Puzzles and Exercises vs. Problems

By | Uncategorized

In September I visited all eight MC2 sites and met with parents. Whenever I hold these meetings, I do a quick math circle activity to help parents understand what’s happening in our classrooms.

This experience gave me the chance to reflect on what it is we do in math circles. I talk a lot about problem solving, and it occurred to me that it would be a good idea to explain what a problem is. Let’s start with what it isn’t (at least spiritually);

A problem is not a puzzle.

A problem is not an exercise.

And, thus, a problem is in the eye of the beholder.

5 + 7 can be a problem for a first grader, if they apply different strategies to get a result. But at an older age, this kind of arithmetic becomes an exercise–something routine and familiar. The point isn’t that exercises are bad–they just aren’t what we do in math circles.

Puzzles can be non-routine, but many puzzles are non-routine to an extreme. They have an answer, but the discovery of that answer often doesn’t transfer to other contexts. This can make puzzles annoying, because the pay off in solving a puzzle sometimes falls flat, like a bad trick (here’s an old post about my favorite annoying puzzle).

A problem has the best qualities of both puzzles and exercises. They are non-routine. There is a cognitive demand in the unfamiliar. You might give up–hence it’s nice to attempt problems in a safe, fun space like a math circle that promotes persistence. And problem solutions aren’t dead ends–they connect. They may equip you to solve other problems–in fact, when you succeed in solving a problem, new problems suggest themselves. If a problem is about 5 x 5 array of squares, can you solve it for 10 x 10 array? n x n? Three dimensionally? What if the squares were triangles?

In math circles, we sometimes use puzzles to hook students at the outset of a session, but generally they are used only as a path to engage in the session’s main problem (or, perhaps, better to say ‘problem space’.) And we largely leave exercises to the standard school classroom.

As an organization we’re happy to say we have a lot of problems. 🙂

Give Me More

By | Uncategorized

Over the past two weeks I’ve attended the opening of all seven of our sites this fall (with #8 this Saturday at Back of the Yards). The most common parent questions:

  • Is there anything like MC2 for kids not yet in 5th grade?
  • My child wants to do even more math. What else is there besides MC2?

Here’s a grab bag of resources to check out!

1. A Math Circle for Grades 1 to 4.
Irene Gottlieb has gone to great lengths to establish a math circle for 1st to 4th graders. She’s rented a space at 1164 N. Milwaukee, and she just published her fall calendar–the first session is on October 10th. Follow the link and sign up!

2. Math for Love
My friend Dan Finkel has great games, a great TED Talk, and great resources on his mathforlove webpage.

3. Art of Problem Solving
Books, online classes, and online community of almost a half million kids.

4. Girl’s Angle
A Math Club for Girls, with events like Math Collaborations, “A mathematically intense alternative to math competitions.”

5. Grab Your Partner: QED!
Last, but not least (not that it’s a competition), engage in some MC2 sponsored mathematical research. On December 7th we’ll host QED: Chicago’s Youth Math Symposium, where students in grades 5 to 12 present their independent research. We’re trying an experiment this year, attempting to match up students with a partner, and then with a QED adviser. Interested? Email And please help us spread around our flyer–thanks!

The Opposite of Math Circles

By | Uncategorized

When the New York Times publishes a big story about math and school children, my inbox fills up.

Most recently, “The Right Answer? 8,186,699,633,530,061 (An Abacus Makes It Look Almost Easy“. Follow the link and check out the first photo. Here’s what I see:

  • A very large group of children gathered together to sit separately and work individually.
  • They work alone on a procedure, which they’ve learned to employ very rapidly.
  • They did not invent the abacus algorithm themselves.  No one is explaining how they arrived at their answers, and why would they?

Each June MC2 holds a Julia Robinson Math Festival, where you’ll find 20 tables of math circle activities. Compare a photo from our festival with the photo from the NYT–I admit that the New York Times’ photographer is better than me:

Here’s what you’ll see at a Julia Robinson Math Festival:

  • A large group of students, with adults, doing mathematics together.
  • People working together on a variety of problems where everyone gets to choose the math that they attempt, at their own pace.
  • Participants solving problems in their own way and explaining their thinking to others.

