Bright, Brave, Open Minds: A Problem Solving Kaleidoscope. Open online course for parents and teachers

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Bright, brave, open minds: A problem solving kaleidoscope is a two-week long open online course in problem solving for parents and teachers of 8-9 year old children.

The registration is closed, but you can still contribute to the crowd-funding campaign for the Open Minds book. If you don’t see the contribution button here, switch from IE to another browser.


December 5. We are sending daily emails to all course participants. Check your spam folder if you are not receiving them.

Here is the full recording of the December 4 live meeting. Some of the questions we discussed:

  • Axelle: Some kids in the video are using words such as “easy”, “obvious”, and I was wondering how that affects another kid who potentially may not find the task that easy, would that shut them down? What experience do you have with that?
  • Stephanie: What are some useful strategies for helping children who tend towards perfectionism learn how to enjoy the struggle you discussed earlier?
  • Targhee: Can you elaborate on how to model making, noticing, and resolving mistakes?
  • Iskra: What happens if the young children aren’t ‘curious’ and are not interested in problem solving? My younger son (6) is perfectly happy with routine math exercises, but as soon as he sees an interesting problem that doesn’t follow the pattern of previous problems, he has an immediate temper tantrum with real tears.

December 4. By requests, we extended course registration to the end of the week. More than ninety people registered. Today we have the first of the two open online meetings – come by at 8pm EST!

December 2. Today is the first day of the course. Over seventy parents, teachers, and math circle leaders signed up to participate. More than three quarters of participants contributed money to crowd-fund the Open Minds book – big thanks! These funds will cover the next step in producing the book: illustrations.
Open Minds Course
If you ever have any questions, email organizers at
Moby Snoodles

About the course

  • Why: Preserve children’s divergent thinking. Develop their critical thinking and problem solving skills. Contribute to making a Creative Commons book about young problem solving.
  • How: Provide a variety of insight problems to young children. Introduce complex, open-ended, and ill-defined problems as a way to teach problem solving skills. Recognize the feeling of being stuck as a necessary step in problem solving. Let children face deep, multi-dimensional problems. Meet other adventurous parents and educators. Contribute to research in math and problem-solving education.
  • Who: The course organizers are Julia Brodsky, former NASA astronaut instructor and math and science teacher, and Dr. Maria Droujkova, math education consultant. The course participants are families, adventurous teachers, math clubs, playgroups, and other leaders of groups doing problem solving with young kids.
  • What: In the first week of the course, we will discuss settings and practices for introducing problem solving to young children. You will look at topics from Julia’s math circle, and discuss how to teach them. In the second week, you will gather your kids and their friends in a casual math circle, try out the topics, and then answer a few questions about your experience.
  • When: Sign up by December 2nd. The main course activities will happen December 2nd through 16th. Expect to spend several hours a week doing course tasks.
  • Where: Main course activities will happen at our online ask and tell hub. The page you are on now will be updated with major links and news. Organizers will send you summary emails. We will have two live meetings online, at the beginning and at the end of the course, and post their recordings to this page.



Julia Brodsky

Maria Droujkova

Maria Droujkova

Week 1, December 2-6

  • Contribute a question about early problem solving to the crowd-sourced questionnaire.
  • Discuss
    • Why do you need a “wait time” in problem solving?
    • Why do we collect and treasure mistakes?
    • What do you do when you are stuck? How do you deal with frustration?
  • Live event questions and answers: attend online or watch the recording.

Week 2, December 9-16

  • Lead your math circle with kids and friends.
  • Reflect, share videos, photos, student observations, comments, and suggestions.
  • Live event questions and answers: attend online or watch the recording.


In the first week, we will ask you to pick three topics you like from the list of the eight topics below. We will then assign one of these three topics to you. We do this so every topic has several people working on it, giving one another ideas, and giving us feedback.

