Charlotte Mason Math: Our Educational Tools

"Woman and Children" painting by Elizabeth Boott Duveneck, public domain

“Therefore, we are limited to three educational instruments––the atmosphere of environment, the discipline of habit, and the presentation of living ideas. The P.N.E.U.* Motto is: Education is an atmosphere, a discipline, and a life.”

— Charlotte Mason, Principle 5

This principle is the key to a Charlotte Mason education. Most of her books consist of drawing out the meaning and implications of this motto.

When we think about applying Mason’s educational principles to math, we must focus on providing the right atmosphere, developing appropriate habits, and presenting living ideas.

What is the mathematical atmosphere of our home or classroom? Is math a natural and welcome part of life? Or does it exist only in schoolbooks and in some nebulous “future” for which our children must prepare?

What about the people in our children’s lives? Do we adults enjoy and use math, or do we dread and avoid it? Is our mathematical worldview positive, eager to learn and grow, or negative, seeing math as a chore to endure?

Continue reading Charlotte Mason Math: Our Educational Tools

Charlotte Mason Math: Practice Your Principles

La Fable, painting by Berthe Morisot

In our search for a Charlotte Mason math education, we must take into consideration Mason’s approach to all learning, not just the things she said about math. We must be guided by the core principles of her philosophy, even in math

“We hold that the child’s mind is no mere sac to hold ideas; but is rather, if the figure may be allowed, a spiritual organism, with an appetite for all knowledge. This is its proper diet, with which it is prepared to deal; and which it can digest and assimilate as the body does foodstuffs.”

 — Charlotte Mason, Principle 9

For instance, we must offer our students living ideas (not mere facts) in math, just as we do in literature and history.

Masons “20 Principles” outline the essentials of her educational philosophy. If we truly apply these principles to math, it can radically transform how we teach the subject.

Let’s examine a few of her principles in more detail…

Continue reading Charlotte Mason Math: Practice Your Principles

Charlotte Mason Math: Reason and Proof

“Woman with Child and Two Children,” Léon Augustin Lhermitte, public domain

The two ideas that Mason considered important in math — rightness and reason — are connected. It is our reasoning that convinces us an answer is right or wrong. How do we know we got a sum correct? We can take the numbers apart and add them another way, to see if we get the same answer. Or we can subtract one of the numbers from the sum and see if we get the other number. Or … well, how would you prove it?

More than anything else, Mason wanted her students to discover in math a sense of immutable truth, a truth that stands on its own, apart from anything we say or do, a truth we can explore and reason about but can never change.

This sense of rightness, of solid, unalterable truth, inspires a feeling of wonder and awe — she calls it “Sursum corda,” a call to worship — that delights our minds. It’s that “Aha!” feeling we get when something we’ve been struggling with suddenly fits together and makes sense.

From the very beginning, children should be doing this sort of informal proof, explaining how they figured things out. Don’t wait until high school geometry to let your children wrestle with ideas.

Continue reading Charlotte Mason Math: Reason and Proof

Introduction to Charlotte Mason Math

Woman with children, painting by Michael Ancher

“The Principality of Mathematics is a mountainous land, but the air is very fine and health-giving. People who seek their work or play in this principality find themselves braced by effort and satisfied with truth.”

— Charlotte Mason, Ourselves

Charlotte Mason (1842-1923) was a British school reformer at the turn of the twentieth century, a contemporary of William James and John Dewey. She advocated strongly for poor children, arguing they were equally capable of learning a wide and liberal curriculum as were the children of privilege.

Mason believed that all children from the time they are born share a natural curiosity and hunger for learning, and the adult’s role is to spread a “wide and generous feast” of inspiring ideas.

She was also a homeschooling pioneer, and the homeschooling revival of the late twentieth century rediscovered and popularized her books. Many found her principles a refreshing balance to the dominant educational paradigm of pragmatism.

Continue reading Introduction to Charlotte Mason Math

Podcast: From Right Answers to Adventure

Notice and Wonder podcast logo with quote by Denise Gaskins

If you find a free hour this week, you may enjoy listening to my latest Notice & Wonder podcast discussion with Sonya and Della about the power of playful math:

We share plenty of tips, stories, and practical advice for bringing a sense of curiosity and exploration into your math lessons.

Plus, the Best Math Game Ever!

I love this podcast, because it always feels like sitting down to chat over coffee with good friends who love kids and love teaching.

Taking our focus off answer-getting can be hard for the adult, because that right answer gives us security that we know what we’re doing. It’s hard to give ourselves the freedom of saying, “I’m going to go into this lesson, and I have no idea where it’s going to go. I have this puzzle, I have this problem, but I don’t know where it will lead.’’

