What are math class and math circles for?

By | QED

I spend a lot of time thinking about how Math Circles of Chicago can be impactful. Many parents give us permission to see their children’s grades and standardized test scores. We have some evidence here and in our surveys, in testimonials we are sent, that we make a difference. While I’m happy that math circles does spillover into the math classroom, improving grades or performance in math class is not what math circles is for.

What I do think math circles is for is harder to measure. I’d like to see our students become more mathematically creative. I’d like them to see connections between different kinds of mathematics, and between mathematics and other subjects, including science and the arts. I’d like to increase the likelihood that our students take active pleasure in participating mathematics.

This is where QED, our math symposium, comes in. Grades and standardized tests don’t often measure creativity, passion, or independent thinking. At QED students identify their own question to answer and then they explore. If we draw an analogy between sports and mathematics, math class is practice; QED is the game (and perhaps math circles themselves are practice games, where every once in a while the coach steps in to provide feedback).

Yesterday I taught a math circle at Payton HS in our Cantor-A1/G program (students currently studying Algebra 1 and Geometry). I was excited about leading the session because it was based in a problem I had newly invented. As far as I know, my students engaged in a set of problems no one had ever tried before. As a teacher it’s a little unnerving to lead students in a session where you don’t know all of the answers, but it’s liberating too. By the end of session we reached a mathematical frontier, a place students in math rarely get to be.

I strongly encourage every math circle family to get involved with QED and let their child explore the mathematical frontier. Like all of our programs QED is free. It’s like a science fair, but it moves a bit faster and is more fun.  Some key information:

  • QED will be held on December 10th at Payton HS. See the QED webpage to learn more.
  • Once you have a project idea and a title you can pre-register. You must pre-register by November 28th.
  • You can enter a project with a partner! We support collaboration (and we support non-collaboration too; going solo is fine).
  • We have a cadre of graduate students and teachers that can advise students that need help getting started or who get stuck. Need help? Fill out this form. Have Questions? Write us at!
  • A year ago I wrote this blog post with QED tips, based on interviews with some teachers that have sponsored many QED projects. This old post describes a day at QED, and this one is a primer on how to take an old problem and come up with a new one.

While I’m happy to hear that our students our doing well in school, I get excited when a student becomes a researcher. Creating new problems and grappling with them–that’s ultimately what I think math circles are for. Come to QED and see what it looks like!

QED Tips

By | QED, Uncategorized

Pre-Registration for QED, Chicago’s Youth Math Symposium, is open until November 13th. But now is the time to get started!

When talking to students and parents about QED, I’ve often emphasized that the hardest part of creating a project is getting started. We have QED brainstorming sessions to help students get over that hurdle. We held one such session today; here are a couple of research ideas participants developed:

  • What if you made a magic square, but instead of adding the numbers, you multiplied and divided them?
  • In how many ways can you color the sides of a square with four colors, if adjacent sides must be different colors?
  • What is the largest set of perfect fractions (unit fractions) that add up to one?
  • How many ways are there to cover a 6×8 lego piece with other bricks?

I also reached out to the greatest experts I know on the subject of school level math research. Julienne Au and Mike Caines sponsor more projects than any teachers in QED history. Some of their advice:

  • It takes time! Deciding on an idea takes time. Once you decide on an idea, it takes time to turn it into a project. There are often confusing results or dead ends in the process of investigating a problem. It takes time to work through these moments, but persistence will pay off. In no way should the time commitment dissuade anyone from working on a project. There are teachers and mentors who are here to share advice and help you through the problem solving process.
  • At the senior level, the hardest part seems to be selecting a topic.  It isn’t easy to find a project that has just the right amount of challenge but also hasn’t been done before.
  • Do not be afraid to ask questions and do not be afraid to make mistakes! Sometimes you get stuck when you’re working on a problem. There’s absolutely nothing wrong with that. The great thing about a project (versus a problem that you get in class) is that there isn’t a “right” answer or a “right” way to do the project. Asking questions and sharing your thoughts with others are great ways to figure out ways to tweak or adjust your project idea.
  • There are many possibilities you can explore and many chances to learn from your mistakes. Sometimes a mistake isn’t actually a mistake, but a step in a better direction. 
  • I like mathematical card tricks and games where you have to figure out some optimal strategy. Anything that gets the audience to participate in the problem solving process is really exciting for me to see!

And what do their students say about QED?

  • They have a great time! The games and QED day are lots of fun. After all is said and done, they are really grateful for the opportunity to talk about their projects with the judges. Some kids may not think of themselves as strong public speakers, but QED was an opportunity to share their thoughts about math and feel more comfortable and confident as a result.

QED 2019: Horsing Around or How to Win $1,000,000/N

By | QED, Uncategorized

Congratulations to all students who participated in QED 2019! You’ll find glamorous photographs in the blogpost following this one, and we hope you are still coveting the ‘fabulous prizes’ you took home Saturday.

