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.


Even a Math Workbook Can Be a Game

Homeschooling Memories…

My youngest daughter wanted to do Singapore math. Miquon Red was her main math text at the time, but we added a bit of Singapore Primary Math 1B whenever she was in the mood.

We turned to the lesson on subtracting with numbers in the 30-somethings.

The first problem was pretty easy for her:

30 − 7 = _____

I reminded her that she already knew 10 − 7.

She agreed, “Ten take away seven is three.”

Then her eyes lit up. “So it’s 23! Because there are two tens left.”

Wow, I thought. She’s catching on quickly.

Mom Always Talks Too Much

We went to the next problem:

34 − 8 = _____

“Now, this one is harder,” I said. “But you know what ten minus eight is, right? So we could take one of these tens and—”

She waved at me to be quiet.

I was just getting started on my standard speech about how to turn a tough subtraction like 34 − 8 into the easy addition of “2 + 4 + two tens left.” But her mind was still on the last problem, specifically on the two tens and the seven.

“If you have 27,” she said, “and you add three more, you get 30. And four more is 34.”

“Um, yes, but…” I interrupted.

She shushed me again.

“And then you can take away the four. And then you can take away the three. And then you can take away one more…It’s 26!”

Mom Learns a Lesson

She continued through the next page that way. For every problem, she started with whatever number struck her fancy, usually containing at least one digit from the problem before. She added enough to get up to the 30-something number in the book.

Only then would she deign to subtract the number in question.

I don’t think she ever saw the point of the mental math technique the book and I were trying to teach, but she did have a lot of fun playing around with the numbers.

In the long run, that’s much more important.


Feature photo: “Laughing Girl” by ND Strupler 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.


There Ain’t No Free Candy

Ah, the infinite chocolate bar. If only it could work in real life! But can your children find the mistake? Where does the extra chocolate come from?

Here’s a hint: It’s related to this classic brainteaser. And here’s a video from Christopher Danielson (talkingmathwithkids.com), showing how the chocolate bar dissection really works.

Happy munchings!


CREDITS: Feature photo (top) by Yoori Koo via Unsplash. “Hershey Bar Math” video by Christopher Danielson via YouTube. The infinite chocolate gif went viral long ago, and I have no idea who was the original artist.

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.


Playful Math Carnival #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!

Dot Grid Doodling

What can you DO with a page full of dots?

Yesterday, I mentioned my new series of paperback dot grid notebooks, and I promised to share a few ideas for mathematical doodling.

Doodling gives our minds a chance to relax, wander, and come back to our work refreshed. And though it goes against intuition, doodling can help us remember more of what we learn.

Math doodles let us experiment with geometric shapes and symmetries. We can feel our way into math ideas gradually, through informal play. Through doodles, our students will explore a wide range of mathematical structures and relationships.

Our own school experiences can make it hard for us to teach. What we never learned in school was the concept of playing around with math, allowing ideas to “percolate,” so to speak, before mastery occurs, and that process may take time.

—Julie Brennan

I like to doodle on dotty grid paper, like the pages in my math journals, but there’s No Purchase Necessary! You can design your own printable dot page at Incompetech’s PDF generator, or download my free coloring book (which includes several pages of printable dot and graph paper).

Patterns in Shape and Angle

To make a faceted mathematical gemstone, start with any shape you like. Then build other shapes around it. What do you notice? Does your pattern grow outward from its center? Or flow around the corner of your page? How is each layer similar, and how is it different?

Arbitrary constraints can lead to mathematically interesting doodles. For instance, create a design out of 45-45-90 triangles by coloring exactly half of every grid square. How many variations can you find?

Symmetry Challenge

Play a symmetry puzzle game. Draw a line of symmetry and fill in part of the design. Then trade with a partner to finish each other’s doodles.

Make more complex symmetry puzzles with additional reflection lines.

Math Doodle Links

  • Who can talk about mathematical doodling without mentioning Vi Hart? If you’ve never seen her “Doodling in Math Class” video series, you’re in for a treat!
  • See if you can draw a rotational-symmetry design, like Don’s “Order 4” graphs.
  • Or experiment with the more flexible rules in John’s “Knot Fun” lesson.
  • And my latest obsession: the “ultimate” tutorial series on Celtic Knotwork, which explores the link between knots and their underlying graphs.
My favorite knot doodle so far.

Inspirations: A Recreational Mathematics Journal
Reflections: A Math Teacher’s Journal
Explorations: A Math Student’s Journal
Contemplations: A Homeschooler’s Journal

Also available through: Barnes-Noble-logo the_book_depository_logo CreateSpace-logo

Before you start doodling: How to Break In Your New Math Journal.


Feature photo (top): Sommermorgen (Alte Holzbrücke in Pretzfeld) by Curt Herrmann, via Wikimedia Commons. [Public domain]

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.


Beauty in Math: A Fable

Have you ever wondered what mathematicians mean when they talk about a “beautiful” math proof?

“Beauty in mathematics is seeing the truth without effort.”

George Pólya

“There’s something striking about the economy of the counselor’s construction. He drew a single line, and that totally changed one’s vision of the geometry involved.

“Very often, there’s a simple introduction of something that’s not logically within the framework of the question — and it can be very simple — and it utterly changes your view of what the question really is about.”

Barry Mazur
The Moral of the Scale Fable


CREDITS: Castle photo (top) by Rachel Davis via Unsplash. “A Mathematical Fable” via YouTube. Story told by Barry Mazur. Animation by Pete McPartlan. Video by Brady Haran for Numberphile.

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.