The Joy of Quantitative Reasoning

Abstract

One of the advantages of focusing on quantitative reasoning is that it spans a wide variety of topics. As incoming president of the National Numeracy Network, I would like to take the opportunity of this editorial to tell my story of intellectual reward from finding common purpose in quantitative reasoning with colleagues from disciplines outside of mathematics. The story starts with an NSF-funded faculty development project (DUE-9952807) to further a QR across-the-curriculum program and the finding from that program that merging authentic context with mathematics brings interaction and collaboration. That joy in learning from and working with colleagues in other disciplines has now expanded to seeking authentic context for all of my mathematics courses and being open to new ways of thinking. Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License Cover Page Footnote Caren Diefenderfer is a professor of mathematics at Hollins University where she has chaired the mathematics and statistics department as well as the division of natural and mathematical sciences. She served as Chief Reader for AP Calculus, 2004-2007. She is president of the National Numeracy Network, which publishes this journal. This editorial is available in Numeracy: http://scholarcommons.usf.edu/numeracy/vol5/iss1/art1 I started working with colleagues at Hollins on a Quantitative Reasoning program in 1998. Our vision was to allow students to choose a quantitative reasoning course in a discipline of their choice in order that their quantitative work would be critical to a topic that was important to them. In order to help faculty members develop quantitative reasoning projects in disciplinary courses, Professor Trish Hammer and I applied for and obtained an NSF Faculty Development grant. 1 The grant allowed us to bring four visiting scholars to our campus. We expected our colleagues to revise ideas that the visiting scholars described. Instead, our colleagues showed great creativity and originality in designing quantitative reasoning projects. The first thing we observed was that the projects they created during the workshops were both more interesting and sophisticated than the “applied” exercises that frequently occur at the end of problem sets in mathematics textbooks. Our colleagues’ projects demonstrated that there is a serious problem with the applied exercises in our textbooks. I had thought that such applied problems would help students understand that learning specific mathematical concepts is important for life. But, the applied problems in the textbooks lacked an authentic context. Students, on the other hand, are familiar with authentic contexts from their work in the sciences, the social sciences, the arts and the humanities. A second observation about the QR projects designed by my colleagues is that they often involved elementary mathematics and sophisticated reasoning. The main importance of these projects to mathematics is that they demonstrate to students that authentic quantitative problems appear in all disciplines. I will give a short description of three of the Hollins quantitative reasoning projects in order to explain the authentic contexts that we have developed. • Professor Andre Spies taught a course titled “France since the Revolution,” before he retired in 2004. The quantitative reasoning project Professor Spies designed relies on an 1869 document of Minard that gives a visual schematic of Napoleon’s march to Moscow and his return. 2 Professor Spies wrote a series of questions that is intended to help students understand the disastrous nature of this event. Students must pay close attention to the numerical information on the schematic (including the temperature in Reaumur) to draw important conclusions about the march. Students agree that this exercise is more interesting than simply reading about the event in a textbook. 1 DUE-9952807 (2000−2003). 2 Minard’s “flow map” is a featured picture on Wikipedia. See http://en.wikipedia.org/wiki/File:Minard.png (accessed December 16, 2011). 1 Diefenderfer: The Joy of Quantitative Reasoning Published by Scholar Commons, 2012 • Professor Ruth Doan teaches a course in U.S. Social History and shows students a 1689 census from Bristol (now Rhode Island). Students work together to understand how the data are organized. Professor Doan uses this assignment so that students can develop a strong sense of “family” in colonial New England. Males were the head of most households, but by carefully observing the household of the Widow Walley, students learn who is and is not included in the census numbers. Another interesting detail of this census is that they list 421 souls and then include two additional names. We don’t know why these two men were not counted as “souls.” Students give theories and must decide if this is a significant issue or a mild annoyance. • Professor Tine Salowey teaches a course in Ancient Art and uses a text of Vitruvius to study the floor plan and 3d elevation of ancient temples. Students use measurements from a small temple fragment to recreate an entire structure based on Vitruvius’ text. These three projects exemplify the way in which the Hollins quantitative reasoning projects apply to a specific discipline and require students to apply elementary mathematical models and use sophisticated reasoning to complete the assignment. What makes many of the QR projects successful is that instructors have developed a scaffolding approach to the final assignment. Most instructors include group work, class discussion and individual writing as part of the project. Several instructors believe that having students create the data (by a survey or by visiting a site) gives students true ownership of the project. Instructors also encourage students to approach the problem from multiple points of view. As a result of working with faculty in developing QR projects, I continue to look for authentic contexts for problems that are connected to the courses that I teach in Quantitative Reasoning, Linear Algebra, and Writing Proofs. I am especially pleased to be a Co-PI on Bernie Madison’s “Quantitative Reasoning in the Contemporary World” NSF grant. As part of this grant, the QRCW team produced a book 3 of case studies in the news that serves as the framework for an introductory quantitative reasoning course. 4 We have identified 30 news articles from a variety of sources that address health, public policy, tax bills, and personal 3 Madison, B. L.,S. Boersma, C. L. Diefenderfer, and S. W. Dingman. 2009. Case studies for quantitative reasoning: A casebook of media articles, 2nd edition. New York, NY: Pearson