Common Sense Mathematics

The main question that the authors address in Common Sense Mathematics is: What do we want our students to remember about our courses ten years from now?  Historically, we as teachers have been given a list of topics to teach or a set curriculum to follow for topic and concept coverage.  While that may be necessary for some mathematics courses, as in PreCalculus or Calculus I, for other courses, it is not.  Bolker and Mast have written a book that motivates a change in how a student’s mind works when approaching a solution to a mathematical problem.  The authors want students to take on the data and numbers they see in everyday newspapers, news feeds, and in the financial arena and use logic and reasoning skills to interpret the information.  

 

Obviously, this is a quantitative book with each chapter starting out with real-life examples to motivate the given topic.  Throughout the text, “just in time” mathematics is used to guide students through problems with the focus being on how to consume numbers rather than on producing numbers.  By the end of the course where the book is used, the authors wish the following questions on numbers would come naturally to the student:

 

 

There are few problems in this book where numbers have been changed for pattern recognition.  Since the problems are drawn from real-life examples, each is unique and requires thought with detailed explanations. 

 

In the opening chapter of the text, “Calculating on the Back of an Envelope”, students learn how to think about questions that need only good enough answers.  The first example from the May 1, 2018 edition of The Boston Globe is titled “There were nearly 100,000 Uber and Lyft rides per day in Boston last year.”  Bolker and Mast breakdown the article by first looking at the statement, “35 million trips in Boston in 2017” by asking, “Should [one] believe?” and not “Does [one] believe?”  Simplifying the numbers, if the average Uber and Lyft driver works 350 days per year, we can divide 35 million rides by cancelling the 35 and counting the zeros, which gives us 100,000 rides per day.  By comparison, we could take 35,000,000 / 365 ≈ 95,890.4109589.  However, Bolker and Mast argue that the latter computation is more time-consuming and not needed.  Chapter 1 moves forward with other applications on “Heartbeats”, a discussion on “Calculators” with scientific notation, “Millions of Trees?”, “Carbon footprints”, and “Kilo, mega, and giga.”  There are over 60 exercises for students to try.  Two that I really enjoyed were 1.8.59, which makes a connection to phishing and Netflix, and 1.8.61 that deals with $100 bills in circulation.

 

Skipping ahead, I also really enjoyed reading Chapter 4 on inflation.  With the early days of the post-pandemic, this is a very timely chapter.  On pages 101-102, Bolker and Mast provide the Federal Bureau of Labor Statistics Inflation Calculator web address and breakdown the percentage increase of the buying power of $42.26 from June 2003 to June 2008 when it was $50.34.  On page 104, Bolker and Mast provide the 1+ trick so that students don’t add percentages but combine them with a single multiplication.  This key concept in first presented in the sections “Consumer Price Index” and “How much is your raise worth?” on pages 104-105.

 

One of the main technology tools that Bolker and Mast stress in the text is the use of spreadsheets to effectively and quickly complete computations.  Many of these examples are presented in Chapter 6 starting with the spreadsheet Salaries at Wing Auto, downloaded from www.ams.org/bookpages/text-63.  The chapter also includes examples of bar graphs on pages 139-141, pie charts on page 141, histograms on pages 142-143, and the bell curve on pages 147-148.

 

Another great and very timely topic is in Chapter 8, “Climate Change – Linear Models.”  Bolker and Mast open the chapter by looking at the spreadsheet, EarthDataRegression2019.xlsx and the regression equation T = 0.0145Y – 14.5750.  They stress that the most important number to look at is the slope, 0.0145 degree Celsius / year, which means that the Earth’s temperature has increased at this average rate between 1960 to 2014.  

 

This book contains many diverse topics and guides the students through examples in a logical way.  While every problem is unique, the goal is for the student to think critically and develop a multitude of problem-solving skills so that they are prepared for 21st-century current events.  I certainly see this book being used in a special topics course, in a mathematics competition, or as a supplemental text for applications.  I will certainly use this text myself for my mathematics finance and sustainability courses.  Thank you Bolker and Mast for writing such an insightful text. 

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Peter Olszewski, M.S., is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Chapter Advisor of the Pennsylvania Alpha Beta Chapter of Pi Mu Epsilon. His Research fields are in mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu or www.personal.psu.edu/pto2. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.