From the Mathematics Support Center (MSC) at Cornell University

Many thanks to:

Tara, Betsy, Marie, Eliza, Ben, David, Pam, Chris, Lindsey, Darien, Reiley, Conan, Mardea, Ely, Ryan, Henrique, Sonya, Belle, Amy, Nathaniel, Clarice, Arthur, Justin, Takema, Victor, Cissy, Tik, Sagnik, Dianna, Ronald, Maria, Raman, Yue, Dick, Shruthi, Val, Louis, Vivian, Matt, Jessie, Harry, Zoe, Matt, Misha, Philip, Michelle, sma, Ebie, Andy, Bill, Tom, Malou, George, Randy, Bev, Doug, Maria, Kelly, Quincy, Mary Ann, Bob, Joy, Jane, Homer, Anil, David, Frances, and Daniel

Special thanks to:

former MSC Tutor, T.V. Raman of Google Research, delivering eyes-free access to information.

The [MSC Stories] video was edited by Film Editor, Daniel Masciari a friend of nearly a decade. He is a fellow alumnus of Actors Workshop of Ithaca. We have shared actor and producer credits over the years and have always enjoyed working together. He is now a professional film editor, mostly working in New York City. He experienced the MSC when he would stop by my office about projects back in the day. He saw what a special place it was and has enthusiastically embraced the opportunity to use his editing chops for [MSC Stories].

Please consider making an Artistic Gift to Daniel in recognition of his artistry and commitment to make the [MSC Stories] video the best it could possibly be.

How to donate: | use PayPal | use Venmo |

Pay to: | dvmreels@gmail.com | @Daniel-Masciari |

What's it for?: | Artist Gift | Artist Gift |

Thank You,

-Dick

**Date:** November 8, 2021 at 8:13:35 PM EST

Hey Dick,

Below is a short reflection about my time at the MSC. I remember you were collecting these, and feel I am able to think more clearly on it now. The story below has been slightly fabricated for the sake of its parabalization.

Working at the MSC was my first real experience in teaching mathematics. In retrospect, I hope the students I worked with took the lesson that they should trust themselves. It seemed to me then that the most approachable, and to some extent effective, teaching method was to engage in the following theatrics: I would pretend to be just as confused as the student, and we would try to work through the problem from first principles, as though the student and I were both navigating the problem for the first time. Of course, as the tutor, I had the advantage of hindsight and the readily available input of my fellow tutors. I remember on one occasion while I played this game, the dialogue proceeded:

Me: "So after you compose your function y = x^3 with the function y = 1, we should expect what? Remember, the function y = 1 is the identity, right?"

Tutee: "So, the function y = 1? No, wait, the identity right? Ah, so we get back y = x^3?"

Me: "Yeah."

Unfortunately the tutee left briefly after this exchange, before he was able to witness the well-placed ridicule I received from my fellow tutors.

Me: "Oh shoot! I'm an idiot. Where did he go; wait, I have to tell him otherwise!"

But I'm fairly hopeful that the tutee learned (one way or another) that you should trust yourself while thinking. The MSC is a place where mistakes are encouraged and people are forgiving. This culture extended beyond just the working hours, and engendered a camaraderie and friendship among everyone present.

Best,

Kabir

**Date:** April 7, 2021 at 11:44:43 AM EDT

Hi Dick,

I'd like to submit a written story. Let me know if you have any suggestions/edits. I realize it's not particularly structured as a narrative, if you have ideas on how to make it flow better I'm all ears.

As soon as I knew I was attending Cornell, I knew I wanted to work at the MSC. I arranged for a Skype interview before I arrived on campus so that I could work there from the first semester. As anyone who has stepped foot in there knows, the MSC is a truly special place of not just learning but community. People who did not have questions would come to sit and study quietly, people would stop by to talk to their friends, and some sleep-deprived students (and off-shift tutors!) would even enjoy naps on the sofa--the MSC welcomed everyone into its doors. I myself would often spend time there even when not on shift, vastly preferring it to the cold and impersonal library study areas. Students would find the tutors whose personality and teaching style best suited them, and religiously come while those tutors were on shift. After finishing at Cornell, I enrolled in a math PhD program at Yale, where I ran into another grad student who remembered me helping her with calculus in the MSC. In appreciation, she invited me on a fall break road trip she was taking back to Cornell to visit old friends, and of course I said yes. I was overjoyed at the chance to check back in with Dick and Harry and a new batch of tutors at the MSC. I walked right up to a student and offered my assistance on a problem they were stuck on, like no time had passed at all. I am currently in the process of searching for jobs (having just completed my PhD), and when I ask myself the question "What kind of place would I like to work at?" I find my mind inevitably wandering back to the culture of the MSC: a place of camaraderie and co-operation.

Best,

Louis

**Date:** February 18, 2021 at 11:26:37 AM EST

Hi Dick,

Here is a short write-up of something I remember -- edit to taste.

I worked at the MSC in Spring 1990 --- and the experience was enriching along many dimensions, especially with respect to understanding how students ended up hitting a stone wall at times because of how Math notation can confuse while intending to be intuitive -- here is one such example.

A studious Sophomore walked in saying "I cant get the right answer on this Calculus problem". So I observed him perform each step of the calculation, he did it perfectly until step n-1. Then he simplified E^{-x} to \log(x).

