Constitution Day – Math and Politics

Sam: It’s a private poll. The press doesn’t have access to it… The only way they’d know what questions were being asked is if they were actually called by one of the pollsters and… Oh my god!

C.J.: Yes.

Sam: A reporter got called by one of the pollsters?

Josh: Wow. What are the chances of that?

Sam: The chances of that are astronomical.

Josh: We can calculate it. They sample 800 respondents…

C.J.: Would the two of you stop being amazed by the mathematics!

(2001). The Leadership Breakfast [Television series episode]. In The West Wing. New York: NBC.

 

Last month the faculty at my college received the following in an email from our Academic Dean:

 

Hello Faculty!

With Constitution Week this week (Sept 15-19), and Constitution Day approaching next Wednesday, Sept. 17, it’s time for all faculty to plan a small segment of their classes, relating it to any aspect of the Constitution.

We do this every year as required by law. Since I don’t teach classes that lend themselves to this kind of activity I have to be more creative.

This term I’m teaching College Mathematics, which is math for non-technical majors. This is the only math class that some of these students will take. It includes discussion of algebra, geometry, statistics, probability and financial math.

This week we’re covering statistics. Based on my firm belief that you can find math in anything,I did a search on ‘constitution statistics’. It led me to the blog Introductory Statistics. I found a post titled “A Statistical Look at the Amendments to the United States Constitution”. It included a table showing the proposed and enacted dates for all twenty-seven of the amendments. I copied the data into a spreadsheet:

 

Amendment Proposed Enacted No. of Months
1 9/25/1789 12/15/1791 26
2 9/25/1789 12/15/1791 26
3 9/25/1789 12/15/1791 26
4 9/25/1789 12/15/1791 26
5 9/25/1789 12/15/1791 26
6 9/25/1789 12/15/1791 26
7 9/25/1789 12/15/1791 26
8 9/25/1789 12/15/1791 26
9 9/25/1789 12/15/1791 26
10 9/25/1789 12/15/1791 26
11 3/4/1794 2/7/1795 11
12 12/9/1803 6/15/1804 6
13 1/31/1865 12/6/1865 10
14 6/13/1866 7/9/1868 24
15 2/26/1869 2/3/1870 11
16 7/12/1909 2/3/1913 42
17 5/13/1912 4/8/1913 10
18 12/18/1917 1/16/1919 12
19 6/4/1919 8/18/1920 14
20 3/2/1932 1/23/1933 10
21 2/20/1933 12/5/1933 9
22 3/24/1947 2/27/1951 47
23 6/16/1960 3/29/1961 9
24 9/14/1962 1/23/1964 16
25 7/6/1965 2/10/1967 19
26 3/23/1971 7/1/1971 3
27 9/25/1789 5/7/1992 2431

 

I emailed a copy of the spreadsheet to my students. I also sent a link to an article summarizing the contents of each amendment.

I have two hours each week with my students to cover that week’s topic. The rest of the class takes place online. The in-class session on Monday night sets the groundwork for the entire week. I have two major topics to cover this week:

  1. Using graphs to visualize data
    1. histograms (bar charts)
    2. pie charts
    3. line charts
  2. Measures of central tendency, ie mean, median and mode

With the amendment data, we used bar charts to see how long most amendments took to enact (one to two years). This led to a discussion of outliers. For example, the 27th amendment took over 200 years to enact. We constructed pie charts to get another view of the distribution and to confirm our earlier conclusion.

But there is also a time element built into the data – proposed and enacted dates. When you want to look at data that occurs over time, you use a line chart (or trend chart). In this case, we aggregated the amendments based on the half-century during which they were enacted. When you plot that into a trend chart, you get an interesting view of the last two centuries of the United States. You can then correlate the lines with social, demographic and political data.

You can find math in anything, if you look hard enough.