Math Journals and Creative Reasoning

Learning math requires more than mastering number facts and memorizing rules. At its heart, math is a way of thinking.

So more than anything else, we need to teach our kids to think mathematically. To make sense of math concepts and persevere in figuring things out. To notice the numbers, shapes, and patterns all around. To wonder about big ideas.

Journaling is a great way to help children learn to see with mathematical eyes. Not just to remember what we tell them, but to create their own math.

Get started with creative math journaling today. Visit the Make 100 Math Rebels Kickstarter page to download the free “How To Be a Math Rebel” sampler pictured above, which contains one of my all-time favorite math prompts.

Make 100 Math Rebels

It doesn’t matter whether your students are homeschooled or in a classroom, distance learning or in person. Everyone can enjoy the experience of playing around with math.

Puzzle from the free Math Rebel Sampler.

Things To Do with a Math Journal

Math journal entries can be quick class notes, or research projects that take hours of experimentation and pondering. Students may do their homework with Math-Rebel-style creative answers, or jot down reflections spurred by a favorite quotation.

Here are a few ideas to get you started…

(1) Break It In: Before you start writing in a new journal, take a few minutes to limber up the pages. This makes your journal easier to use, and helps it last longer. See How to Break In Your New Math Journal.

(2) Math Doodles: Doodling gives our minds a chance to relax, wander, and come back to our work refreshed. And though it goes against intuition, doodling can help us remember more of what we learn. See Dot Grid Doodling.

(3) Notice and Wonder: Whenever your children need to learn a new idea in math, or whenever they get stuck on a tough homework problem, that’s a good time to step back and make sense of the math. Kids can write their noticings and wonderings in the math journal. Or you can act as the scribe, writing down (without comment) everything child says. See Ever Wonder What They’d Notice? by Annie Fetter, Beginning to Problem Solve with “I Notice/I Wonder”, and Noticing and Wondering with Older Kids.

(4) Create Word Problems: I love having students make up their own story problems. See this blog post for examples.

(5) Story Diagrams: Enjoy a living math book, and then diagram the story.

(6) Don Steward’s Median: Don Steward’s blog is a rich source of creative math prompts. For example, try these playful investigations of grid geometry.

(7) Festival Math: Try a set of math puzzles from the Julia Robinson Festival.

(8) Don Cohen’s Puzzles: Or explore Don Cohen’s Map to Calculus for Young People. My students especially enjoyed the Infinite Cake series.

(9) Prime Number Game: (two players) The first player writes any whole number. On each succeeding turn, copy the previous line, replacing any one number with an equivalent multiplication of two new factors. Factoring 1 times a previous number does NOT count! The player who writes the last line (leaving no move for the opponent) loses the game — unless this happens within the first three lines, in which case the first player loses for picking such a boring number. For examples, see John Golden’s Running Out of Options.

(10) Save the Cats: Explore the possible arrangements of cats on chairs, and discover how to check math problems without an answer key in Math Journals: Save the Cat!

(11) Do a Math Experiment: Almost anything your child notices or wonders can lead to a math experiment. For example, one day my daughter played an online math game

Your Turn

I’ll continue adding to this list over the next few weeks. But I’d love to hear your ideas, too.

Please share your favorite writing prompts or journal activity ideas in the comments section below.

3 thoughts on “Math Journals and Creative Reasoning

  1. Hi, Denise:
    First, I was sent to you by Joseph, relating to the monthly math blog postings, as he said he thinks you may need a post this week. I post integrated GED lesson plans each day which try to link the mathematics for that lesson together with a science and reading topic.
    Second: thank you so much for encouraging math journals! When I first began my student teaching, I was told by my supervisor that I was not to use journals, projects, portfolios, or any other interesting new technique I’d just learned during my MAT. Now, exactly 20 years later, I am so glad to see these ideas finally being accepted and used.
    Thank you, and I hope that we can be of mutual support on our blogs,
    Warm Regards,
    -Shira

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