Math, Guitars, and a House of Cards

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Last week the New York Times published, “Make Your Daughter Practice Math. She’ll Thank You Later. The way we teach math in America hurts all students, but it may be hurting girls most.

It’s the sort of article that leads me to write a Comment, but many people beat me to it. Typical were responses about a father forcing the child to memorize times tables, which the child resented at the time, but boy was dad proud the day that PhD was earned (this Comment was an ‘NYT Pick’).

The editorial compares learning math to learning a musical instrument. Just like learning to play the guitar, “Simply understanding how a chord is constructed isn’t the equivalent of being able to play the chord….The word “rote” has a bad rap in modern-day learning”.

The piece argues that math teaching places too much emphasis on conceptual understanding, and not enough on the kind of drill that makes reciting times tables automatic.

The problem is that the author here doesn’t take the analogy far enough. True, the goal of playing a guitar is not understanding why a chord is a chord, but the goal of playing a guitar is also not playing chords.

The goal is to make music.

So what’s the object of doing math? It’s not doing times tables. It’s conceptual understanding itself.

Now, I don’t actually disagree that kids need to be fluent mathematically, just as there is value in learning to play individual chords on a guitar as a route to playing a full piece. But memorizing times tables is actually the equivalent of memorizing where your fingers go rather than actually placing those fingers properly on the fret board.

So how do you learn to ‘play’ math the right way?

What is 9 x 7? 63. How do I know this?

  • 10 x 7  is 70. To get 9 7’s, 70 – 7 = 63.
  • 5 x 7 = 35 and 4 x 7 = 28, and 35 + 28 = 63.
  • 10 x 10 = 100. 9 x 11 = 99. 12 x 12 = 144. 11 x 13 = 143. I see a pattern. Since 8 x 8 = 64, multiplying 1 less than 8 by 1 more than 8 is 63. Later in Algebra I’ll be able to connect this to the full generalization that (x + 1)(x – 1) = x^2 – 1, a special case of what’s called a, “Difference of squares.”
  • It’s 63 because I have it memorized.

The memorization came after I made connections. This result fit into an overall structure, with the truth of any one piece fitting into a larger picture. And, moreover, it fit into a future picture. When it came time for Algebra, my experience learning arithmetic fit. I didn’t go on to memorize the distributive property and the difference of squares pattern, I connected them to prior learning.

“Rote” has a bad rap in modern math learning for good reasons. The article goes on to say, “But girls especially could benefit from some extra required practice, which would not only break the cycle of dislike-avoidance-further dislike, but build confidence.”

My 25 years of teaching experience tells me the opposite. When students learn by rote, they are two years away from never being successful in math again. When the math you know is a disconnected, unstructured house of cards, you don’t know when it will fall apart, but you know that it will.


JRMF 2018: Thank Yous!

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About 200 people attended our second annual Julia Robinson Math Festival–woo-hoo!

Some thanks are in order. Many people volunteered to run our tables:

  • CPS Teachers from all over the city: Matt Rosenberg (Lakeview), Rutha Dixon (Dunne), Christine Kim (Wildwood), Serg Cvetkovic (Kelly), Lisa Cash (Goudy), Marco Mendez-Duarte (Budlong), Emily Nuttall, and a special thanks to Kevin Lee who led a table and also set things up from the inside as a Payton staff member
  • Faculty, along with Graduate and Undergraduate students: Janis Lazovskis (UIC), James Drimilla (Loyola), Lia O’Bryan (UChicago), Eugenia Cheng (SAIC)
  • Community Members: John Brown, Abhinav Gandi, Kristin Merrill, Zach Fogelson, and Alexa Katz
  • High School Students: Michael Klyachman, Hoon Shin, Juan Renteria, Jiahaochen Jiang, Vidhi Singh, and Ashley Razo

And the biggest thanks goes to Matt Moran, who put the whole thing together. Thanks Matt!

Check out the next post for photos!

Sounds Like They Might Be Talking About MC2

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In Deborah Peart’s recent essay on Edutopia, she makes the following points about kids’ development of math identity:

  1. Math experiences need to be about more than just numbers.
  2. Math needs to be a positive experience for kids.
  3. Children should be the agents of their own learning.

To which I would say–sound familiar ? MC2 is an organization that promotes (1) Allowing kids to experience novel mathematics to (2) build a life long love of math where (3) they may ultimately participate in QED, our math symposium, and present research on a problem they themselves created!

Those interested in MC2 should also check out Hilde Kahn’s post, “Closing the Excellence Gap,” on FutureEd. “If we’re really serious about increasing the number of low-income students and students from underrepresented groups who are learning math at the level required to contribute to our increasingly computational world, we should take a page from the playbook of those who are already successful: We should provide high-quality math enrichment for many more kids, as early in their educational lives as possible.”


