## Parents: Math Is Figure-Out-Able

I love listening to podcasts during my morning walk with the dogs. One of my favorites over the past year has been Pam Harris and Kim Montague’s Math is Figure-Out-Able podcast.

Figure-out-able. What a great word!

Figure-out-able sums up what I mean when I tell parents that math is “applied common sense.” Kids can use the things they know to figure out things they don’t yet know.

And figuring things out like that is fun, like a mental game where we play with the ideas of numbers, shapes, and patterns.

Usually, the podcast targets teachers, and the hosts try to show how they can help students learn to mathematize — to think mathematically. Over the past few weeks, however, Pam and Kim have been talking directly to parents about how to help their children learn math.

## The Principality of Mathematics

Here’s the full quote:

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

— Charlotte Mason, Ourselves

### Charlotte Mason and Math

Math was not one of Charlotte Mason’s primary interests. She didn’t think or write as deeply about it as she did other subjects.

She even wrote, “It is unnecessary to exhibit mathematical work done in the P.U.S. as it is on the same lines and reaches the same standard as in other schools.”

This leaves us modern parents and teachers having to read our own interpretations into her words. It should be no surprise when we come to different conclusions. Someday, perhaps, I’ll publish my own vision for a Charlotte Mason approach to homeschooling math.

In the meantime, the following articles describe a method that allows even the youngest children to explore the Principality of Mathematics:

In the years since writing those posts, Sonya and Lacy combined all their ideas into an easy-to-implement program that I think Mason herself would have enjoyed. Here’s my review:

CREDITS: Quote background photo (top) by Kalen Emsley via Unsplash.com.

## Not Attained by Chance

I’ve been collecting quotes about life and learning. They make great discussion-starters or essay/journaling prompts.

This is one of my favorites.

“Learning is not attained by chance, it must be sought for with ardor and attended to with diligence.”

[Aw, face it. They’re all my favorites. That’s why I collect them!]

If you like quotes, too, you might enjoy browsing my collection:

## Math as a Verb

Here’s the full quote:

I like to play games. Almost any type of game.

I also like to play math.

If you’ve known enough mathematicians, you may have noticed that this isn’t unusual. I’m not sure if a love of games and puzzles among mathematicians exceeds a love of music among mathematicians, but both are strong and intersect.

Math in play is also a way of teaching mathematics. I think that as a metaphor, it best describes how I want to teach math.

I am constantly seeking ways to get my students thinking about math as a verb. It is about doing, not just about having right answers or the end product.

Games help set the culture I want to develop: Teaching students that multiple approaches and strategies are valued; trying is safe; and conversations about why, how, and discovery are the goals.

—John Golden
Yes, Playing Around

CREDITS: “Football outside Jakarta” photo by Robert Collins on Unsplash.

## FAQ: Playful Math for Older Students

My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

Here are a few ideas to get your older children playing with math…

## The Value of Puzzles

I love puzzles. Don’t you?

Here are several examples of river-crossing puzzles you and your kids can try. They date back at least to the time of Alcuin, the famous scholar from the court of Charlemagne.

I wish someone would write a whole math curriculum devoted entirely to puzzles.

### W.W. Sawyer on the Value of Puzzles

Master teacher W.W. Sawyer didn’t write a curriculum, but he often used puzzles in the classroom.

“It is quite possible to use simultaneous equations as an introduction to algebra. Within a single lesson, pupils who previously did not know what x meant can come not merely to see what simultaneous equtions are, but to have some competence in solving them.

“No rules need to be learnt; the work proceeds on a basis of common sense.

“The problems the pupils solve in such a first lesson will not be of any practical value. They will be in the nature of puzzles.

“Fortunately, nature has so arranged things that until the age of twelve years or so, children are more interested in puzzles than in realistic problems.”

—W. W. Sawyer, Vision in Elementary Mathematics

Then he gives this example:

“A man has two sons. The sons are twins; they are the same height. If we add the man’s height to the height of one son, we get 10 feet. The total height of the man and the two sons is 14 feet. What are the heights of the man and his sons?”

### Try This at Home

Not only can children solve puzzles like this, but even better — they can make up story puzzles of their own. You could spend a whole week or more making up silly height puzzles for each other to solve. By the time you were done, your kids would have a great introduction to algebra!

Maybe I never grew up. Because I still prefer puzzles over “real world” math problems.

CREDITS: “Boat puzzles” comic from xkcd.com.
[THE FINE PRINT: I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

## More Dover Samples

“Without mathematics you can’t do anything! Everything around you is mathematics. Everything around you is numbers.”

—Anna Claybourne, I Can Be a Math Magician

Dover Publications sent out a new email today with fun coloring and craft samples. And several puzzles from I Can Be a Math Magician: Fun STEM Activities for Kids by Anna Claybourne.

Enjoy!

THE FINE PRINT: I am an Amazon affiliate. If you follow the book link above and buy something, I’ll earn a small commission (at no cost to you).

## W.W. Sawyer’s Rules of Mathematics

“In the beginnings of arithmetic and algebra, the main purpose is not to get the pupil making calculations. The main purpose is to get him into the habit of thinking, and to show him that he can think the problems out for himself.

“Pupils ask ‘Am I allowed to do this?’ as if we were playing a game with certain rules.

“A pupil is allowed to write anything that is true, and not allowed to write anything untrue!

“These are the only rules of mathematics.”

—W. W. Sawyer, Vision in Elementary Mathematics

[THE FINE PRINT: I am an Amazon affiliate. If you follow the link and buy something, I’ll earn a small commission (at no cost to you). But this book is a well-known classic, so you should be able to order it through your local library.]

### Inspired by Sawyer’s Two Rules

I love this quote so much, I turned it into a printable math activity guide. I hope it helps inspire your students to deeper mathematical thinking.

Here’s the product description…

Join the Math Rebellion: Creative Problem-Solving Tips for Adventurous Students

Take your stand against boring, routine homework.

Fight for truth, justice, and the unexpected answer.

Join the Math Rebellion will show you how to turn any math worksheet into a celebration of intellectual freedom and creative problem-solving.

Help your students practice thinking for themselves as they follow the Two Rules of the Math Rebellion: “A pupil is allowed to write anything that is true, and not allowed to write anything untrue! These are the only rules of mathematics.”

## Magical Mathematics

In fact, mathematics is the closest that we humans get to true magic. How else to describe the patterns in our heads that — by some mysterious agency — capture patterns of the universe around us?

CREDITS: Photo by Greg Rakozy via Unsplash.com. I am an Amazon affiliate. If you follow the book link and buy something, I’ll earn a small commission (at no cost to you).

## FAQ: I’ve Ruined My Daughter

My daughter is only eleven, but I’m afraid I’ve ruined her chance of getting into college because she is so far behind in math. We’ve tried tutors, but she still has trouble, and standardized testing puts her three years below grade level. She was a late reader, too, so maybe school just isn’t her thing. What else can I do?

Standardized tests are not placement tests. They cannot tell you at what level your daughter should be studying. They aren’t designed that way. The “placement” they give is vague and general, not indicative of her grade level but rather a way of comparing her performance on that particular test with the performance of other students.

There can be many different reasons for a low score. I’ve listed a few of them in my post In Honor of the Standardized Testing Season.