Topic name

Math and problem solving objectives

Introduction Problems: A Sampler

Diversity in problems; multiple solutions; hidden assumptions

Strange Statements: Logic

True/false statements; syllogisms; paradoxes; divergent thinking and analysis of problems and solutions

Tiling Puzzles

Symmetry; tilings; reflections, rotations, translations; verbalizing visual-spatial concepts

Problem Debates

Math communication; elaboration; idea defense; team work


Recursion; cycles; using problem solving to explore a topic in-depth


Symmetry in life, science, and the arts; use and misuse of our brains’ preference for symmetry

Lateral Solutions

Start at the end and work backwards; use and misuse of common structures and analogies in series of problems

Game Festival

Math magic and party tricks; problem solving in board games; community building

Questions and answers

What is this all about?
We hope more people will recognize the need and the fun of early problem solving. We want to invite many parents and teachers to develop their own problem solving materials. It is natural for young children to approach each problem as a non-standard problem, and to play with it. In contrast to giving prescribed tools, we aim to preserve the divergent thinking and open-mindedness of young children. “Aha!” problems sound easy, but require surprising, insightful solutions. Such problems give kids the power of looking for elegant, unexpected solutions in all life situations. An insight problem keeps the solver stuck for a good while as a challenging, but natural and creative part of problem solving. Our goal is to help all math circle participants, students and teachers alike, to welcome being stuck!

Problem solving is the cornerstone for all mathematics, and a part of every mathematical discipline – but it is not easy to master. Problem solving cultivates open-mindedness, requires many approaches, and teaches how to face fears and limitations. To learn that playful bravery, children need a safe and supportive environment, and sympathetic adults to model mistake-making and being stuck. That’s what our math circles are about.

Has anybody tried these materials yet?
Julia’s Art of Inquiry math circle, as well as several other math circles, homeschool and private school groups tried and refined these materials. You can see some reports at the Art of Inquiry website and the Homeschool Post article. This course is the last stage in pilot testing the materials before publishing them as a book. We appreciate any and all feedback!

Do I need a background in math or science to lead math circles?
No! You just need to be open to exploration and discovery. You will get support from other participants, while sharing your thinking and observations.

What specific math topics will I learn?
The course is a kaleidoscope of topics and problems. It’s not about a particular branch of mathematics, but about inspiring you to seek and pose complex, intriguing problems in any field.

Is it important to do the lessons in a sequence?
No. Each lesson covers a different topic. You can take lessons in any order.

What if my kids are older or younger?
Some math circles have tried these materials with children younger than 8 and older than 9. If you know how to adapt tasks, you can try with older or younger kids.

Can I participate if I don’t work with kids?
Yes, you can get some grown-up friends together for a math circle. Problem solving adventures aren’t just for children! We have done these activities at parent and teacher workshops, as well as professional seminars and conferences.

What is the price and what resources will I need?
You need the internet to participate, and some household objects (paper, markers, toys) for the activities. You may also want to invest in an easel, whiteboard, or just big sheets of paper. You will also need children to play with the problems – or other adults who are curious.
You will have an opportunity to support our cause by paying for this course at the price you name. The money supports Creative Commons open media, the studies in family math, and our courses and workshops. Large donations and small contributions are all welcome! At the supporter page, we will list and honor each contributor.

Some questions to explore during your math circle
1. What’s more fun for children – to solve complex multi-step problems or simple problems?
2. How do children deal with the challenge of being stuck?
3. How does age and schooling background affect divergent thinking skills?
4. What makes a problem interesting?
5. What are the sources of parent frustration when teaching problem solving?
6. Are young children ready to deal with “insight” problems?
7. Do thinking skills acquired in math circle transfer to different areas of learning?
Open Minds course

20 comments on “Bright, Brave, Open Minds: A Problem Solving Kaleidoscope. Open online course for parents and teachers
  1. Hey dear Julia, it sounds great¡

    Thank you for sharing, i am interested, will be very helpful for me with Ela.

    How can i give my contribution to the course through credit card only, is it possible?

    Much affection

    • MariaD MariaD says:

      Irene, when you start registering, there are two payment options, both working with credit cards: “Proceed to checkout” uses PayPal, or you can pay through Amazon. See you in the course!

  2. Kat says:

    So I contributed and downloaded the book…is that all I need to do to register?