I asked him how he got that and he confidently said "that is the definition of Log(x)".

I told him it was not, and he confidently pulled out his class-notes saying Yes it is -- the Professor wrote it on the board.

So I asked him to show me what the Professor had written, and sure enough his notes read

"If f(x) = e^x, then F^-1(x) == log(x)"

It took me a while to explain the function inverse notation vs negative exponentiation to him --- but it illustrates how Math notation while intending to be intuitive and often confuse.

--raman

--

♉Id: kg:/m/0285kf1 🦮♉

--

♉Id: kg:/m/0285kf1 🦮♉

**Date:** March 24, 2021 at 3:49:26 PM EDT

Hi Dick,

In the end I've decided I just don't want to film a video. But, here's a written testimony.

Good luck with the project! I enjoyed the open house last weekend.

Best,

Vivian

I worked at the Math Support Center starting in my sophomore year (2014-2015), and then as a head tutor from 2015 to 2017. As is the case for many undergraduate math tutors everywhere, it was my first major teaching experience. I learned so much about teaching from the students and other tutors there, and I use that knowledge to this day to inform my class design and office hours as a graduate student. At one point at an orientation session my senior year, I explained to new tutors that I think of tutoring and homework help as akin to spotting someone while they are lifting weights. A spotter can spot someone who is lifting much heavier weights than the spotter can handle, because a lifter who is lifting 200 pounds is doing so because they have already lifted, say, 195 pounds, so the spotter is responsible at most for the last five pounds. Similarly, the students are the ones who have been attending lecture and attempting the homework, so as a tutor I am doing my job best when I am only helping with the smallest possible amount of understanding. I was really happy with this metaphor at the time (and I still use it!) but it's worth noting that it was really a product of the environment at the MSC. I remember talking to other tutors about how many students you'd be able to help if you restricted yourself to saying only things like "Have you read the chapter?", "How do you think this relates to the material you've seen?" and "What do you think we should try next?". At some point I decided that although the tutoring center largely just promises to help students in large lower-level courses like linear algebra and calculus, I was equipped with my understanding of math and these strategies, and therefore I should be able to help any student with questions about any undergraduate course.

It's worth noting that the MSC was also a fun place to hang out, with plenty of gadgets and games curated largely by Dick, but with help from the rest of us tutors. At various times the MSC serves as a type of headquarters for mathematical activities in the Cornell math department. For example, when Math Club hosted game nights, we used board games from the MSC. My first year at the MSC, it also served briefly as a T-shirt distribution center. I had been chatting with Dick about a T-shirt I'd designed, and he suggested I could design a Cornell/MSC-themed shirt. Over winter break, I came up with a design that played off of the idea that many of the letters of "Cornell" are common math symbols when written in the blackboard bold font. For example, C represents the complex numbers, R represents the reals, and N represents the natural numbers. In the spring, I contacted a T-shirt company and put up posters around the department. We got 50 shirt orders in the first batch; assuming there might be more interest once the shirts had arrived, I ordered 75 shirts. We sold the shirts for $7 each, which was just enough for us to break even on costs from just the original 50 orders. In fact all 75 shirts sold, and we used the profits to buy a set of Zome for the center. As time went on, some math department faculty started asking about the shirts. In the end, the department took over production, and the shirt became an official Cornell math department T-shirt. I believe that every undergraduate receives a free shirt when they declare a math major. As a side bonus, the Zome was a great investment, which added to the center's collection of math games.

I ended up designing another shirt for the MSC, but never implemented it (although I have a nice drawing of it on my website). This was a set of 4 mutually orthogonal 5x5 latin squares, realized as generalizations of "SET" cards. To unpack that a bit, an n x n latin square is an n x n grid where each small square contains one of n symbols, and where each row and column contains each of the symbols exactly once. So, a filled sudoku grid is a 9x9 latin square, since each row and column contains each digit from 1 to 9 exactly once. In the game of SET, there are cards of three different colors (red, green, and purple), so you could form a 3x3 latin square by making a grid of SET cards, where each row and column has exactly one card of each color. Now, two latin squares with two different sets of symbols are "mutually orthogonal" if any pair of symbols occurs exactly once in the grid. Going back to the cards: SET cards also have one, two, or three symbols on them. So we can make a numbers-latin square, a 3x3 grid where each row and column contains a 1 card, a 2 card, and a 3 card. But we can overlay this with our colors grid, so that if we look at the colors it's a latin square AND if we look at the numbers it's a latin square. The mutual orthogonal constraint says that there's exactly one card in the whole grid with a specified number and color (for example, exactly one card with one red symbol, and exactly one card with two green symbols, and so on).

SET cards have four properties in total: color, number, shape, and shading. So we can imagine setting up not just two mutually orthogonal latin squares, but four of them. This is mathematically possible, but not for 3x3 latin squares. For 5x5 latin squares, however, we can have 4 mutually orthogonal latin squares. So, to extend the SET cards to the 5x5 squares, we need each color to have 5 options, not just 3. For example, these "generalized" SET cards can be red, green, purple, yellow, or blue, instead of just red, green, and purple. This is exactly the design I've drawn; a 5x5 grid of generalizations of "SET" cards, so that any two characteristics form mutually orthogonal latin squares.

Last modified: Ithaca, NY Tue, Nov 9, 2021 at 3:09 AM GMT