Mulling things over

Tonight at school we had our inductions into Cum Laude (like national honor society) and Mu Alpha Theta (the math honors society). And our guest speaker gave a rousing speech about his life, and how it’s okay to have fear, but the biggest hurdle to doing something significant with your life is accepting the fear and moving on in spite of it. Accept it, own it, be afraid, and then still forge forward.

At the end, he said something powerful. The first thing one needs to do to when leading a purposeful life is to say what it is that you want to do. Articulate it aloud. And that is scary. Making it public so you can hear yourself say it, but also so someone else can hear you say it. So it becomes real instead of this thing that bounces around in your head but never gets out. And so at the end, he told everyone to be quiet, and he was going to say something he wanted to do, and then afterwards there should be silence… and when anyone else wanted to say something they wanted to do — something they would declare out loud — they should stand up and say it, and then remain standing. This was an open invitation to the students in these honors societies, but also to the parents and teachers there as well.

The speaker said: “I want to change the world.”


A little more silence where everyone looked around and felt uncomfortable.

Then a student — one courageous student — got up and said something. And remained standing.

And then another. And another.

The head of the upper school said something. Then more students. Then a parent. Then me. Then another math teacher. Then more students.

At the end, every student made a declaration, and a few adults too. It is scary. But it also showed me how much courage our kids have. Their declarations ranged from showing others that girls can do math and science to spreading love to making people laugh to promoting peace to inventing something to becoming a biochemist to making a mark on the world. Big things and small things, lofty things and concrete things, but all things that share with the room a sense of self and a sense of purpose.

I loved watching this.

I also loved and hated how hard it was for me to come up with my thing. My purpose in life. I said:

I want to make it so that kids see math as an artistic and creative endeavor.

And I meant it. Because you know what has been bouncing around in my head that I have been having trouble articulating? I am now pretty good at coming up with deep and conceptual approaches to mathematical ideas. And I’m okay at promoting mathematical communication. And I’m transitioning to having kids do groupwork all the time, to learn from each other — so I am not the sole mathematical authority in the room.

But all of that said: I don’t think I teach math in a way to shows how it is an art form, how deeply creativity and mathematics are intertwined. And I know that this is one of my charges as a teacher moving forward. It’s going to be an uphill challenge, and one that will likely take me many years to wrap my head around. The hurdles are significant. Having a set non-problem-solving-based curriculum which doesn’t allow time for much mathematical “play,” nor for the inclusion of rich problems with multiple entry points, is the largest hurdle. But there must be ways — activities or units here and there — that can illuminate the artistry and creativity of doing and discovering mathematics. And I want to be involved in finding ways for this to happen. Yes, this happens at math circles. Yes, this happens at math clubs. Yes, this happens at summer math programs. That’s where the love and excitement and understanding of the beauty of mathematics unfolds for many students. But I want to find a way for this to happen in a normal classroom, with normal students, with the normal constraints. That (one of) my purposes.



  1. Thank you for sharing such a powerful and moving experience. I have thought of, mulled over, tried and failed, tried and succeeded a little with the idea you shared,… I would like to be a part of this endeavor and would like to share what I understand and practice and most of all learn from others with the same passion for math and leaning

    1. Well we must then figure this out! I am now brainstorming… The things that immediately have come to mind in this brainstorming:

      1. Create a unit in a traditional curriculum that is centered around problem solving.
      2. Reading Polya’s “How to Solve it” is going to be invaluable to this
      3. Finding rich problems with draw together branches or topics of mathematics, that have multiple entry points, is key
      4. Having kids devise their own extension problems based on a given problem feels important to me … How can we generalize? What additional questions pop up? Where we can go from here? (Or have them come up with their own problems, period.)
      5. Creative a research project for kids to investigate — where they can see the failures and triumphs that accompany mathematical investigation. This could start at the beginning of the year and carry through in little bits each quarter. Different questions for different pairs of kids. It has to be personal.
      6. Really talking explicitly about the artistry and creativity that math truly is — and find and present examples of unexpected results or multiple approaches to the same problem that illustrate that. Maybe make a tradition of doing that once a week on a particular day.
      7. Somehow making it so the process and articulation of the mathematical processes gets prioritized over the product. If it is being evaluated, it is being evaluated for “oh that’s an interesting approach even though it didn’t work out… where did things go wrong?” rather than “oh that approach didn’t work out, so you should have been more clever.”
      8. Having kids do a lot of guessing/estimating/playing around with concrete ideas before generalizing. In other words, explicitly talk with them about building intuition.
      9. Before trying anything of this sort in the math classrooms, have students write a paragraph responding to this prompt: “Math is a creative artform.” And then have them respond to the prompt after making an explicit push in this direction. That might be one barometer of if you are succeeding/failing.
      10. Utilizing AMC/NYML problems which don’t directly tie into one specific point in the curriculum… solving these problems requires mathematical creativity, leaps of thought…
      11. Always have kids look at and articulate the bigger picture while working on an individual problem.

