Mathematics Is Worthy

“When I began my college education, I still had many doubts about whether I was good enough for mathematics. Then a colleague said the decisive words to me: it is not that I am worthy to occupy myself with mathematics, but rather that mathematics is worthy for one to occupy oneself with.”

Rózsa Péter
Mathematics is beautiful
essay in The Mathematical Intelligencer

Rózsa Péter and the Curious Students

I would like to win over those who consider mathematics useful, but colourless and dry — a necessary evil…
 
No other field can offer, to such an extent as mathematics, the joy of discovery, which is perhaps the greatest human joy.
 
The schoolchildren that I have taught in the past were always attuned to this, and so I have also learned much from them.
 
It never would have occurred to me, for instance, to talk about the Euclidean Algorithm in a class with twelve-year-old girls, but my students led me to do it.
 
I would like to recount this lesson.
 
What we were busy with was that I would name two numbers, and the students would figure out their greatest common divisor. For small numbers this went quickly. Gradually, I named larger and larger numbers so that the students would experience difficulty and would want to have a procedure.
 
I thought that the procedure would be factorization into primes.
 
They had still easily figured out the greatest common divisor of 60 and 48: “Twelve!”
 
But a girl remarked: “Well, that’s just the same as the difference of 60 and 48.”
 

 
“That’s a coincidence,” I said and wanted to go on.
 
But they would not let me go on: “Please name us numbers where it isn’t like that.”
 
“Fine. 60 and 36 also have 12 as their greatest common divisor, and their difference is 24.”
 

 
Another interruption: “Here the difference is twice as big as the greatest common divisor.”
 
“All right, if this will satisfy all of you, it is in fact no coincidence: the difference of two numbers is always divisible by all their common divisors. And so is their sum.”
 
Certainly that needed to be stated in full, but having done so, I really did want to move on.
 
However, I still could not do that.
 
A girl asked: “Couldn’t they discover a procedure to find the greatest common divisor just from that?”
 

 
They certainly could! But that is precisely the basic idea behind the Euclidean Algorithm!
 
So I abandoned my plan and went the way that my students led me.
 

— Rózsa Péter
quoted at the MacTutor History of Mathematics Archive

For Further Exploration

Note: When the video narrator says “Greatest Common Denominator,” he really means “Greatest Common Divisor.”


The Challenge Continues

This is my third contribution to the blogging challenge #MTBoSBlaugust.

I’m aiming for at least one post each week. A simple, modest goal. But if I manage it, that will be four times the pace I’ve set in recent months.

So far, so good…

CREDITS: “Pink toned thoughts on a hike” photo courtesy of Simon Matzinger 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.

Everyone Deserves to Enjoy Math

“In 2018, I want to change the world.

I want to make it possible for more children to claim math as their favorite subject.

Math is how we describe our world when words are not enough. Everyone deserves to speak math and to play math, to enjoy its beauty and its power.”

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


CREDITS: Background photo by Bobby Johnson on Unsplash.

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Quotable: Keith Devlin on Mathematical Thinking

“At heart, mathematical thinking is little more than formalized common sense. It always has been. Which means it is something we can all do.”

— Keith Devlin
How Today’s Pros Solve Math Problems

If you have some time to spend pondering big ideas, dig into Devlin’s entire series of posts about what real-world mathematics looks like and the implications for math education:

And a related series on K–12 school math:

“Make no mistake about it, acquiring that modern-day mathematical skillset definitely requires spending time carrying out the various procedures. Your child or children will still spend time ‘doing math’ in the way you remember.

“But whereas the focus used to be on mastering the skills with the goal of carrying out the procedures accurately — something that, thanks to the learning capacity of the human brain, could be achieved without deep, conceptual understanding — the focus today is on that conceptual understanding.

“That is a very different goal, and quite frankly a much more difficult one to reach.”

— Keith Devlin
All The Mathematical Methods I Learned in My University Math Degree Became Obsolete in My Lifetime


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 Education Carnival 115—Women of Mathematics

Welcome to the 115th edition of the Playful 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.

In honor of Women’s History Month, this carnival features quotes from fifteen women mathematicians.

If you would like to jump straight to our featured blog posts, click here to see the Table of Contents.

Let the mathematical fun begin!

The Women of Mathematics

They came from many countries and followed a variety of interests.

They conquered new topics in mathematics and expanded the world’s understanding of old ones.

They wrestled with theorems, raised children, published articles, won awards, faced discrimination, led professional organizations, and kept going through both success and failure.

Some gained international renown, but most enjoyed quiet lives.

They studied, learned, and lived (and some still live) as most of us do — loving their families and friends, joking with colleagues, hoping to influence students.

I think you’ll find their words inspiring.

“What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved.”
Julia Robinson (1919–1985)

 

“All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”
Karen Uhlenbeck (b. 1942)

Continue reading Playful Math Education Carnival 115—Women of Mathematics

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!


CREDITS: 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!


CREDITS: 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.