Silly contests and serious art fairs

We try to keep QED from being too serious. Lawrence Tanzmann runs our annual Guesstimathon, an internet-free challenge with prompts like, “The number of times Horse appears in the song Old Town Road” or “The number of pages in the first edition of the Harry Potter series” (you can find all the prompts here). The Lowest Positive Integer game asks you to pick the smallest number that no one else does–this year’s winner chose 19 (here’s the distribution of entries). Most popular was our million dollar lottery. You could enter as many times as you like (someone entered 1 billion times), with the unfortunate side effect that the grand prize was $1,000,000 divided by the number of entries. Generously we rounded up the five hundredths of a cent grand prize to a penny.

The highlights, of course, were the QED entries themselves. While some of the project names were also silly (A Can of Worms, Frogs on a Log, Peppermint Experi-MINT), the mathematical content was anything but. Like an Art Fair, there was no competition between entries, just the opportunity to share what you created with the public. Every judge I spoke to after the event was deeply impressed by the level of work they saw.

Judges from all over

We’re proud that we draw judges from many walks of mathematical life, from professors to post-docs to graduate and undergraduate students, teachers from primary to middle to high school, along with some combinations of parent-engineer-financial industry wiz-data scientist. Thanks to you all!  Stu Abram, Maneesha Pradeep, Paul DeRonne, Nailea Curiel, Rutha Dixon, Sam Dodds, Aimee Hart, Jaime McLauglin, Marco Mendez-Duarte, Cornelia Mihailia, Jeremy Judge, Sarah Reitzes, Youjin Lee, Graham Rosby, Minh-Tam Trinh, Matt Rosenberg, Hannah Butler, Melissa Ramirez, Serg Cvetkovic, Abhinav Gandhi, John Marchetta, Faith Medlock, Maxime Bergeron, Kara Fischer, Nate Harman, Edward Huh, Peyton Morgan, Todd Pytel, Kristen Schreck, Eric Xu, and Kevin Zhou.

A word of thanks for our sponsors and friends

Peter Tingley went all out as this year’s QED speaker. Dr. Tingley, a professor at Loyola, obtained 600 hackey sacks with QED & Loyola logos to give away (see the photo), for teaching both the mathematics and the practice of juggling. Lawrence Tanzmann ran the Guesstimathon for the nth year running, where I know n to be somewhere between 4 and 7. Steve Starr hosted our Visiting Students who we expect to return in 2020 with new projects!

Julienne Au managed the judges and Mike Caines managed QED’s logistics; that they did so while also managing the logistics of having their newborn onsite was all the more impressive. Lead judges Paul DeRonne, PJ Karafiol, Dan Kang, and Matt Moran made everything run smoothly. Esperanza Baeza, Anabelle Mendez, Grace Shin, Ralph Banasiak, Paul Buckner, and Dzevida Duheric took care of everything else. Go team QED!

The American Mathematical Association again gave every QED participant a recreational math book, and Wolfram gave them each Mathematica, Wolfram Programing Lab, and Wolfram Alpha, the most advanced mathematics software in the world. Chicago’s own Citadel provided food and shirts. Thanks to you all!

QED Updates, Juggling News

By | QED, Uncategorized

QED, our annual math symposium is just around the corner. We have important announcements!

  • The pre-registration deadline for QED has been extended due to the recent school closure. Please pre-register by Tuesday, November 19th. (The previous deadline was the 12th). High School students, be reminded that your project papers must be submitted by that date! Middle schoolers do not need to submit papers in advance. Pre-register here!
  • Are you still looking for a project idea? MC2 teachers just conducted a problem brainstorming session–email if you’d like to see one!
  • If you aren’t ready to participate in QED this year, we take visitors. Sign up here to get an intro to QED, visit projects, try our Guesstimathon, brainstorm an idea for next year (while eating pizza), and attend the QED Talk.
  • Speaking of our QED Talk, this year’s speaker is Peter Tingley of Loyola University. Dr. Tingley is a leader of the Chicago Math Teacher’s Circle, and, I claim, he will teach every QED participant and guest how to juggle. We will provide the juggling balls–just come ready to learn.

So, QED. Imagine a science fair. But with math and computer science projects. Where you do things like guess the number of calories in a single serving of Chocolate Chip Cookie-Doug Cheesecake from the Cheesecake Factory. And you learn how to juggle.

You have to come.

Congratulations: QED Turns Gold; Tricolorability for Pre-Teens

By | QED, Uncategorized

When our judges saw Lillian Jirousek’s project at QED they were blown away. Now they aren’t the only ones.

Congratulations to Lillian for earning best in category (math!) at the state science fair, which came with a $2,000 scholarship! In her project, “The Mercurial Matrix,” Lillian explored the relationship between the adjacency matrix and walks on graphs.

Kudos for Amanda Ruch and Sara Rezvi for recently publishing, Untangling the “Knot” Your Typical Math Problem in the 25th Anniversary issue of Teaching Children Mathematics. Sara and Amanda based their article on an activity they implemented in MC2’s summer camp in 2018. Amanda is the lead teacher for MC2’s Haynes level (5th and 6th graders); Sara is the city wide lead for Brahmagupta (7th and 8th graders).