So, if you haven’t signed up already, it’s time to register your 3rd to 8th grader for our June 2nd Julia Robinson Math Festival. Our friend and colleague Eugenia Cheng just let us know she’ll be there to run a table! (And you should check out the new book, Power in Numbers: The Rebel Women of Mathematics by Talithia Williams, featuring none other than Dr Cheng herself!)

Free, high quality, for all kids. Sounds like they may be talking about us.

News–All of it Good

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I’ll get right to it–we have a LOT of good news!

  • 70 donors gave $10,517 as part of our #ILGiveCommunity fundraiser, and an anonymous donor gave a $10,000 match. Thanks to all 71 of you!
  • The Mathematical Association of America announced that for the 3rd consecutive year it will be giving MC2 an award!
  • The Springboard Foundation renewed (and doubled!) its funding for MC2, which will support our opening a 7th site in the fall!
  • MC2 is coordinating a free mini-camp that Eugenia Cheng will hold for local high school students. In addition to her many achievements, Planet Money fans should listen to her talk about infinity on yesterday’s Indicator Podcast.
  • The Illinois Council of Teachers of Mathematics announced that Sendhil Revuluri will be given this years Lee Yunker Mathematics Leadership Award. Sendhil is a current and founding Board Member of MC2, and his leadership has been essential in MC2’s development into a premier free and accessible math circle for kids across Chicago!


Free Eugenia Cheng Summer Mini-Camp for High Schoolers!

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Join Dr. Eugenia Cheng as she leads three afternoon workshops from July 23rd to the 25th! This program is free and any current student in grades 9-12 can apply.

Dr. Cheng is an internationally famous mathematician, author, pianist, and chef! Her books include How to Bake Pi and Beyond Infinity, and she regularly writes for the Wall Street Journal; check out her Ted talks and appearance on the Stephen Colbert Show on Youtube. Currently she is the scientist in residence at the School of the Art Institute of Chicago.

From Dr. Cheng:

“Math isn’t just about numbers and equations.  It’s not just about solving problems or getting the right answer. So what is it about?  In this mini camp we will explore high level abstract math in an open-ended and accessible way, particularly appealing to visual and hands-on learners. We will emphasize creativity rather than following rules, discovery and investigation rather than facts, choices and possibilities rather than right and wrong, and structures to be built rather than problems to be solved. We will delve into some abstract mathematics typically only seen in grad school, or in advanced undergrad math classes, but which I have been teaching to art students at SAIC for several years.  In the process we will see how math helps us think more clearly about anything and everything in the world around us, with specific examples including questions of social justice including tolerance, privilege, prejudice and equality. Thus we will see that “abstract” doesn’t mean “irrelevant”, but rather, that abstract thinking can help us understand urgent issues in the world around us. The only prerequisites are curiosity and an open-mind about what math really is.”

Program Information:

  • The Mini-Camp will be held from 12:30PM-3:30PM on July 23rd, 24th, and 25th at Payton Prep, 1034 N. Wells.
  • 20 students will be invited to attend.
  • To apply, students must complete the lottery registration at along with the google form at You will need to provide a math teacher’s name and email address as a reference, along with a short statement about why you would like to attend.
  • Complete the application by May 18th; we will begin to notify students about admission on May 20th.

You’re Supposed to Say No

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Yesterday I had lunch with my good friend Sam Dyson, director of the Hive, which promotes teen learning through the internet. Like a good therapist, Sam tends to push, and yesterday he wanted to know what Math Circles of Chicago really trying to achieve. What does success look like? What’s the ‘why’?

Like many Americans, movie quotes are cultural touchstones, and what came to mind was this exchange from “Stand and Deliver,” the film about the great math teacher Jaime Escalante and his quest to bring AP Calculus to an underserved school in Los Angeles:

  • Escalante: Do you want me to do it for you?
  • Student: Yes.
  • Escalante: You’re supposed to say no!

In my own classroom, when I saw them struggling, the first question I always asked them was, “Do you want my help?”  When a student got to the point where they said, “No,” I felt they had succeeded.

To get to this point, kids need a lot of things–experience with challenging and unusual problems, a collection of heuristics (rules of thumb) that transfer from problem to problem, and membership in a community of like minded people.

So what is success for a program like Math Circles? The same, I think, as for any educational program. When students develop their own agency, they have succeeded. Just say no.

Math Camp for Adults

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Around this time of year I start pointing out summer math camps that are taking place in Chicago and around the country. Check out these suggestions from last year:

Recently, I just came across Math Camp for Adults. What really caught my attention was that this summer’s sessions are being led by Will Dunham, the author of “Journey Through Genius,” one of my all time favorite popular press math books. Why should the kids have all the fun?