Podcast: Using Math Journals and Games

Posted on by Denise Gaskins
mother and daughter math journaling

I have a new podcast interview, and I think you’ll enjoy it!

Check out Cindy Rollins’s The New Mason Jar on your favorite podcast app, or listen on the website:

Go to the podcast ❱

Here’s an excerpt…

Writing to Learn

Just as a nature journal records our children’s explorations and discoveries in nature, so a math journal tracks our children’s explorations in the world of mathematics.

    In a math journal, children record their experiences with numbers, shapes, and patterns through drawing or writing. Journaling teaches them to see with mathematical eyes — not just to remember what we adults tell them, but to create their own math.

      The process of writing forces children to pin down their thoughts, to transform nebulous concepts into firm ideas, to struggle with vagueness and build understanding.

        As William Zinsser says in his book Writing to Learn: “Writing is how we think our way into a subject and make it our own. Writing enables us to find out what we know, and what we don’t know.”

          Through journaling, children develop a richer mathematical mindset. They begin to see connections and grow confident in their ability to think through new problems.

          We had a great discussion! Listen to the whole thing:

          Go to the podcast ❱

           
          * * *

          Are you looking for more creative ways to play math with your kids? Check out all my books, printable activities, and cool mathy merch at Denise Gaskins’ Playful Math Store. Or join my free email newsletter.

          This blog is reader-supported. If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.

          “Podcast: Using Math Journals and Games” copyright © 2025 by Denise Gaskins. Image at the top of the post copyright © AntonLozovoy / Depositphotos.

          Math Journal: Playing with My Own Ignorance

          Posted on by Denise Gaskins
          photo of a girl wondering about math

          Mary Everest Boole, wife of English mathematician George Boole, once described algebra as “thinking logically about the fact of our own ignorance.”

          This definition made me chuckle. Like any human being, I am ignorant on many things, but I usually avoid thinking about that.

          So I wondered what would happen if I took Mrs. Boole’s advice and tried thinking logically about my ignorance.

          How far could I go?

          Perhaps you’d like to try this experiment with your children. All you need is a pen and paper or a whiteboard and markers and a bit of curiosity.

          Math Journaling Adventures series by Denise GaskinsAnd if you enjoy this exploration, check out my Math Journaling Adventures project to discover how playful writing activities can help your students learn mathematics. Preorder your books today!

          Continue reading Math Journal: Playing with My Own Ignorance

          FAQ: Can I Use Your Books as a Math Curriculum?

          Posted on by Denise Gaskins
          Father helping girl with math homework

          I recently listened to you on Cindy Rollins’ podcast, and I was captivated by your perspective on math. It was exciting, freeing, and wonder-filled. I would absolutely love to be able to teach in the ways you described.

            We use early-elementary Saxon Math right now, which is thorough, but has SO MUCH to do that I’ve always struggled to do it all. Then I feel like I’m missing things, and I never know quite what is important. And yet, the actual lessons move so slowly that my kids get bored with the repetition.

              I use a published curriculum because I have no idea of an appropriate scope and sequence, or similar flow of learning. With your playful approach to math, how do I know where to start, and what to do each day?

                Do you have a suggested order to approach your books to have a full math approach? A sort of curriculum, per se, using your books.

                [For those who missed my chat with Cindy Rollins about a Charlotte Mason approach to math, you can listen to it here.]

                Continue reading FAQ: Can I Use Your Books as a Math Curriculum?

                FAQ: Real Math for Early Learners

                Posted on by Denise Gaskins
                photo of family hiking a rocky trail

                “I love your image of math as a nature walk. My children are ready to start their homeschooling journey, and I want to put them on the right track from the beginning. How can I help them think about math and problem-solving without using a textbook?”

                The most difficult part of teaching our children real math is to change our own way of thinking about the subject you’ve already taken that step, so it looks like your family’s learning journey is off to a great start.

                [For readers who are wondering what I mean by math as a nature walk, check out this post. You may also enjoy my article on natural learning: Math with Young Children.]

                Continue reading FAQ: Real Math for Early Learners

                Memories: The Oral Story Problem Game

                Posted on by Denise Gaskins
                photo of sheep in a field

                Homeschool Memories…

                Perhaps you’ve heard me mention the oral story problem game. It was one of my favorite ways to get my children thinking about math, back in our early days of homeschooling. We played in the car on the way to soccer practice, or while we washed dishes, or sitting in the lobby waiting for a doctor’s appointment.

                The rules are simple: I’ll make up a math problem for you to solve. And then you make up one for me.