  3. Надя says:

    Здравствуйте, Юлия и МАрия,
    я хотела бы прояснить уровень этого курса, его детализацию – будете ли Вы разбирать подробно все аспекты обучения математике, так как это пытался сделать Звонкин, например, – но в его случае мы имеем дело с дневником, а мне бы хотелось получить работающую методологию, которую можно воспроизвести.
    Понятно, что бОльшая часть работы с детьми строится на импровизации и понимании детской психологии, но и конкретные способы донесения идеи до ребенка были бы очень важны.
    Также хочу прояснить способ, которым Вы собираетесь общаться с аудиторией на своем онлайн курсе. Это будут видео-лекции? или исключительно переписка по е-мейл и участие в форумах-обсуждениях и написание эссе?
    Спасибо заранее.

    • MariaD MariaD says:

      Translation of the question:
      Hello Julia and Maria,
      I would like to clarify the level of this course and its details. Will you describe all aspects of math pedagogy, as Zvonkin tried [in his book “Math from Three To Seven – MariaD]? But in his case, it’s a diary, while I want a working methodology I could reproduce.

      I understand that working with kids mostly relies on improvisation and on understanding children’s psychology. But particular methods of making ideas accessible to kid would be very important. I also want to clarify the method of communication in the course. Will there be video-lectures? Or just email correspondence, forums, and writing essays?

      Thank you in advance,


      Thank you for the detailed questions. You are right: we do want to invite participants to learn a methodology. The methods center on inquiry and exploration – for teachers as well as students. Therefore, the challenge is to describe enough particulars for participants to get started, but leave plenty of freedom for their own decision-making.

      For example, how many activities are in each session? The session called “Lateral Solution” has eight suggestions. When I last tried this session, my students did two activities in an hour. That’s because we modeled and roleplayed problems, and kids wanted to suggest their own versions of these stories. Most people reported having time for four of five activities. So, each activity has Teacher’s Notes with suggestions on how to run it. But they are open suggestions – there is still enough decision-making for each teacher to make activities their own.

      The communication in the course will happen four ways:
      – Ask and Tell forum, where participant will put written or video descriptions of their math circles, and discuss problem-solving in general.
      – Emails with course news – participants can reply, which Julia and I will see
      – Book chapter drafts from Julia
      – Two live interactive online events, at the beginning and at the end of the course: mostly questions and answers

      The most action, we hope, will happen when participants run their local math circles during the second week of the course!

      • Nadezhda says:

        Hello Maria and thanks a lot for your reply and my question translation (I should have done that myself though)
        So I think I’ve got an idea about the course, and it seems that pre-requisite here would be a group of interested people whom I will “teach” == “awake inquiry and exploration” for at least the duration of this course.
        I hope I will be able to set this group to make the most out of it. I have my6 y.o. daughter and maybe some of her class mates will join,let me see.

        In the mean time a good idea would be to explore the materials of your web site, there is various activities description as I could see which makes a lot of sense!
        thanks for your enthusiasm,
        all the best –

  4. P says:

    I can not find tab to register. Also will the course be in evenings ? Want ot know as I am working. Thanks.

    • MariaD MariaD says:

      Hello P, try switching from Internet Explorer to another browser if that’s what you use; or else check if you disable JavaScript. These are two causes of the big green REGISTER button not showing.

      We have two live one-hour meetings in the course, both in the evenings EST time. However, they aren’t necessary to participate. You can send your questions ahead of time, and view recordings on the meetings later. Everything else you can do on your own time, because course participants are all over the world.

  5. Sheryl Morris says:

    Have I managed to register? There was a register button and I selected it. I tried selecting various monetary amounts to contribute, from there nothing happened. Cheers.

    • MariaD MariaD says:

      Sheryl, we did not get your registration – something glitched. Please try again. After you enter the number from zero to infinity, click the green CONTRIBUTE button, which will take you to the very short registration form. If it does not work, please let me know so I can register you by hand.

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  1. […] It was sent out as 'free', but they included the following: "The course is free, though if you could donate for future book publishing, that would be greatly appreciated." Bright, Brave, Open Minds: A Problem Solving Kaleidoscope. Open online course for parents and teache… […]

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