Grades: 6–12
Student goals:
– Formulate problems in a way that enables students to use a computer and other tools to help solve them
– Logically organize and analyze data
– Create a hypothesis to explain the data

Procedure:
– Import local economic, civic, and infrastructural data
– Compare different datasets to find relationships
– Create a hypothesis that uses historical or socioeconomic information to explain the observed relationship

To begin the lesson, you will have your students pick a major city and then plot some data for the surrounding metro area. In this case I have chosen Atlanta, and I am plotting the populations of all towns in a 50-mile radius:

It makes sense that the central, downtown region would have the highest population and that the populations for the other regions would decrease in relation to their distance from the center.

But looking just at the population alone doesn’t tell a very complete story about the region. It is often instructive to look at ratios of quantities or to look at two quantities at the same time. As an example, have your students plot the population density in each town in the region:

As you can see, even though areas west of downtown Atlanta have similar populations to those that are east or south, they have very different population densities. Maps like these create wonderful jumping-off points for students to incorporate local history and demographics to create a hypothesis to explain an asymmetric or a priori unexpected result like this. Now have your students explore other city properties—this shows you a list of all the possible properties for a city:

Another direction a student can go is to compare regions like Atlanta with other major cities in the US or the world. One feature that stands out in the maps above is the distribution of cities. They are roughly distributed along the major roadways. One could then hypothesize that there is a correlation between the number of freeway miles within a city and the population of that city. To have your students test this, first have them construct a list of the 100 largest cities in the US:

Next, construct a dataset consisting of the population of each city and the number of freeway miles in that city:

There doesn’t seem to be an obvious correlation. What about comparing the number of freeway miles to the number of miles that cars drive on the freeways every day? One might expect to see a correlation here:

Here there is a strong correlation.

To give your students a better sense of what is correlated and what is not, have them compare the number of freeway miles to the number of miles traveled annually by public transportation:

There seems to be a correlation here. Will there be a correlation between the number of freeway miles traveled and the number of public transportation miles traveled?

There is a similar trend as seen with the freeway miles. It is instructive to ask students if they expected this correlation or not before looking at the data. Because the number of freeway miles is strongly correlated with the number of freeway miles traveled, one should definitely expect to see a correlation here as well.

In a similar manner, does one expect the number of public transportation miles traveled to be correlated with the population of each city?

It does not seem to be strongly correlated. You might have suspected this because the populations are not correlated with the freeway miles, even though the freeway miles are correlated with public transportation miles traveled.

As I said earlier, though, the population doesn’t always tell the complete story of a region. You might expect that the more tightly packed citizens are, the more apt they are to use public transportation because traffic is likely to be congested. To check this hypothesis, have your students compare population density to public transportation miles traveled:

While not very tightly correlated, there is definitely still a correlation. Ask your students to synthesize what they have learned about correlations so far by thinking about how population density would compare with the number of freeway miles. Do they expect to see a correlation between these two properties?

Again, while not very strong, there is definitely still a correlation there. But this is a somewhat strange observation in light of the previous explanation. If the hypothesis for the correlation between population density and public transportation use is that when people are closer together they are more likely to use public transportation—to avoid traffic and congestion—then why is it that the more densely packed the population, the more freeway miles there are?

Questions like these are fairly complicated and not easily answered by plots like these alone. Students will have to bring other knowledge in order to answer them. Also, this is an instructive lesson in the difference between correlation and causation. Just because two quantities track together does not mean they influence each other. Lessons like this provide an ideal starting point for students to explore data, find consistencies and inconsistencies, and create and defend hypotheses.

This post concludes the Wolfram Language in the Classroom series. I hope this series has given you some ideas on how to incorporate computational thinking methods into your classroom, regardless of the subject you’re teaching. If you’d like to learn more about the Wolfram Language and how it can be used in the classroom, please check out these online resources:

• Get help and share lesson plans on Wolfram Community.
• The Wolfram Demonstrations Project has over 10,000 interactive knowledge apps to spur creativity.
• A large collection of training videos are available on demand, like the Computational Thinking in the Classroom workshop.

To see more posts in this series, please click here.

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