      Add more thoughts below!

  2. What a beautiful post – I got chills reading it, as if I was there at the inductions. I wish I was a student in your class as you implement your goal. And thanks for all the suggestions!

  3. Yes, yes, yes! This is also what I want. I want all of my students to experience the fun we have in math club just exploring math for fun. I love it when someone writes what I have been thinking!

  4. Bravo! What impressed me the most: it was a STUDENT who was the first and most courageous of all. Thanks for sharing this, and especially for sharing YOUR goal. Keep us in the loop as you progress with it! :)

  5. This is fantastic, Sam. All of the bravery that you describe in the assembly—the bravery of committing oneself through an act of vulnerability—really moved me. Know that as your own mathematical values, tastes, passions, and perspectives continue to expand and flower, you will continue to bring your whole self to your students and change their hearts, minds, and lives as a consequence. Congrats on making such a fantastic and public next step as a teacher.

  6. This really is a great post. And the thing that I keep on thinking is that mathematical creativity doesn’t need to be about art or especially great problems, though of course those are great. Creativity comes in to the classroom when we leave room for it by allowing there to be a gap between what our kids can solve inefficiently and what they can solve efficiently.

    Consider: I’m hanging out with a 3rd Grader today, and she asks me “What’s 6 times 8”? I say, “Dunno. What’s a good problem to start with?” She decides to start with 5 times 8. Clearly, she’s thinking that she’ll start by counting 5 eights, and then add one more eight at the end. But — and this was the really cool part — she decides instead to count 8 fives. That’s obviously easier. She quickly ends up with 40, and then she returns and adds on an eight and lands on 48.

    I’d call this a really creative moment for this kid. And ruining it for her would be the easiest thing in the world. All we’d have to do is give her a maximally efficient way to tackle the problem.

    1. I agree! And I hope it didn’t make it sound like I wanted all math to be “art.” I meant artistic in the creative and beautiful sense, the multiple approaches sense, the sensibility and feeling sense… not the “picture” sense! An artFORM, I suppose I meant.

  7. Thought you might enjoy reading about this school…maybe you have already heard about it.

    1. Thanks for passing that along. I DEFINITELY have heard of it, and wow. If only I were good enough at math to even be considered worthy of working there.

  8. Hey I don’t know if you’re looking for recommendations for things to read/do in support of this endeavor, but if you are, check out the book _Out of the Labyrinth_ by Bob and Ellen Kaplan, and also the week-long Math Circle Summer Institute in July. It is focused on running a math circle, but I picked up some good insights there as an attendee with a classroom teacher’s perspective.

    1. I actually own the book, but I am finding it challenging to read. I’m not much into it, honestly. However I’ve really wanted to go to the Math Circle Summer Institute a lot lot lot!

  9. SAAAAAAMMMM!!! It’s like you’re in my head! But your words come out so much better than mine.

    I’ve been thinking about two things a lot:
    (1) I think one of the reasons I love teaching high school students so much is that they’re so freaking brave, as shown in your example. Holy moly…I have so much to learn from them.
    (2) Yes, yes, yes, to encouraging more creativity in mathematics…to giving kids space to breathe and to play. I know you’re not advocating for more “art” in mathematics, necessarily, but here’s one thing I did this week, that made me feel like, “Yes, this is true mathematics.”

    1. Love your resources re: fractals in that post. I’m def going to do this at the start of the year next year, because we start with Pascal!!!

  10. Loved it! And will one day try this in my classroom, I spent 25 years wanting to be a teacher and never told no one, until I did and now I teach!

    1. This is the best short story ever. Seriously. Thank you! If you ever want to do a guest post on this blog about how you came to teaching, I’d love to post it. I was one of those people who knew in JUNIOR HIGH that I wanted to be a teacher, and I just went for it. But I know there are so many other paths that got people into teaching, and I love hearing all their stories! No pressure, but if you do want to, comment again and I’ll shoot you an email.

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