Education in general – Page 2 – Denise Gaskins' Let's Play Math

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.]

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Memories: The Oral Story Problem Game

Posted on January 8, 2025August 13, 2025 by Denise Gaskins

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…

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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.

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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

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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.

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Oh, Internet, Thou Fickle Friend!

Posted on November 4, 2024November 1, 2024 by Denise Gaskins

Whew! I just finished going through ALL of my massive Internet Math Resources pages and fixing the links that had broken since the (too long ago) last time I checked.

Way too many broken links. Pages lost to the ether: fun old hobby sites of a teacher who retired and lost their school-sponsored page, sites that have set up a payment wall, and sites that still exist but have been rearranged, breaking all the old connections.

Many I was able to fix, some I had to delete.

But still, there are plenty of great links left, so if you’re looking for an interesting way to play with math, head over and explore:

Hopefully, everything works now.

Until the next time…

* * *

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.

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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?

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