Forming Our Future

Eight months ago I wrote a post about our first attempt at interdisciplinarity at the Crimson Summer Academy. It was a start. Perhaps even a good start, but still no more than a start. This summer we are keeping the same theme, “Forming Our Future,” and are hoping to do better with it. I suggest that you pause to re-read that earlier post of mine—written right after that first experience—before continuing here.

Let me repeat a paragraph from last year’s post:

This summer our theme was “Forming Our Future,” which was more-or-less a focus of all subjects. My guess is that that idea was much too abstract for the large majority of our students. My course, Quantitative Reasoning, did indeed try to focus on that theme (maybe 50% of the time) and we included plenty of non-math topics. Did anyone else include any math in their courses? I think not.

Here are our current thoughts on Quantitative Reasoning, a.k.a. QR, as shared with my colleagues last week:

We would love to have explicit connections with Science and Writing. In more general terms, we connect to the overarching theme by following Alan Kay’s dictum: “The best way to predict the future is to invent it.” So this is our tentative outline in the meantime:

Sophomore QR:

  • Unit 1: Algebraic Models (How can math describe and predict the real world?)
    • Families of Functions
    • Linear Models
    • Numbers and Percentages
    • Exponential and Quadratic Models (including exponential decay)
  • Unit 2: Demographics and Models of Voting (What should we do when there is no majority?)
    • What is a democracy? What about gerrymandering?
    • Demographics and Your Community
    • Ranked Choice Voting
    • Electoral College
    • Boston and Cambridge (different voting systems with different goals)
    • Project and Presentations

Junior QR:

  • Unit 3: Cryptology (protecting your passwords, your credit cards, and your country)
    • Substitution and Caesar Ciphers
    • Mods, Affine Ciphers, Reciprocals, Invertibility
    • Vigenère and Playfair Ciphers
    • Public-key Cryptography: RSA
  • Unit 4: Applied Statistics (cases solved by the well-known firm of JKL Private Investigators, with the student as intern)
    • The Case of the QR Quizzes
    • The Case of Income Inequality
    • The Case of Pandemic Procedures
    • The Case of Towering Tuition
    • The Case of Practical Politics
    • The Case of Health Horrors

We will be holding our annual spring faculty meeting early next month. I’ll do my best to articulate my vision of interdisciplinarity, and we’ll see if there will be enough buy-in from my colleagues. Here are some relevant thoughts from the well-known mathematician Charles Dodgson, perhaps more familiar to you in his pseudonym Lewis Carroll:

“Would you tell me, please, which way I ought to go from here?”
“That depends a good deal on where you want to get to,” said the Cat.
“I don’t much care where–” said Alice.
“Then it doesn’t matter which way you go,” said the Cat.
“–so long as I get SOMEWHERE,” Alice added as an explanation.
“Oh, you’re sure to do that,” said the Cat, “if you only walk long enough.”

Categories: Math, Teaching & Learning