                The kids always loved trying to stump me.

                This problem from Henry Ernest Dudeney’s Amusements in Mathematics reminded me of those days. This is exactly the way my eldest loved to torture me…

                Continue reading Memories: The Oral Story Problem Game

                Charlotte Mason Math: Practical Tips for a Living Math Education

                Posted on by Denise Gaskins
                “Young italian woman with two sleeping children on coast’ painting by August Riedel, public domain

                Focus on the logic of reasoning.

                Correct answers are important, of course, but as children explain their thinking, they will often catch and fix mistakes on their own.

                “Two and two make four and cannot by any possibility that the universe affords be made to make five or three. From this point of view, of immutable law, children should approach Mathematics; they should see how impressive is Euclid’s ‘Which is absurd,’ just as absurd as would be the statements of a man who said that his apples always fell upwards, and for the same reason.”

                 — Charlotte Mason, Towards a Philosophy of Education

                “Most remarks made by children consist of correct ideas badly expressed. A good teacher will be wary of saying ‘No, that’s wrong.’ Rather, he will try to discover the correct idea behind the inadequate expression. This is one of the most important principles in the whole of the art of teaching.”

                 — W. W. Sawyer, Vision in Elementary Mathematics

                • Tip: If you’re not sure how to draw out your child’s reasoning, read Christopher Danielson’s wonderful examples and advice on talking math with your kids: Talking Math with Your Kids.

                Continue reading Charlotte Mason Math: Practical Tips for a Living Math Education

                Charlotte Mason Math: Wrong Answers and Slovenly Teaching

                Posted on by Denise Gaskins
                "Playing with the kittens" painting by Emile Munier, public domain

                The second place where a surface-level reading of Charlotte Mason’s books can lead to misunderstanding involves the treatment of wrong answers. Mason wrote:

                “… quite as bad as these is the habit of allowing that a sum is nearly right, two figures wrong, and so on, and letting the child work it over again. Pronounce a sum wrong, or right — it cannot be something between the two. That which is wrong must remain wrong: the child must not be let run away with the notion that wrong can be mended into right.”

                 — Charlotte Mason, Home Education

                Does this call to mind images of your own childhood schoolwork? It does for me: laboring over a worksheet or quiz and then taking it to my teacher to be graded. Right was right, and wrong could not be mended. In such a performance-oriented setting, mistakes can take on the flavor of moral failure.

                Is this authoritarian approach the way Mason wants us to teach math to our children? Where is the summa corda — the joyful praise — in that?

                No. Please, no. Very definitely no.

                Mason wanted us to avoid slovenliness in our teaching. In this passage, she warned against several forms this might take.

                Continue reading Charlotte Mason Math: Wrong Answers and Slovenly Teaching

                Charlotte Mason Math: The Trouble with Manipulatives

                Posted on by Denise Gaskins
                “Mother Playing with Child” painting by Mary Cassatt, public domain

                Two passages in Charlotte Mason’s writing about math are in my opinion widely misunderstood. The first relates to the proper use of manipulatives.

                Mason believed strongly in the importance of physical objects and oral work (mental math) in early math education. In her priorities, the use of written calculation fell in distant third place.

                “A bag of beans, counters, or buttons should be used in all the early arithmetic lessons, and the child should be able to work with these freely, and even to add, subtract, multiply, and divide mentally, without the aid of buttons or beans, before he is set to ‘do sums’ on his slate.”

                 — Charlotte Mason, Home Education

                Continue reading Charlotte Mason Math: The Trouble with Manipulatives

                Charlotte Mason Math: Finding Time for Big Ideas

                Posted on by Denise Gaskins
                “Woman and Child in the Grass” painting by Renoir

                “Teachers have seldom time to give the inspiring ideas, what Coleridge calls, the ‘Captain’ ideas, which should quicken imagination. How living would Geometry become in the light of the discoveries of Euclid as he made them!”

                 — Charlotte Mason, Towards a Philosophy of Education

                The Captain ideas are the great Truths of a subject, the things that make our minds wake up and pay attention, that energize our thoughts and make us yearn for more.

                In math, living ideas are the big principles that tie together many branches of the subject. Things like:

                • Proportion — where two quantities are connected so they scale up or scale down in tandem. For instance, if we double the number of cars in the driveway, that automatically doubles the number of tires.

                • Transformation — how we can change things while keeping important attributes the same. Like, if we shrink a square, its area will change, but the angles stay the same.

                Continue reading Charlotte Mason Math: Finding Time for Big Ideas