Amanda and Sara’s lesson concerned ways in which mathematicians can use the tricolorability to distinguish knots. Pulling off this topological lesson for 5th and 6th graders involved pipe cleaners, colored pencils, and a willingness to explore.

Congratulations to you all!

QED Review

By | QED, Uncategorized

Another QED is in the books! Thank you:

  • Bridget Tenner, our wonderful speaker!
  • Lawrence Tanzmann, for another intriguing Guesstimathon!
  • Mike Caines, for running the show!

What’s a Guesstimathon? Well, what’s the world record for the number of people doing the Floss Dance? And no googling–Guesstimate! See this year’s Guesstimathon questions and rules if you are interested. 

Dr. Tenner talked about how her tastes in math developed when she started out–Sudoku, origami, crafts, the Game of Set, Logic puzzles, Dots and Boxes. This led her to Combinatorics–where the problems can be easy to understand but very hard to solve! She went on to talk about the surprising mathematics of avoidance–some strings are easier or harder to avoid than you think!

Lots of work goes on behind the scenes–thanks to Mike Caines for his hard work making sure that QED came off without a hitch. We had students from across the city, and judges from across the mathematical world–professors, Phd Students, secondary and primary teachers, engineers, data scientists, and everything in between. Be sure to check out the photos in my last blog post, and we hope to see all of you at QED 2019!


QED: A great place to visit!

By | QED, Uncategorized

Over the past few weeks I’ve been making the grand tour of our seven math circle sites. Several parents have gotten interested in QED, our Math Symposium, and were disappointed that pre-registration had just ended. They wanted to know–couldn’t there be some way for their kids to come see projects and be part of the event, to inspire them to come next year?

There is now!

If you’d like to visit QED on December 1st, please complete this google form. (5th-12th graders only please.)

10:00AM Welcome and Tour Projects

11:00AM Participate in the Guesstimathon

Noon Pizza and Project Brainstorming

1:00PM Keynote Talk, Bridget Tenner, Professor of Mathematics, DePaul University

Note that the Mathematical Association of America has donated books that we will give away–every student will receive at least one (and probably two!)


QED: Quite (an) Excellent Day

By | QED, Uncategorized

Our research symposium is a wrap! Last Saturday 130 students attended the latest annual QED, and the consensus was that this was our most outstanding symposium to date!

Check out our photographs in the post below to get of a sense of what a special day it was! There are lots of thanks to go around:

  • Lawrence Tanzman, MC2 Board Member, and senior Jason Chen, QED participant(!) ran our annual Guesstimathon. (For those not in the know, the Guesstimathon asks participants to guess a range of values for certain fun facts–highlights from this year included, “The number of people who watched all episodes of ‘Stranger Things 2’ within 24 hours of its release,” and, “The number of tweets President Donald Trump has made on his account as of December 1st, 2017.” No technology allowed to help guess the answers, of course!)
  • UIC’s Daniel Groves gave our keynote address, focusing on geometry, starting in the plane and ending up on the sphere, giving a flavor of what non-Euclidean geometry is for the novice.
  • Our 32 judges hailed from across the mathematical spectrum:
    • Postdocs, graduate students, and undergraduate students from UIC, UChicago, and DePaul–Ben Usha, Tim Black, Maxime Bergeron, Janet Page, Samuel Dodds, Mariya Sardarli, and Nathan Lopez, along with professor Lynn Narasimhan.
    • Community members with math and science backgrounds–John Brown, Hal Finkel, Nate Harman, Peyton Morgan, Jerry Winn, Jim Mallernee, Kelly Hally (math circle parent!), Rob Creel, Oren Livne, Peter Morfe, Zach Fogelson, Nolan Winkler, Jesse Wang, and Lucie Weng.
    • Middle and high school teachers–Joe Ochiltree, Rutha Dixon, Matt Rosenberg, Serg Cvetkovic, Stu Abram, Aimee Hart, Alison Ridgway, Mike Calderbank, along with PJ Karafiol, who is now a principal but is still a math teacher at heart!
  • Our sponsors: Dell, which gave out drones(!) to some of our high school participants; Wolfram, which shared many prizes and is providing free access to Mathematica and Wolfram Alpha to every student who had a project in QED; the American Mathematical Society, which donated over $2,000 in books to give away; and Citadel, which paid for tshirts, pizza, and some truly excellent ear muffs along with other gifts. Moreover, several Citadel employees helped judge QED projects!
  • A special thanks to Benjamin Walker who took most of the photos in our montage below.
  • The folks behind the scenes who organized the judging and kept the event running smoothly–Julienne Au, Matt Moran, Mike Caines, Dan Kang, and Scott Galson.
  • Finally, thanks to all of the teachers who supported these students create such outstanding projects. 🙂

QED 2018 will be held on Saturday, December 1st. Get those projects started now!