    That’s a scary situation to be in as the adult who’s used to being in control of everything.

      But we’re exploring this landscape of math. There are a lot of cool things to discover, and we’ll find something. We may not find the answer, but we’ll find something interesting, if we just explore it.

      — Denise Gaskins,
      “From Right Answers to Adventure”

       
      * * *

      If you enjoy listening to podcasts, check out my other interviews here.

      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.

      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.

      If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.

      “Podcast: From Right Answers to Adventure” copyright © 2024 by Denise Gaskins. Podcast logo copyright © 2024 Sonya Post.

      New Podcast: Notice and Wonder

      Quotation from Notice and Wonder podcast

      When I was a novice homeschooler, our local Moms’ Night Out provided mentoring and kept me sane. We’d leave the children home with their dads and meet up at a local restaurant for a cup of coffee, a slice of pecan pie, and a robust discussion of educational philosophy.

      This spring, my friend Sonya Post launched a new podcast called “Notice & Wonder” — and it captures that same feeling perfectly.

      Sonya explains: “What is Notice, Wonder, Discover? It’s the development of cognitive skills, without which you have never learned anything in your life. We are developing the underlying skills that will make anyone more proficient at learning anything.”

      I’ve had the privilege to join Sonya for three episodes of the podcast so far, and I’ve thoroughly enjoyed our conversations.

      Here’s a taste…

      Continue reading New Podcast: Notice and Wonder

      If Not Methods: Reasoning About Subtraction

      Father and son reasoning about subtraction

      We’ve been examining the fact that, while there may be only one right answer to a math problem, but there’s never only one right way to get that answer.

      What matters in math is the journey. How do your children make sense of the problem and reason their way to that answer?

      As always, real math is not about the answers but the thinking.

      But if we don’t want to give our children a method, how can we teach? What if we pose a problem and the child doesn’t know how to solve it?

      What if our children get stumped on a subtraction calculation like 431 – 86?

      Continue reading If Not Methods: Reasoning About Subtraction

      Podcast: How to Transform Math Lessons without Changing your Curriculum

      Homeschooling math together - photo

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

      Check out Pam Barnhill’s 10 Minutes to a Better Homeschool on your favorite podcast app, or listen on the website:

      Go to the podcast ❱

      Here’s a couple of excerpts…

      Continue reading Podcast: How to Transform Math Lessons without Changing your Curriculum

      Musings: If Not Methods, Then What?

      Last week, I quoted Pam Harris calling out a foundational myth of math education, the idea that we need to teach kids the methods that work on even the most difficult math problems.

      “We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.

        “We would be far better served to teach kids to think about the most common kinds of questions WELL, and let technology handle the crankiest.”

        —Pam Harris

        Since many of us grew up in schools that taught these methods, they may feel like the only sensible approach to math. Without the standard procedures, how will our kids learn to do math?

        If we don’t teach subtraction with borrowing/renaming, how can students figure out calculations like 431 − 86? If we don’t teach fraction rules, how will they handle problems like 1 1/2 ÷ 3/8?

        Continue reading Musings: If Not Methods, Then What?

        Celebrating Spring with Playful Math Carnival 172

        Playful Math Carnival 172

        Welcome to the 172nd edition of the Playful Math Blog Carnival, a buffet of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.

        The carnival went on hiatus for a couple of months due to unexpected life issues facing our volunteer hosts. But we’re back now, and ready to celebrate!

        By tradition, we start the carnival with a puzzle in honor of our 172nd edition. But if you’d rather jump straight to our featured blog posts, click here for the Table of Contents.

        Try This: Lazy Caterers and Clock-Binary Numbers

        172 is a lazy caterer number: Imaging a caterer who brought a single large pie to serve the whole party. He needs to cut it into as many pieces as he can, using the fewest (straight) cuts he can get away with.

        • If each guest gets one piece of pie, what sizes of parties (numbers of people) can the lazy caterer serve?
        • Can you find a pattern in the lazy caterer sequence?

        But for those of you who have followed the carnival for years, you may remember we played with the lazy caterer back in Playful Math 106. (That time, the caterer was serving pizza.) So here’s a bonus activity we’ve never done before…

        The first several stages of a pattern are as follows:

        Clock Binary pattern image

        • What do you notice about this pattern of shapes?
        • What is the next shape in the sequence?
        • Can you figure out how the shape below fits into the pattern?

        Clock Binary puzzle image

        This pattern sequence was named clock binary by its creator, noelements-setempty.

        • What questions can you ask about this sequence?
        • How are these shapes like the binary numbers?
        • How are they different?

        Click here for all the mathy goodness!