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.


New Book: Word Problems from Literature

The posts on my Let’s Play Math blog are, for the most part, first-draft material. Of course, I’ve proofread each post — many times! because I’m a perfectionist that way, and yet I still miss typos :-/ — but these articles haven’t gotten the sort of feedback that polishes a book manuscript.

Well, now I’m taking some of the best of my old blog posts, expanding them with a few new games or activities, and giving them that book-quality polish. Let me introduce my newest series, the Playful Math Singles.

Under Construction …

The Playful Math Singles from Tabletop Academy Press will be short, topical books featuring clear explanations and ready-to-play activities.

I’m hoping to finish up two or three of these this year. Watch for them at your favorite online bookstore.

The first one is done …

Word Problems from Literature: An Introduction to Bar Model Diagrams

You can help prevent math anxiety by giving your children the mental tools they need to conquer the toughest story problems.

Young children expect to look at a word problem and instantly see the answer. But as they get older, their textbook math problems also grow in difficulty, so this solution-by-intuitive-leap becomes impossible.

Too often the frustrated child concludes, “I’m just not good at math.”

But with guided practice, any student can learn to master word problems.

Word Problems from Literature features math puzzles for elementary and middle school students from classic books such as Mr. Popper’s Penguins and The Hobbit.

For each puzzle, I demonstrate step by step how to use the problem-solving tool of bar model diagrams, a type of pictorial algebra. For children who are used to playing with Legos or other blocks — or with computer games like Minecraft — this approach reveals the underlying structure of a math word problem. Students can make sense of how each quantity in the story relates to the others and see a path to the solution.

And when you finish the puzzles in this book, I’ll show you how to create your own word problems from literature, based in your children’s favorite story worlds.

Free Online Preview

Buy now at your favorite online bookstore.

If you’re using these word problems with your children, consider buying them the paperback companion Word Problems from Literature Student Workbook.

… and People Like It!

A screen shot from this past weekend:

“I found this method really clarified for me what was going on visually and conceptually. Particularly when it came to more complex questions, for which I would normally write out an equation, I felt that thinking about what was going on with the bars actually made more sense … This is a wonderful book for those who want to support their children in finding better ways to work on word problems.”

—Miranda Jubb, Amazon customer reviewer


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.


Visualizing Word Problems with Bar Model Diagrams

A friend emailed me, frustrated with her child’s math lesson on bar diagrams: “Why do they have to make it so complicated? Why can’t we just solve the blasted problem?”

I told her bar models themselves are not the goal. The real question for parents and teachers is:

  • What can you do when your child is stumped by a math word problem?

To solve word problems, students must be able to read and understand what is written. They need to visualize this information in a way that will help them translate it into a mathematical expression.

visualizing-word-problems

Bar model diagrams are one very useful tool to aid this visualization. These pictures model the word problem in a way that makes the solution appear almost like magic.

It is a trick well worth learning, no matter which math program you use.

Visualization

https://www.youtube.com/watch?v=HKsYDzQK8Zw

“Visualization is the brain’s ability to see beyond what the eyes can see, and we can develop visualization in many ways.”

The Bar Model Explained

https://www.youtube.com/watch?v=I6Ipio8JntU

“A bar model is a way to represent a situation in a word problem using diagrams — in particular, using rectangles.”

https://www.youtube.com/watch?v=i7LAHc1qvig

“This is one of the ideas that children learn in mathematics: the use of diagrams to represent quantities, especially quantities which are unknown.”

Word Problems from Literature

I’ve written a series of blog posts that explain bar model diagrams from the most basic through to solving multistep word problems. Check them out:

I’ve started working on a book about bar model diagrams, and I’d love to hear your input. Have you tried using them? Do they help your children? What questions do you have?

Update: My New Book

You can help prevent math anxiety by giving your children the mental tools they need to conquer the toughest story problems.

Check out Word Problems from Literature: An Introduction to Bar Model Diagrams—now available at all your favorite online bookstores!

And there’s a paperback Student Workbook, too.


CREDITS: Videos and quotations from Dr. Yeap Ban Har’s YouTube channel. “Girl doing homework” photo (top) by ND Strupler and “math notebooking equal fractions” by Jimmie 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.


Confession: I Am Not Good at Math

I want to tell you a story. Everyone likes a story, right? But at the heart of my story lies a confession that I am afraid will shock many readers.

confessionPeople assume that because I teach math, blog about math, give advice about math on internet forums, and present workshops about teaching math — because I do all this, I must be good at math.

Apply logic to that statement.

The conclusion simply isn’t valid.

Continue reading Confession: I Am Not Good at Math

What Do We Mean by ‘Understanding’?

“You understand something if you have the ability to view it from different perspectives.

“Changing your perspective makes your mind more flexible, it makes you open to new things, and it makes you able to understand things.”

— Roger Antonsen
Math is the hidden secret to understanding the world

Check out the speaker’s footnotes for links and interesting tidbits about the images in the video.


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.


Prof. Triangleman’s Abbreviated List of Standards for Mathematical Practice

How can we help children learn to think mathematically? Live by these four principles.

PTALSMP 1: Ask questions.

Ask why. Ask how. Ask whether your answer is right. Ask whether it makes sense. Ask what assumptions you have made, and whether an alternate set of assumptions might be warranted. Ask what if. Ask what if not.

PTALSMP 2: Play.

See what happens if you carry out the computation you have in mind, even if you are not sure it’s the right one. See what happens if you do it the other way around. Try to think like someone else would think. Tweak and see what happens.

PTALSMP 3: Argue.

Say why you think you are right. Say why you might be wrong. Try to understand how someone else sees things, and say why you think their perspective may be valid. Do not accept what others say is so, but listen carefully to it so that you can decide whether it is.

PTALSMP 4: Connect.

Ask how this thing is like other things. Try your ideas out on a new problem. Ask whether and how these ideas apply to other situations. Look for similarities and differences. Seek out the boundaries and limitations of your techniques.

— Christopher Danielson

And a Puzzle

Practice applying Professor Triangleman’s Standards to the puzzle below. Which one doesn’t belong? Can you say why someone else might pick a different one?

wodb


multfrac-300An expanded version of the standards originally posted in Ginger ale (also abbreviated list of Standards for Mathematical Practice). Feature photo by Alexander Mueller via Flicker. This post is an excerpt from my book Multiplication & Fractions: Math Games for Tough Topics, available now at your favorite online book dealer.


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.