I recognize the value in sharing mathematical cultural practices like the use of an abacus. And I’ve seen how participation in competition can help children identify with the subject.

But I firmly believe that if we want math to be accessible to all, we need to build events where our children have choice, collaborate, and create and explain their own mathematical thinking.

In conclusion–Julia Robinson Math Festivals and Math Circles for all!


What Good Teaching Looks Like

By | Uncategorized

Our vision for math circles is two fold.

  1. We want children in math circles to have fun, to actively engage in rich and unusual mathematics, and to want to do more math in the future.
  2. We want to support a community of teachers who are striving to make #1 happen.

Teaching is difficult. What lay people (non-teachers) often fail to understand is that good teaching is the product of an environment where teachers feel like part of a community, where they hang out with other teachers–let’s face it, to commiserate–but ultimately to share ideas and to improve.

I know MC2 is growing as an organization because I can see evidence of that teaching community in all of the work that we do.

This is what good teaching looks like: Notice how the mathematics here from our summer program that is being ‘discussed’ is the creation of a student–not the teacher. Notice that 13–13!–other students have shared their thinking about that first student’s work.

If you look at other photographs from the summer program in the blog post that precedes this one, you’ll see much more indirect evidence of good teaching. You’ll see students working together, you’ll see students engaged in tasks beyond what’s usually taught in school classrooms, and, you’ll see kids in a math class…smiling.

In our surveys, you’ll see kids saying things like: “The things you learn in math circles, you don’t really learn in school,” and that what they liked best was that, “It is engaging and involves everyone.” And parents: “‘At camp my daughter was challenged and enjoyed having a voice,” as well as, “My child was exposed to mostly drill and practices kind of math. And as a result didn’t like math. To him math is something he has to do in school. But through math circles he now tasted the creative + engaging side of math. He is interested in math now.”

These photographs and these words are a reflection of our community of teachers!




Summer Thanks!

By | Uncategorized

Our camps at Zizumbo and Payton have now concluded, and I wanted to give a few words of thanks! To Chris Allen, Cynthia Ortiz, and the staff at Zizumbo, thank you for being so welcoming! This was our first summer on the southwest side, and it was a pleasure to spend time in such a beautiful building with such a wonderful staff!

At Payton, thanks going out to Mary Grubich and David Adamji for coordinating the space, and to Judy, Cookie, and the rest of the team for taking care of us every day. Math Circles of Chicago launched at Payton eight years ago, and it still feels like home.

Finally, the greatest part of our success is a result of the hard work of our teaching staff: Amanda Ruch, Rutha Dixon, Graham Rosby, Lisa Cash, Alison Ridgway, ably supported by Rileigh Luczak, Nina Tansey, Lauren Sands, Michael Klychmann, Isabel Juarez, and Kara Fischer–thanks to you all!

The best way I can recognize our teachers and counselors is through sharing survey comments parents made at the end of the camp:

  • My daughter used to love math. After a few years of bad math experiences, my daughter hated math. Thank you for helping her find her way back to her love of this subject!
  • I loved seeing E, work on the problems at home. He was eager and driven to solve the problems. (particularly math hall of fame.)
  • My daughter has had a 20+ point gain and received an A letter grade in math since participating in this program
  • A. has passed math and didn’t believe she could do it. At camp she was challenged and enjoyed having a voice.
  • My daughter was very hesitant about coming to Math Circles and repeatedly told me “I do not need help in math”. I told her it wasn’t really about help but having fun w/ math. After the first day, she came home so happy and couldn’t wait to go back.
  • My son inherited my math anxiety, it’s been hard for him, and occasionally teachers at school have been overwhelmed and less than helpful when he’s had difficulties. This has been so helpful! I appreciate it so much! It’s so much more help!
  • She has learned how to apply math outside of the classroom setting. She has always enjoyed math and understood it. Now, she knows some different strategies to solve certain problems; which is so much more interesting.
  • My child was exposed to mostly drill and practices kind of math. And as a result didn’t like math. To him math is something he has to do in school. But through math circles he now tasted the creative + engaging side of math. He is interested in math.
  • Math Circles allowed my son to work together with other kids his own age solving challenging math problems, & had fun while he also made new friends from different parts of the city. He learned to see math in a different light beyond typical classroom problems.

