Morning Coffee – 28 Oct 2019

Morning Coffee image

One of the best ways we can help our children learn mathematics (or anything else) is to always be learning ourselves.

Here are a few stories to enjoy with your Monday morning coffee:

“When you’re working every day, you’re not thinking, ‘What impact is this going to have on the world?’ You’re thinking, ‘I’ve got to get this right.’”

—Gladys West
quoted in Dr. Gladys West: The Black Woman Behind GPS Technology

  • I like to keep a quick game in reserve for spare time in my homeschool co-op class. Kent Haines explains Sprouts and suggests ways to launch math discussions.

“I don’t get irritated by these mistakes. I desperately wait for such mistakes. Yes! Because I think it is a golden opportunity for the teacher to spot a student thinking this way. It presents just the right context and time for driving an enriching mathematical conversation in the whole class.”

—Rupesh Gesota
Part-2: Re-learning and Enjoying Polynomial Division with students

“To teach students SSS congruence without pointing out why this is so interesting is harmful for two reasons. First of all, this is an amazing result. It is the our job to point out amazing results! Triangles are rigid figures in a way that other polygons are not.”

—Rachel Chou
Teaching the Distributive Property

CREDITS: Feature photo (top) by Kira auf der Heide via Unsplash. “Morning Coffee” post format inspired by Nate Hoffelder at The Digital Reader.

Math That Is Beautiful

One of the sections in my book Let’s Play Math: How Families Can Learn Math Together — and Enjoy It encourages parents to make beautiful math with their children.

Do you have trouble believing that math can be beautiful?

In “Inspirations,” artist Cristóbal Vila creates a wonderful, imaginary work studio for the amazing M.C. Escher. You’ll want to view it in full-screen mode.

How many mathematical objects could you identify?

Vila offers a brief explanation of the history and significance of each item on his page Inspirations: A short movie inspired on Escher’s works.

Read about the inspirations, and then try making some math of your own.

“I looked into that enormous and inexhaustible source of inspiration that is Escher and tried to imagine how it could be his workplace, what things would surround an artist like him, so deeply interested in science in general and mathematics in particular. I imagined that these things could be his travel souvenirs, gifts from friends, sources of inspiration…”

—Cristóbal Vila
Inspirations: A short movie inspired on Escher’s works

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.”

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

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

A Map of Mathematics

Pure mathematics, applied math, and more — all summarized in a single map! Watch the video by physicist and award-winning science writer Dominic Walliman:

Walliman says, “To err is to human, and I human a lot. I always try my best to be as correct as possible, but unfortunately I make mistakes…”

  • Can you find three mistakes in the map?

Check your answers in the description on Walliman’s YouTube page.

If you enjoy this video, you can purchase the poster (or T-shirt, coffee mug, tote bag, etc.) at Red Bubble.

CREDITS: Map of Mathematics poster by Dominic Walliman via Flickr (CC BY-NC-ND 2.0).

Hidden Figures Teaching Resources

Are you taking your kids to see the movie Hidden Figures? Check out Raymond Johnson’s blog post for references and teaching ideas:

If you know of any other resources, please share in the comments below. And as I find new goodies, I’ll add them to the list below.

Teachers and Students in Action

Lesson Plan Resources

Background Information

Before computers were machines, computers were people who computed things. This complicated task often fell to women because it was considered basically clerical. That’s right: computing triple integrals all day long qualified as clerical.

— Samantha Schumacher
Hidden Figures Movie Review