Ten years from now, what do you want or expect your students to remember from your course? Our answers to those questions profoundly shaped our approach to teaching the QR course at UMass Boston. From a ten year perspective most thoughts about the syllabus – “what should be covered” – seem irrelevant, especially for students who are not in a STEM field. What matters more will be how students approach a problem using the tools they carry with them – common sense and common knowledge – not the particular mathematics we chose for the curriculum. This has changed how and what we teach. In our QR course, we focus on problems suggested by the news of the day and on subjects that we know matter to students, like credit card debt and student loans. We practice “just in time” mathematics, introducing tools only when they are really needed. This approach has changed how we teach and how we assess student’s preparation for the course. In this talk we discuss how we use common sense and common knowledge in our QR course with exercises and examples of classroom activities that are built from real data in moderately complex everyday contexts

1. Common Sense, Common
Knowledge and Mathematics:
Reflections on Teaching
Quantitative Reasoning
NECQL 2015
Yale University
May 9, 2015
Ethan D. Bolker and Maura B. Mast
University of Massachusetts Boston

2. This is your students’ last math class ever.
What do you want them to remember
ten years from now?
• Read the news. Don’t skip the numbers.
• Numbers can make sense – use common
sense.
• Technology used wisely is your friend.
• This course was
• surprising
• interesting
• useful
• fun
• memorable …

3. The course we designed
• Real stories from life and the news
• Parse numbers with estimation, common sense
and the minimal amount of just-in-time
mathematics
• Exercises call for short essays – no “circle the
answer and on to the next”
• Exams are open book open notes open
computer and internet – just like life.
• Excel, search and the Google calculator do a lot
of the routine work
• NSF CCLI funding to develop the text

4. Syllabus -Table of Contents
First third: Numbers (a few at a time)
• Fermi problems (do you believe it?)
• Units and conversions (MPG vs GPM)
• Percentages (why are they so painful? 1+ trick)
• Weighted averages (GPA, Consumer Price Index, …)
Second third: Data
• Excel (mean, median, mode, histograms)
• Linear models (electricity bill, tax policy, regression)
• Exponential models (growth, interest, debt)
Last third: Chance
• Probability (gambles, raffles, insurance, the house advantage)
• Independence (runs, lottery winners, hundred year storms)
• Dependence (false positives, prosecutor’s fallacy)

5. Problems to work today (handout)
N minutes - in a small group if you wish
• What’s in the daily news?
• A million trees?
• [No Excel]
• Breast cancer odds
Then we’ll discuss answers, and student
answers

6. Conclusion
• Teaching QR as (common sense + some mathematics)
is more work than more traditional ways but more
fun too
• Some students thought so:
• I think that hardest part about this class was thinking. When you
usually enter a math class the only thinking that you have to do
is remember equations but in this math class I had to do
research and find things on my own to help me out to answer a
question.
• For the love of all that is good, why is an English
major/poet/musician forced to take math all these years? I am
not well-rounded or more comfortable with math, it has just
drawn out my college career, costing me time and money that I
don't have. I will never use math in my life, the types that I will
employ I learned in elementary school. This was the best math
class I have ever taken though.

7. Next steps
• The MAA will publish Common Sense
Mathematics – probably next January
• Until then it’s free on the web (see handout)
• Workshop at MathFest, August 2015 in
Washington, DC
• Minicourse at JMM, January 2016 in Seattle
• Ethan’s retired (mostly) and Maura’s moving
on to deaning at Fordham, so keeping CSM
up to date is your responsibility now …
• Questions