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Two Views of a Tax Cut

Caren Diefenderfer used this case study as the basis for a writing assignment during the spring of 2008 at Hollins University in Roanoke, VA. This case study was written by Bernie Madison at the University of Arkansas.
This material was originally developed by the the National Numeracy Network
as part of its collaboration with the SERC Pedagogic Service.

Summary

This assignment is based on two graphs that appeared in the New York Times on April 7, 1995. The graphs provide "Republican" and "Democratic" views of a proposed tax cut. The graphs each measure the percent of "something" and in the assignment, students will compare the two graphs and determine whether both graphs are valid representations of the proposed tax cut.

Learning Goals

  1. To become a more "savvy" reader of graphs/visuals that appear in print.
  2. To understand the power and complexities of working with percentages.
  3. To improve multi-step problem solving skills.
  4. To understand that two different graphs can represent the same data.

Context for Use

I used this assignment in an Introductory Quantitative Reasoning class of seventeen students and this assignment came toward the end of the semester. Early in the semester we reviewed the basic ideas of calculating percents and the importance of interpreting percents and percentages in a variety of homework problems.Throughout the semester we discussed and produced a variety of graphs, often via Excel activities.

Description and Teaching Materials

One page assignment handout (Microsoft Word 238kB May14 08)
Excel file to discuss in class (Acrobat (PDF) 15kB May14 08)
Course Syllabus (Microsoft Word 44kB May16 08)
Course Schedule (Microsoft Word 34kB May16 08)

Teaching Notes and Tips

We spent half of a class period (roughly 30 minutes) discussing the graphs in this news article and understanding what they represent. Students were given one week to complete the writing assignment.

I have found that the most difficult part of this assignment for students is to come to grips with what each of the graphs is measuring. As I read the papers that students submitted, it was clear that even though we discussed this in class (at some length), the majority of students did not understand that the two graphs are measuring two different values. The Republican view considers "How much taxes would fall for families in each group" and the Democratic view considers the "Share of tax cuts assigned to each income group." Each graph includes a percent scale on the vertical axis and students need to wrestle with and understand that the percents given for each income group are different because they are percents of different "wholes" and are not contradictory.

Instructors who use this case study must think carefully about how much "scaffolding" they wish to provide for students and this will depend on the abilities and sophistication of the students in the class. My ultimate goal is for students to read an article of this sort and be able to question the given information and determine whether the numbers (percents) are valid. In my class, I explained how to set up a spreadsheet that will give both the amount per income group that taxes will fall and the share of the entire tax cut for each income group, based on a particular (and artificially created) total tax cut amount of $1 million. (You may download this Excel file to discuss in class (Acrobat (PDF) 15kB May14 08)this excel spreadsheet.) I was hoping that students would be able to follow similar procedures and answer question #5 using the $245 billion figure. I will rethink how I approach this when I next use this case study.

Assessment

This assignment was the fifth of six "Quantitative Reasoning in the News" writing assignments that students completed in this course (April 21 on my schedule). As such, it came toward the end of the semester and students had some experience with knowing what I expected them to do. Most students submitted a one or two page paper that included calculations. Several students submitted an electronic excel file to support their work.

Students are given the opportunity to revise each of these six papers and submit a final QR portfolio at the end of the semester. As soon as I grade these final portfolios, I'll add some comments here comparing the students' first draft with their final paper for this assignment.

I also taught this course in the fall of 2008 and using this assignment again. I want to create grading rubrics for these "Quantitative Reasoning in the News" assignments and also hope to incorporate a peer review process to make the assignments more accessible to students and easier for the instructor to grade.

References and Resources