Julia Robinson 2019: Best Ever!

By | Uncategorized

315 people–that’s the way to end the year! We were happy to host our largest group ever for a Julia Robinson Math Festival. Woohoo!

Thanks again to Matt Moran who put the event together, and the wide range of people who ran the tables:

  • Professors Eugenia Cheng, Dhruv Mubayi, Selma Yildirim
  • Teachers Martin Bentley, Serg Cvetkovic, Christine Kim, Joe Ochiltree, Eric Rios, Graham Rosby, Sanya Singh, and Angela Tobias
  • Doctoral Students Hana Ahreum, Sara Rezvi, and Sarah Reitzes
  • Undergraduate Math and Math Ed Major Peter Smith
  • Tech Guru Abhinav Gandhi
  • Parents Kristin Merrill and Donella Taylor

A very special day–I’ll post some photos in a minute!


Primary Math Circles?

By | Uncategorized

The question I’m asked most frequently is, “Can my 4th graders come to math circles?” The answer is generally no (see our FAQ here).

Irene Gottlieb asked the same question, but she refused to take no for an answer. Instead, she went off and started a math circle on her own!

Interested? If you have a child in 1st to 4th grade check out Irene’s website. This is not an MC2 program, but it’s in the same spirit–it’s free!

Their next session will be on June 17th, and it meets in Chicago at a trampoline park. What’s not to like?

Congratulations: QED Turns Gold; Tricolorability for Pre-Teens

By | 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!

An End of the Year Celebration in the Form of a Festival

By | Uncategorized

Please join us in closing out the school year by attending our 3rd annual Julia Robinson Math Festival!

Where:             Payton Prep, 1034 N. Wells

When:              Saturday, June 1st, 1PM-3PM

Who:                 3rd-8th Graders and their parents

What:               A gymnasium filled with more than a dozen activities featuring unusual, fun, weird, inspiring, easy/hard/everything in between, MATH!

How do I sign up?

See you there!

PS. Teachers and high schoolers–please volunteer to help us run this thing! Email if you are interested. 🙂

Hermione Granger was a Terrible Student

By | Uncategorized

MC2 teachers across the city write each other all of the time to make suggestions and improve our plans.

After teaching last week at Lane Tech, Peter Smith reflected, “I had initially thought that the students would struggle with this problem, since I know I did when I first encountered it. However, about a third of the class instantly knew the punchline.” His question: What should we do when this happens?

This is a question for both teachers and students. I was reminded of Hermione Granger in Harry Potter. Hermione always knew the answers, and her response to this situation was inevitably the same: she raised her hand as quickly as possible, waved that hand aggressively, and immediately blurted out the answer.

I’d like the Hermiones out there to know there are other options.

  1. Help others. This can be the 2nd worst option after blurting out. It all depends on the help you offer. Students (and teachers) often ask leading questions. My standard bad example is, “Could you use the Pythagorean Theorem?”
  2. Ask others non-leading questions. The best questions in a math class are those that transfer to many other questions. Here’s a better question: “Do you know any related theorems?” Other questions to try: “What’s the unknown?” “Can you make a table?” “Can you make a simpler problem?” The beauty of transferable questions is that you are teaching someone a habit of mind–questions they can always ask themselves whenever they get stuck.
  3. Wait. Give everyone else time to think. Works for students and teachers alike.
  4. Try to solve the problem in a new way. You might already know the answer because someone showed you how to do it before. Can you come up with your own method?
  5. Create your own problem. Generalize. Take a 2 dimensional problem and make it 3 dimensional. Change the rules of the game. A great way to pass the time as you give others time to think for themselves.

We can all out perform Hermione in the classroom if we can learn to assert less, ask more, and create our own challenges. And, most importantly, we’ll be better students and teachers if we concern ourselves with everyone’s learning, rather than only our own!