How & Why (Understanding Math) – Page 4 – Denise Gaskins' Let's Play Math

Morning Coffee: Professional Development for Homeschooling Parents and Other Teachers

Posted on February 5, 2025February 19, 2025 by Denise Gaskins

Morning Coffee Lifelong Learning for Parents

Lately, I’ve spent most of my writing time thinking about the value of narration—the Charlotte Mason approach to teaching by getting kids to put ideas in their own words.

For students, I’m writing a new series of Math Adventure Journals to get them thinking about math and putting those thoughts into words. If you’re interested, sign up to be notified when the Kickstarter goes live.

But we parents can harness the value of narration in our own learning. After all, one of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.

To that end, I’ve decided to relaunch my “Morning Coffee” series of professional development posts for homeschooling parents.

Here’s How It Works

As I read articles and follow rabbit trails around the internet, I’ll collect the posts that speak to me. Then I’ll share these in a printable format with journaling pages for your response.

Since I’m interested in math education, many of the articles I read will be about math—but the principles of learning apply to every subject we teach.

To kick off the series, let’s start with one of my favorite articles ever…

Morning Coffee # 1: Learning to Ask Good Questions

Download your printable Morning Coffee journal

David Butler’s post Twelve matchsticks: focus or funnel presents an interesting math puzzle. But even better, it opens up a rabbit hole of thought-provoking posts about how to talk with children—or anyone:

“The approach where you have an idea in your head of how it should be done and you try to get the student to fill in the blanks is called funnelling. It’s actually a rather unpleasant experience as a student to be funnelled by a teacher. You don’t know what the teacher is getting at, and often you feel like there is a key piece of information they are withholding from you, and when it comes, the punchline feels rather flat.”

The printable file includes links to three more articles as I follow the rabbit around the internet. Enjoy!

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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: Professional Development for Homeschooling Parents and Other Teachers” copyright © 2025 by Denise Gaskins. Image at the top of post copyright © Kira auf der Heide / Unsplash.

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

Posted on January 22, 2025January 22, 2025 by Denise Gaskins

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 January 15, 2025January 5, 2025 by Denise Gaskins

“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

Charlotte Mason Math: Practical Tips for a Living Math Education

Posted on November 27, 2024October 27, 2024 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 November 20, 2024November 27, 2024 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 November 13, 2024November 20, 2024 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 November 6, 2024November 13, 2024 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 October 30, 2024November 26, 2024 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?

Charlotte Mason Math: Our Educational Tools

Posted on October 23, 2024October 30, 2024 by Denise Gaskins

"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