Common Sense Mathematics is a text for a one semester college-level course in quantitative literacy. The text emphasizes common sense and common knowledge in approaching real problems through popular news items and finding useful mathematical tools and frames with which to address those questions.
We asked ourselves what we hoped our students would remember about this course in ten year’s time. From that ten year perspective thoughts about syllabus–“what topics should we cover?"–seemed much too narrow. What matters more is our wish to change the way our students' minds work–the way they approach a problem, or, more generally, the way they approach the world. Most people “skip the numbers" in newspapers, magazines, on the web and (more importantly) even in financial information. We hope that in ten years our students will follow the news, confident in their ability to make sense of the numbers they find there and in their daily lives.
Most quantitative reasoning texts are arranged by mathematical topics to be mastered. Since the mathematics is only a part of what we hope students learn, we've chosen another strategy. We look at real life stories that can be best understood with careful reading and a little mathematics.
Sample stories involve:
- Back of an envelope estimation
- Discounts, inflation and compound interest
- Income distribution in the United States
- Electricity bills
- The graduated income tax
- The economics of credit cards
- Paying off a mortgage or a student loan
- Lotteries, gambling, insurance and the house advantage
- False positives and the prosecutor's fallacy
We augment common sense and some mathematics with instruction on critical use of spreadsheets and the internet, providing students with more tools that that they will take beyond the classroom.
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About the Authors
Ethan Bolker was born in Brooklyn, New York in 1938. In his first year at Erasmus Hall High School he was hooked by Hugo Steinhaus’s Mathematical Snapshots. In his senior year he captained the Math Team, then went on to major in mathematics at Harvard College, where he earned his degree summa cum laude. He turned down medical school to continue in mathematics at Harvard, where Andy Gleason supervised his PhD.
Bolker was an instructor at Princeton University and an Assistant and Associate Professor at Bryn Mawr College before coming to UMass Boston as a Full Professor in 1972. He retired in 2014 and awaits official endorsement of his Emeritus status. While at UMass he chaired the joint Mathematics and Computer Science Departments for 12 years. He earned the Chancellor’s Award for Scholarship in 1979 and for Teaching in 2003.
Dr. Maura Mast became Dean of Dean of Fordham College at Rose Hill in August 2015. She is the first woman to be dean of the college and the first dean with a background in science and mathematics. Prior to coming to Fordham, she was Vice Provost for Undergraduate Studies and Associate Professor of Mathematics at the University of Massachusetts Boston.
Mast earned her PhD in mathematics from the University of North Carolina and her Bachelor of Arts degree from the University of Notre Dame with a double major in mathematics and anthropology. Dr. Mast is an active researcher in the field of differential geometry, primary focusing on understanding geodesic behavior as a means of exploring the relationship between geometric properties and analytic properties of a manifold. Before coming to UMass Boston, she was associate professor of mathematics at the University of Northern Iowa; she has also held visiting positions at Northeastern University, Wellesley College and the University of Notre Dame. Dr. Mast has been recognized repeatedly for her teaching abilities: she received the Chancellor’s Award for Excellence in Undergraduate Teaching from the University of North Carolina, the College of Natural Sciences Dean’s Award for Teaching Excellence from the University of Northern Iowa, and the Science Dean’s Award for Outstanding Achievement in Teaching, Research and Service from the University of Massachusetts Boston. Dr. Mast is a successful grant writer and has received National Science Foundation and other funding for her research and teaching projects.