Social Justice Mathematics Project 1: "Demographic Changes in Congress"
Overview
This project will allow students to gather data on changes in congressional diversity in order to understand its relationship to population demographics. Students will:
- Gather data on changes in congressional diversity over time (gender, ethnicity)
- Display data in tables and graphs.
- Compute percent change.
- Use linear regression to model changes over time
- Solve systems of linear equations to determine when two variables will be equal
- Draw conclusions and make recommendations based on data
Social Justice Mathematics Project 1: "Demographic Changes in Congress" Overview
This project will allow students to gather data on changes in congressional diversity in order to understand its relationship to population demographics. Students will:
- Gather data on changes in congressional diversity over time (gender, ethnicity)
- Display data in tables and graphs.
- Compute percent change.
- Use linear regression to model changes over time
- Solve systems of linear equations to determine when two variables will be equal
- Draw conclusions and make recommendations based on data
Social Justice Mathematics Project "Gathering data"
The US is becoming more and more diverse, and while the 117th US Congress is the most diverse over time, the question remains whether we are making enough progress given the changes in demographics among the population. Viewpoints on important topics like immigration, criminal justice, the 2nd amendment, education, womens rights, etc. are all in flux, and it appears that the US population is more polarized than ever. It is important for educators and their students to consider how Congress is changing in order to understand whether perspectives held by the population will be represented in laws. This project will use mathematics to predict changes in congressional diversity in the future.
Fill in the Blanks on the following data
95th congress
- Senate (100 Members): ____Men__2_ Women, ___ African American, __Hispanics, ___Asian Americans,___ Native Americans, __Non-White, ____White
- House of Represenativces (435 Members):____Men___ Women, ___ African American, __Hispanics, Native Americans, __Non-White, ____White
- 105th Congress
- Senate (100 Members): ____Men__9_ Women, _17__ African American, __Hispanics, ___Asian Americans,___Native Americans, __Non-White, ____White
- House of Represenativces (435 Members):____Men___ Women, ___ African American,__Hispanics, ___Asian Americans,___Native Americans, __Non-White, ____White
- 111th Congress
- Senate (100 Members): ____Men_17__ Women, ___ African American, __Hispanics, ___Asian Americans,___Native Americans, ___Non-White, ____White
- House of Represenativces (435 Members):____Men___ Women, ___ African American, __Hispanics, ___Asian Americans,___Native Americans, ___Non-White, ____White
- 116th Congress
- Senate (100 Members): __74__Men_26__ Women, ___ African American, __Hispanics, ___Asian Americans,___Native Americans, __Non-White, ____White
- House of Represenativces (435 Members):__334__Men_101__ Women, ___ African American, __Hispanics, ___Asian Americans,___Native Americans, ___Non-White, ____White
Suggested Data Resources:
https://www.brookings.edu/wp-content/uploads/2021/02/Chpt-1.pdf
https://cawp.rutgers.edu/history-women-us-congress
https://cgsnet.org/ckfinder/userfiles/files/New_Member_Demographics_116_Congress.pdf
https://www.statista.com/statistics/198423/senators-in-the-us-congress-by-gender-since-1975/
Social Justice Mathematics Project "Working with the data"
2. Determine the percent change of woman and of non-White members of Congress from the a) 95th Congress to the 105th Congress b) 105th Congress to the 111th Congress c) 111th Congress to the 116th Congress and d) 95th Congress to the 116th Congress
3. Fill out the following table using years as the input and percentage of total for the output
House of Representatives
| Year/Category | Men | Women | White | Non-White |
| 1977 | ||||
| 1997 | ||||
| 2009 | ||||
| 2019 |
Senate
| Year/Category | Men | Women | White | Non-White |
| 1977 | ||||
| 1997 | ||||
| 2009 | ||||
| 2019 |
Social Justice Mathematics Project "Plotting the data"
Plot each of the (year, number of group) points on a four graphs (one for gender Senate, one for gender/House, one for race (white vs. non-white)/Senate and another for (white vs. non-white)/House). Use different colors and/or shapes to identify the different groups. You may print this sheet out or take snapshots or scans of your TI-84 Screen. If you use the latter follow the steps below.
