Cultivate Mathematical Curiosity

“Cultivating thinking skills is the main reason for teaching math. It is the mind’s perfect playground for shaping up.

To begin developing thinking, you must first have a child who is curious. For without curiosity, there is only forced thinking.

The problem with traditional math is it jumps to the punchline.

Absolutely no mystery or suspense is developed in traditional math books. Why? Apparently, someone thought math was without mystery. That math is a definitive subject of rules and algorithms that all have been discovered.

We must persuade children that math is a worthy pursuit through interesting stories, examining quirky math properties, and asking good questions.”

— Lacy Coker
5 Tips to Cultivate Math Curiosity

The Mind’s Perfect Playground

My K-2nd-grade homeschool co-op math class will be following many of the tips in Lacy’s article.

Our topic is “Math Storytime,” so we’ll be starting with picture books, exploring the ideas they bring up, and finding things to notice and wonder about.

I’m looking forward to it.

But picture books aren’t just for little kids. They can be great discussion-starters at any age. Have you enjoyed math books with your students?

I’d love to hear your suggestions!


Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Bekah Russom on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Learning Mathematics Is a Deep Mystery

Of all the myths about mathematics, the one I find most blatantly wrong is the idea that some people are just born knowing the answers. In my experience, when you confront a genuine puzzle, you start out not knowing, no matter who you are.

Moreover, “knowing” the answers can be a trap; learning mathematics is about looking at what you thought you understood and seeing that there’s deeper mystery there than you realised.

— Dan Finkel
A Mathematician at Play Puzzle #1

Puzzles for Learning Mathematics

If you’d like to practice learning mathematics by confronting genuine puzzles, Dan’s “A Mathematician at Play” series looks like a wonderful place to start.

Some of these puzzles are classics, others are original. All of them involve some kind of thinking or insight that strikes me as pretty, or surprising, or delightful.

— Dan Finkel
A Mathematician at Play Puzzle #1

Dan plans to post new puzzles on the Math 4 Love blog every Monday for the next few months. And sharing spoilers on each following Friday, if you want to verify your answers.

Check it out!


Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo courtesy of Amy on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Learning Math Requires Imagination

“Teach mathematics the way we learn any other subject: Make it visual, make it concrete, not dependent on meaningless, abstract symbols, employ all the senses!

If math is such an important subject (and it is) why teach it in a way that is dependent on a child’s weakest mental ability: memory, rather than her strongest mental ability: imagination?”

— Geoff White
The Grade 10 Math Crunch, or Hitting the Wall at Grade 10

Mathematics and Imagination

How can we stir up our students’ imagination?

Teachers have struggled with this question for years — perhaps since the beginning of the profession.

Consider these comments by W. W. Sawyer in Mathematician’s Delight:

“Earlier we considered the argument, ‘Twice two must be four, because we cannot imagine it otherwise.’ This argument brings out clearly the connexion between reason and imagination: reason is in fact neither more nor less than an experiment carried out in the imagination.

“People often make mistakes when they reason about things they have never seen. Imagination does not always give us the correct answer. We can only argue correctly about things of which we have experience or which are reasonably like the things we know well. If our reasoning leads us to an untrue conclusion, we must revise the picture in our minds, and learn to imagine things as they are.

“When we find ourselves unable to reason (as one often does when presented with, say, a problem in algebra) it is because our imagination is not touched. One can begin to reason only when a clear picture has been formed in the imagination.

“Bad teaching is teaching which presents an endless procession of meaningless signs, words and rules, and fails to arouse the imagination.”


Wednesday Wisdom features a quote to inspire my fellow homeschoolers and math education peeps. Background photo by Mehmet Kürşat Değer on Unsplash.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.

Mindset for Learning Math

Playing with a new image editor, I came across this Winston Churchill quote. What a great description of how it feels to learn math!

If you have a student who struggles with math or is suffering from a loss of enthusiasm, check out Jo Boaler’s free online course on developing a mathematical mindset:

Or explore some of the playful activity ideas for all ages in her Week of Inspirational Math.


howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


How to Talk Math With Your Kids

A friend shared this video, and I loved it! From Kent Haines, a father who happens to also be a math teacher…

“I hope that this video helps parents find new ways of interacting with their kids on math topics.”

Kent Haines

More from Kent Haines

Advice and Examples of Talking Math with Kids

Danielson-Talking Math

If you enjoyed Kent’s video, you’ll love Christopher Danielson’s book and blog.

