How to Succeed in Math: Answer-Getting vs. Problem-Solving

Posted on by Denise Gaskins

You want your child to succeed in math because it opens so many doors in the future.

But kids have a short-term perspective. They don’t really care about the future. They care about getting through tonight’s homework and moving on to something more interesting.

So how can you help your child learn math?

When kids face a difficult math problem, their attitude can make all the difference. Not so much their “I hate homework!” attitude, but their mathematical worldview.

Does your child see math as answer-getting? Or as problem-solving?

Answer-getting asks “What is the answer?”, decides whether it is right, and then goes on to the next question.

Problem-solving asks “Why do you say that?” and listens for the explanation.

Problem-solving is not really interested in “right” or “wrong”—it cares more about “makes sense” or “needs justification.”

Homeschool Memories

In our quarter-century-plus of homeschooling, my children and I worked our way through a lot of math problems. But often, we didn’t bother to take the calculation all the way to the end.

Why didn’t I care whether my kids found the answer?

Because the thing that intrigued me about math was the web of interrelated ideas we discovered along the way:

  • How can we recognize this type of problem?
  • What other problems are related to it, and how can they help us understand this one? Or can this problem help us figure out those others?
  • What could we do if we had never seen a problem like this one before? How would we reason it out?
  • Why does the formula work? Where did it come from, and how is it related to basic principles?
  • What is the easiest or most efficient way to manipulative the numbers? Does this help us see more of the patterns and connections within our number system?
  • Is there another way to approach the problem? How many different ways can we think of? Which way do we like best, and why?

What Do You think?

How did you learn math? Did your school experience focus on answer-getting or problem-solving?

How can we help our children learn to think their way through math problems?

I’d love to hear from you! Please share your opinions in the Comments section below.

CREDITS: “Maths” photo (top) by Robert Couse-Baker. “Math Phobia” photo by Jimmie. Both via Flickr (CC BY 2.0). Phil Daro video by SERP Media (the Strategic Education Research Partnership) via Vimeo.

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

Posted on by Denise Gaskins

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

Posted on by Denise Gaskins

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

Posted on by Denise Gaskins

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.

Even a Math Workbook Can Be a Game

Posted on by Denise Gaskins

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.

Rabbit Trails and Fibonacci Poetry

Posted on by Denise Gaskins

Homeschooling Memories…

Well, I hadn’t planned on spending my day that way. But one of the great things about homeschooling is the freedom to follow rabbit trails.

While browsing the Carnival of Homeschooling, I found a link to Farm School blog’s article Fib Foolery, which sent me to Gotta Book for his articles The Fib and More Fibbery (read the comments on both threads, but be warned that some are crude) and several other posts, all of which set me off on a morning of poetic fun.

A “Fib” is a Fibonacci poem. It’s based on syllable count, like a haiku, but the lines follow the Fibonacci counting series: 1, 1, 2, 3, 5, 8… Each number is the sum of the previous two numbers.

I knew what I was going to share at our Tuesday Teatime and Poetry Reading that afternoon.

Here’s the best one I’ve come up with so far:

Math:
Word
Problem,
Mental play.
Archimedes shouts,
“Eureka! I figured it out.”

The Kids Join the Fun

While we always enjoyed our tea and poetry times, that day was the only one that inspired the kids to actually write poetry themselves.

My 7yo dd was so proud to be able to count syllables and write:

Cat.
Soft.
Pretty,
But sleeping.

While my 12yo ds really took off, creating more than a dozen Fibs. His first two are still his favorites:

Ducks
Have
No luck,
But they do
Have many feathers.
Hunters like to shoot ducks a lot.

and

Paul
Is
Revered
A lot by
Paul Revere’s Fan Club.
What is Paul’s last name, anyway?

Wouldn’t you like to try it, too? Please share your Fib in the comments below!

Feature photo: “Rabbit” by Save the Bay 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

Posted on by Denise Gaskins

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!