Quotable: Then and Now

“I used to think my job was to teach students to see what I see. I no longer believe this. My job is to teach students to see; and to recognize that no matter what the problem is, we don’t all see things the same way. But when we examine our different ways of seeing, and look for the relationships involved, everyone sees more clearly; everyone understands more deeply.”

Joe Schwartz
Then and Now


[Feature photo (above) by jenn.davis via Flickr (CC BY 2.0).]

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Playful Math Education Carnival 104 via Travels in a Mathematical World

mtap104Check out the new carnival of playful math for all ages at Travels in a Mathematical World blog. Each month’s carnival brings you a great new collection of puzzles, math conversations, crafts, teaching tips, and all sorts of mathy fun.

This month’s post features measurement games, algebra activities, paper folding, math podcasts, the secret to avoiding commitment, a variety of number puzzles, and much more.

Click Here to Go Read the Carnival Blog!

Hey, Blogger, Can You Spare a Time?

Do you write an education or family blog? Classroom teacher, math coach, homeschooler, parent, college professor, unschooler — anyone interested in helping kids play around with math? Please consider volunteering to host the MTaP blog carnival for one month.

We still need volunteer hosts for most of 2017.

You choose the month that fits your schedule and decide how much effort you want to put in. Writing the carnival can take a couple of hours for a simple post — or you can spend several days searching out and polishing playful math gems to share.

If you want more information, read the MTaP Math Education Blog Carnival home page. Then let me know which month you want.


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 Inspirations: Why Study Mathematics?

why-study-math

What teacher hasn’t heard a student complain, “When am I ever going to have to use this?” Didn’t most of us ask it ourselves, once upon a time?

And unless we choose a math-intensive career like engineering, the truth is that after we leave school, most of us will never again use most of the math we learned.

But if math beyond arithmetic isn’t all that useful, then what’s the point?

If you or your student is singing the “Higher Math Blues,” here are some quotations that may cheer you up — or at least give you the strength of vision to keep on slogging.

We Study Mathematics…

To Understand Creation

I don’t want to convince you that mathematics is useful. It is, but utility is not the only criterion for value to humanity. Above all, I want to convince you that mathematics is beautiful, surprising, enjoyable, and interesting. 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? Mathematics connects ideas that otherwise seem totally unrelated, revealing deep similarities that subsequently show up in nature.

— Ian Stewart
The Magical Maze

That vast book which stands forever open before our eyes, the universe, cannot be read until we have learnt the language in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word.

— Galileo Galilei
quoted by Clifford Pickover, A Passion for Mathematics

To Train Our Minds

The investigation of mathematical truths accustoms the mind to method and correctness in reasoning, and is an employment peculiarly worthy of rational beings.

— George Washington
quoted by William Dunham, The Mathematical Universe

I told myself, “Lincoln, you can never make a lawyer if you do not understand what demonstrate means.” So I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what “demonstrate” means, and went back to my law studies.

— Abraham Lincoln
quoted by William Dunham, The Mathematical Universe

To Understand History

In most sciences, one generation tears down what another has built, and what one has established another undoes. In mathematics alone, each generation adds a new story to the old structure.

— Herman Henkel
quoted by Noah benShea, Great Quotes to Inspire Great Teachers

Biographical history, as taught in our public schools, is still largely a history of boneheads: ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant generals — the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.

— Martin Gardner
quoted by G. Simmons, Calculus Gems

I will not go so far as to say that constructing a history of thought without profound study of mathematical ideas is like omitting Hamlet from the play named after him. But it is certainly analogous to cutting out the part of Ophelia. For Ophelia is quite essential to the play, she is very charming. . . and a little mad.

— Alfred North Whitehead
quoted in The Viking Book of Aphorisms

To Appreciate the Beauty

The mathematician does not study pure mathematics because it is useful, he studies it because he delights in it, and he delights in it because it is beautiful.

— Henri Poincaré
quoted by Theoni Pappas, More Joy of Mathematics

A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful. The ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

— Godfrey H. Hardy
A Mathematician’s Apology

And Most of All, to Play

Mathematics is a world created by the mind of men, and mathematicians are people who devote their lives to what seems to me a wonderful kind of play!

Constance Reid

At age eleven, I began Euclid, with my brother as tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world.

— Bertrand Russell
The Autobiography of Bertrand Russell

I love mathematics … principally because it is beautiful, because man has breathed his spirit of play into it, and because it has given him his greatest game — the encompassing of the infinite.

Rózsa Péter
quoted by Rosemary Schmalz, Out of the Mouths of Mathematicians

Did you enjoy these? You can find plenty more on my Math & Education Quotations page.

  • I would LOVE to hear YOUR favorite mathematics, education, or inspirational quote. Please share in the Comments section below!

 photo exploreMTBoS_zpsf2848a9a.jpgNever Ending Math Problem photo (above) by Danny via Flickr (CC BY 2.0). This post is part of the #MTBoS #MtbosBlogsplosion blogging challenge.


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.


My Favorite Math Games

Take a break from textbook math and enjoy yourself!

I like to use games as a warm-up with my co-op math circle. Some homeschoolers make every Friday a game day, and some turn gaming into a family lifestyle.

favorite-math-gamesIf you’d like to add more play to your family’s day, check out Cait’s 2017 Gameschooling Challenge.

“Playing games with your kids offers a host of educational benefits, plus you build relationships and make memories. I am constantly amazed by the amount of learning that happens when I sit down to play games with my children.”

—Caitlin Fitzpatrick Curley
Gameschool Challenge

Family Games for All Ages

“Games put children in exactly the right frame of mind for learning difficult things. Children relax when they play — and they concentrate. They don’t mind repeating certain facts or procedures over and over, if repetition is part of the game.”

Peggy Kaye
Games for Math

Accessible to Young Children

“Coming back from winter break can be hard. Everyone is sleepy, unfocused, and daydreaming of the holiday gifts that await them at home after school. And that’s just the teachers!”

—Andrew Gael
Beat the Back to School Blues…Play a Math Game

For Elementary Students

“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”

Peggy Kaye
Games for Math

Middle School to Adult

“Mathematics is mental play, the essence of creative problem solving. This is the truth we need to impart to our children, more important than fractions or decimals or even the times tables. Math is a game, playing with ideas.”

—Denise Gaskins
Let’s Play Math: How Families Can Learn Math Together—and Enjoy It

Your Turn: What Are Your Favorite Games?

They don’t have to be math! Please share in the comment section below!


 photo exploreMTBoS_zpsf2848a9a.jpgThis post is part of the #MTBoS #MtbosBlogsplosion blogging challenge.


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 Build Your Math Blog’s Audience

New Year, New Blog!

The first way to make your math blog grow is to write posts. Here’s an #MTBoS blog challenge that seems doable: Only one post a week, so maybe even I can keep up.

With the start of a new year, there is no better time to start a new blog! For those of you who have blogs, it is also the perfect time to get inspired to write again! Please join us to participate in this years blogging initiative…

Click Here for Details

Join the Math Education Blog Carnival

Once you’ve got your post blogged, please share it with us!

The Math Teachers at Play (MTaP) blog carnival is a monthly collection of tips, tidbits, games, and activities for students and teachers of preschool through pre-college mathematics. We welcome entries from parents, students, teachers, homeschoolers, and just plain folks…

Click Here to Learn More


[Spiral fractal photo (above) by Kent Schimke 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.