Charlotte Mason Math: Living Books

Posted on by Denise Gaskins
“The Reading Lesson” painting by Jonathan Pratt, public domain

[An addendum to my earlier Charlotte Mason Math series.]

“Our business is to give [children] mind-stuff, and both quality and quantity are essential. Naturally, each of us possesses this mind-stuff only in limited measure, but we know where to procure it; for the best thought the world possesses is stored in books; we must open books to children, the best books; our own concern is abundant provision and orderly serving.”

— Charlotte Mason, Toward A Philosophy of Education

Most homeschool teachers, whatever our curriculum or schooling approach, understand the importance of teaching with living books. We read aloud biographies, historical fiction, or the classics of literature. We scour library shelves for the most creative presentations of scientific topics that interest our children, and encourage our high school students to go back to the original documents whenever possible.

And we teach math with a textbook.

Not that textbooks are inherently bad, because math is an abstract science. We need to meet the ideas  — the “mind-stuff” — of math on their own terms, and textbooks can help with that.

But it’s not enough.

Continue reading Charlotte Mason Math: Living Books

Morning Coffee: Anyone Can Learn Math

Posted on by Denise Gaskins
Morning Coffee Lifelong Learning for Parents

One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

Here are a few stories to read as you sip your morning brew:

Once again, my rabbit hole started with a thought-provoking blog post from Dan Finkel…

“Not everyone can become a great artist — but a great artist can come from anywhere.”
—Ego, from Ratatouille

    “Ego’s parsing of the phrase anyone can cook is not obvious, and it’s not really the primary meaning of the phrase. The truth is, there are really three meanings all wrapped up there: anyone can learn to have the joy and pleasure of cooking in their life, even if they don’t become a master chef. Some people will get serious about it. And the visionaries who change the way we think about the art can come from anywhere — lock them out of the field and we all suffer.”
    —Dan Finkel

    Read more about how anyone can learn math in this third installment of professional development for homeschooling parents.

     
    * * *

    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 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.

    “Morning Coffee: Anyone Can Learn Math” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

    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.

            Morning Coffee: When Math Makes You Feel Stupid

            Posted on by Denise Gaskins
            Morning Coffee Lifelong Learning for Parents

            One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

            Here are a few stories to read as you sip your morning brew. . .

            Download your printable Morning Coffee journal

            This week’s rabbit hole started with a thought-provoking newsletter from Dan Finkel, which led me to his blog…

            “Everyone who learns math is familiar with the experience of being stuck on some new idea or problem, banging their head against it, and then, when they finally understand the answer (or having someone tell them), feeling stupid. There’s something fundamental in the nature of mathematics that makes it easy once you get it, and impossible before.

              “These jumps in comprehension can be thrilling, and they’re one reason math is so fun. But they do create a challenge for the student. The evidence that you learned something hard is that you feel like you’re stupid. That stupidity is essential to the process. Students need to know this feeling is the norm when it comes to learning math.”

              —Dan Finkel and Katherine Cook, The centrality of stupidity in mathematics

              Read more about the value of feeling stupid in this second installment of professional development for homeschooling parents.

               
              * * *

              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 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.

              “Morning Coffee: When Math Makes You Feel Stupid” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

              Puzzle: Henry Dudeney’s Pebble Game

              Posted on by Denise Gaskins
              photo of girl playing with pebbles on the beach

              English mathematician and puzzle-meister Henry Ernest Dudeney once wrote:

              “It may be said generally that a game is a contest of skill for two or more persons, into which we enter either for amusement or to win a prize. A puzzle is something to be done or solved by the individual.

                “The example that I give here is apparently a game, but, as in every case one player may win if he only play correctly, it is in reality a puzzle. The interest, therefore, lies in attempting to discover the leading method of play.”

                Below is the puzzle game as Dudeney explained it.

                Play it for fun at first, then see if you can solve the puzzle.

                Continue reading Puzzle: Henry Dudeney’s Pebble 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

                Charlotte Mason Math: How Shall We Teach?

                Posted on by Denise Gaskins
                Woman withchildren painting by Dorothy Kate Richmond, public domain

                Even in Mason’s day, testing drove much of educational policy, but we must not allow ourselves to fall into the trap of teaching for a test. Just as we do not study history in order to win a trivia contest, so we do not study math merely to produce answers on an exam.

                “Arithmetic, Mathematics, are exceedingly easy to examine upon and so long as education is regulated by examinations so long shall we have teaching, directed not to awaken a sense of awe in contemplating a self-existing science, but rather to secure exactness and ingenuity in the treatment of problems.”

                 — Charlotte Mason, Towards a Philosophy of Education

                Remember Mason’s twin goals of rightness and reason. Even if you use a math book that focuses on memorizing rules and cranking out answers, you and your child can look for the ideas behind the rules: “Why does this work? How can we know for sure?”

                Not just because the book says so, but because you search out and discover the innate sense of it. That is the essence of mathematics.

                Continue reading Charlotte Mason Math: How Shall We Teach?