Cause and Effect
by Abigail Mitchell

Lesson:  The importance of apportionment

Part of unit:  Day 7 of unit on Fair Division

Objectives:  

Students will understand the real life effects of apportionment. 
Students will apply apportionment methods to allocation decisions.

Rationale: 

The topics I am teaching in my Discrete Math class deal with the
many different methods used to apportion the United States House
of Representatives. Although my students have no real problem with
the mathematical steps they have to perform, they do not comprehend
the significance behind the different methods. I often find it necessary to include the historical background to illustrate the political and social ramifications of the apportionment process. It is at this stage of the lesson that I tend to lose the attention of the students, since the history portion will not be tested. I had hoped to spark their interest by having them read an editorial that discussed apportionment and the subsequent gerrymandering that often occurs as a result. My reason for using the Cause and Effect model was to give them the opportunity to see the personal agendas that so often control apportionment on the state level and the far-reaching effects it can have.

Summary:

This lesson began with a short review of the previous night's homework. I also took a few minutes to review the information from the last lesson because I had taught it before the weekend and I wanted to refresh my students' memories. From there we moved into the Cause and Effect lesson. First, I asked my students to read an editorial from a Georgian newspaper. I then asked a few basic questions to ensure their understanding. The editorial contained some rather large words so, as a class, we used a dictionary to define egregious, gerrymandering, and incumbent. After accomplishing these preliminary objectives, we were now able to establish the question for the lesson:  "The author feels the new senate districts are unfair. Why?" We then followed through all the steps of the Cause and Effect model.  I included a chart with all of the answers that my first class had provided me.

Lesson Effectiveness:

For the goals that I began this lesson with, I believe it was extremely effective. I felt that my students definitely got a feel for how reapportionment can influence national, state, and even local government. They also became aware of the personal agendas that so often sway political decisions whereby large groups of people are affected. I was extremely impressed with the astute thought process exhibited by so many of my students. Initially, the lesson was met with resistance but, by the end many of my students were diligently working and eager to participate. Also, while this lesson was more oriented for social studies rather than math, I think the connection between the two became apparent to my students. I think they began to see that the abstract concepts we have been studying have real life uses that could affect their lives.

Suggestions for Improvement: 

The major problem I encountered with this lesson is that a select few students tended to dominate the discussion. Some of my classes seemed to rely solely on these domineering students when they were stumped.  In addition, I would change my own tendency to guide the discussion the second and third time I taught this lesson. Since I had very few expectations about where I wanted the discussion to go, my first class's results were far more reflective of their own ideas. Unfortunately, I found that when my second and third classes become stuck on a cause or effect, I had ideas of my own that I tried to interject to persuade the direction of discussion. I would also give my students more background on the article before they began reading. My first class had some confusion on the ideas presented in the article. Even with these impediments, the results I got from this lesson were right on target, and I plan to use it again in the future.

  Conclusion:                                                Generalization:

   Districts should change according to population.        Political interests can become more
                                                               powerful than popular interests.
   People should speak up if they don't like the
   political system.                                          Everyone wants power.

   Shifts in power could affect the Presidential race.     No matter what system we set up,
                                                               any major decision at hand will be
   Apportionment affects a lot of things.                  manipulated by human nature.