House of Represenatives Time vs. Gender by percentage
House of Represenatives Time vs. White/Non-White by percentage
Senate Time vs. Gender by percentage
Senate Time vs. White/Non-White by percentage
TI Calculator Steps
Step 1 Press STAT
Step 2 Press EDIT
Step 3 Enter Congress Number Designation (e.g. 117 for 117th Congress) in L1
Step 4 Enter Percentage for each successive group (Men, Woman, White, non-White) in L2, L3, L4, L5S
Step 5 Press STATPLOT
Step 6 Highlight ON for Plot 1 (Leave L1 and L2 as the columns)
Step 7 Follow Steps 5 and 6 for Plot 2, except change second column to L3
Step 8 Press 2nd Quit
Step 9 Press Graph
Step 10 Press ZoomStat
Step 11 Follow similar steps for each table
Social Justice Mathematics Project "Finding a linear model"
When data appear to be linear, the calculator can be used to determine a line of best fit by using linear regression.
Calculator Set Up
- Make sure that your calculator has the Plots Off, Y= functions cleared, the MODE and FORMAT are set at “stage left”, and the lists are cleared.
- Turn the Diagnostics on by doing the following
- Press 2nd the CATALOG (2nd of 0). Press the teal D button (ALPHA of x-1) This brings you to the items in the catalog that start with D.
- Arrow down until you reach the command DiagnosticOn and press ENTER.
- Press ENTER a second time. Later, when you perform a linear regression, you will see an “r” value. If that value is close to a ±1 there’s a strong correlation to the data, meaning the data points can be modeled by the line well.
Performing a Linear Regression
- To find an equation that matches the data you see, you need to perform a linear regression on the data. Press the STAT menu and arrow to the right to the CALC menu. Choose option 4:LinReg (ax+b). Type L1, a comma, L2, then the VARS button, arrow over to Y-VARS, choose 1:Function, the 1:Y1 option, then press ENTER.
When you press the GRAPH button a line that matches your data points will also be in your viewing window. Pressing the Y= button will give you the equation of that line. Repeat the steps changing L2 to L3, L4, and L5 for each linear regression.
Write down the Equations for each of the lines that models the percentage of each category.
- House of Representatives: Male
- House of Representatives: Female
- House of Representatives: White
- House of Representatives: Non-White
- Senate: Male
- Senate: Female
- Senate: White
- Senate: Non-White
Social Justice Mathematics Project "Analyzing data and drawing conclusions"
As noted in the introduction, the US is becoming increasingly diverse.(See table below). While Congress (both the House and the Senate have become more diverse) it could be argued that the change in Congress is not keeping up with demographic changes. These are also institutions that are dominated by men. Choose one of the following relationships to study (Gender changes, white vs. Non-white changes) to study. Answer the following questions.
1. Given the equations that model the relationships you are studying, when do the models predict that the number of individuals of the two groups you are comparing will be the same. (Solve the system of equations Algebraically or use the FIND INTERSECTION functions on the calculator-see below). How does this compare with the predicted proportion of individuals of each group among the US population.
2. What are things that schools can be doing to ensure that there is more representation from diverse viewpoints, beliefs, etc. in the future in Congress and in other positions of power?
3. What kinds of skills should be taught in school to help create a better society where individuals from diverse backgrounds can thrive?
Find the intersection of the two lines:
(source: https://education.ti.com/en/customer-support/knowledge-base/ti-83-84-plus-family/product-usage/11958)
• Press [2nd] [CALC] [5] to select 5:interesect from the CALCULATE menu.
• When First curve? is displayed, press the up and down directional keys, if necessary, to move the cursor to the first function, then press [ENTER].
• When Second curve? is displayed, press the up and down directional keys, if necessary, to move the cursor to the second function, then press [ENTER]..
• When Guess? is displayed, use the left and right directional keys to move the cursor to the point that is your guess as to the location of the intersection, and then press [ENTER].
The cursor is on the solution and the coordinates are displayed.