It’s a short book with plenty of great stories, advice, and conversation-starters. While Danielson writes directly to parents, the book will also interest grandparents, aunts & uncles, teachers, and anyone else who wants to help children notice and think about math in daily life.

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.
 
“You don’t need to love math. You don’t need to have been particularly successful in school mathematics. You just need to notice when your children are being curious about math, and you need some ideas for turning that curiosity into a conversation.
 
“In nearly all circumstances, our conversations grow organically out of our everyday activity. We have not scheduled “talking math time” in our household. Instead, we talk about these things when it seems natural to do so, when the things we are doing (reading books, making lunch, riding in the car, etc) bump up against important mathematical ideas.
 
“The dialogues in this book are intended to open your eyes to these opportunities in your own family’s life.”

— Christopher Danielson
Talking Math with Your Kids


CREDITS: “Kids Talk” photo (top) by Victoria Harjadi via Flickr (CC BY 2.0). “Parent Rules” by Kent Haines.

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


Math Humor and Copywork

Homeschooling Memories…

The more years we spent homeschooling, the more I appreciated Charlotte Mason’s work and tried to incorporate her ideas into our laid-back, eclectic, not-quite-unschooling program.

We never fit the typical Charlotte Mason mold. Mosquitos and natural laziness limited our nature walks, and our version of narration was much too informal.

But those are just techniques, methods.

What really interests me in Mason’s writing is the philosophy behind the methods. Two points resonated: That we must respect our children as persons in their own right. And that we must provide a generous, wide-ranging feast to their minds.

Striving to live out those principles had a profound influence on our day-to-day homeschooling.

Which Brings Me to Copywork

I’ve never managed to keep a diary-style journal, though as the years roll by, I wish I had. But I’ve always enjoyed saving favorite tidbits from the books I read.

Mason called it a commonplace book. I call it my “magpie” journal, where I collect my treasure of shiny things.

And so I brought copywork into my homeschooling system. I taught English spelling, grammar, and mechanics through living language. My favorite exercise was to write a short quotation on the whiteboard, leaving out all punctuation and capital letters, for my children to edit.

Do you use copywork or keep a commonplace book? I’d love to hear your experiences or read one of your favorite quotations.

Please comment below!

Math Humor Quotes

As you probably guessed, my personal magpie journal overflows with mathematics. Inspirational, insightful, or simply instructive — if it catches my eye, I grab it. But my kids always prefer the funny bits.

Here are a few of my favorites:

Arithmetic is neither fish nor beast; therefore it must be foul.

—Anonymous

Mathematics: a wonderful science, but it hasn’t yet come up with a way to divide one tricycle among three little boys.

—Earl Wilson

Logic is a systematic method of coming to the wrong conclusion with confidence.

—Anonymous (similar to a comment by Morris Kline)

You propound a complicated mathematical problem: give me a slate and a half an hour’s time, and I can produce a wrong answer.

—George Bernard Shaw

I pulled these quotations from the (out of print) Dictionary of Mathematical Quotations by Donald Spencer. Quotes range from thought-provoking to inane, including an assortment of “anonymous” bumper-sticker or T-shirt-style quotes not usually included in a quotation book. I do wish Spencer had included documentation with the quotes. Even though I’d probably never look them up, I’m still curious about where the quotes came from.

If you’d like to add mathematical copywork to your school repertoire, you’ll find the following online sources useful:


CREDITS: Feature photo (top) by Bruce Guenter via Flickr (CC BY 2.0).

howtosolveproblemsWant to help your kids learn math? Claim your free 24-page problem-solving booklet, and sign up to hear about new books, revisions, and sales or other promotions.


How You Can Play with Math #106

Do you enjoy math? I hope so! If not, browsing this post just may change your mind.

Welcome to the 106th edition of the Math Teachers At Play math education blog carnival — a smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college. Let the mathematical fun begin!

By tradition, we start the carnival with a puzzle in honor of our 106th edition. But if you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Try This Puzzle

If you slice a pizza with a lightsaber, you’ll make straight cuts all the way across. Slice it once, and you get two pieces.

If you slice it five times, you’ll get a maximum of sixteen pieces. (And if you’re lucky you might get a star!)

  • How many times would you have to slice the pizza to get 106 pieces?

Click here for all the mathy goodness!