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.
People 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.
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.
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
“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.
How can we help children learn to think mathematically? Live by these four principles.
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.
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.
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.
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
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?
CREDITS: An 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 (CC-BY 2.0, text added). This post is an excerpt from my book Multiplication & Fractions: Math Games for Tough Topics, available now at your favorite online book dealer.
From Peggy Kaye’s classic book Games for Math:
“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.
“Children throw themselves into playing games the way they never throw themselves into filling out workbook pages.
“The games solidify the achievements of children who are already good at math, and they shore up children who need shoring up. They teach or reinforce many of the skills that a formal curriculum teaches, plus one skill that formal teaching sometimes leaves out — the skill of having fun with math, of thinking hard and enjoying it.
“If you play these games and your child learns only that hard mental effort can be fun, you will have taught something invaluable.”
* * *
This blog is reader-supported.
If you’d like to help fund the blog on an on-going basis, then please join me on Patreon for mathy inspiration, tips, and an ever-growing archive of printable activities.
If you liked this post, and want to show your one-time appreciation, the place to do that is PayPal: paypal.me/DeniseGaskinsMath. If you go that route, please include your email address in the notes section, so I can say thank you.
Which I am going to say right now. Thank you!
“The Value of Math Games” copyright © 2016 by Denise Gaskins.
Homeschoolers have an advantage in teaching math: As our students grow, our own understanding of math grows with them because we see how the ideas build on each other.
This is especially true for those of us with large families. We pass through the progression of concepts with each student, and every pass lays down another layer in our own minds.
If you’d like to short-cut that process, check out Graham Fletcher’s Making Sense of Elementary Math video series. He’ll walk you through the topics, showing how manipulatives help build early concepts and gradually give way to abstract calculations.
“Understanding the vertical progression of mathematics is really important in the conceptual development of everyone’s understanding. This whole Making Sense Series has truly forced me to be a better teacher.”
— Graham Fletcher
“My oldest son has somehow developed the horrid habit of counting on his fingers. We worked on the math facts all summer. He knows the answers in simple form, such as 9 + 4, but if it’s in a bigger problem like 249 + 54, he counts up to add or counts down to subtract, all using fingers. My younger children have no problem with mental math, but he can’t seem to get it. Are there any tips or tricks to stop this?”
Counting on fingers is not a horrid habit, it is a crutch. Please think for a moment about the purpose of crutches. The blasted things are an uncomfortable nuisance, but there are times when you can’t get anywhere without them. And if you need them, it does you no good for a friend to insist you should crawl along on your own.
That is how your son feels right now about his fingers. He is struggling with something his younger siblings find easy, and he can tell that you are frustrated. His confidence is broken, in a cast, and needs time for healing. So he falls back on what he knows he can do, counting up the answer.
Think positive: this means he still believes that math ought to make sense — that to understand what he is doing is more important than to guess at an answer. You want him to value sense-making, because otherwise he will try to memorize his way through middle school and high school math. That is the road to disaster.
I’ve loved James Tanton’s How to Be a Math Genius videos for years. He offers great problem-solving tips like:
Seriously, those are wonderful videos. If you haven’t seen them before, go check them out. Be sure to come back, though, because I’ve just heard some great news.
Tanton has joined up with the NaturalMath.com team of Maria Droujkova, Yelena McManaman, and Ever Salazar to put together a book for parents, teachers, math circle leaders, and anyone else who works with children ages 3–10.
It’s called Avoid Hard Work, and it takes a playful look at ten powerful problem-solving techniques.
For more details about Avoid Hard Work, including a 7-page pdf sample with tips and puzzles to enjoy, check out the crowdfunding page at Natural Math:
Read the questions and answers. Try the activities with your children. And donate to support playful math education!
Welcome to the 97th edition of the Math Teachers At Play math education blog carnival: a monthly 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.
A few articles were submitted by their authors, but most were drawn from the immense backlog in my rss reader. If you’d like to see your blog post featured next month, be sure to send it in yourself. Our hosts are busy parents and teachers who have limited time to scour the Internet for goodies.
To add a bit of color, I’ve thrown in several favorites from my newly updated Math with Living Books pages. Some (affiliate) links go to Amazon.com, where you can read descriptions and reviews — but there’s no need to buy. Most of these books should be available through your local library.
If you’d like to skip directly to your area of interest, click here:
Please: If you enjoy the carnival, would you consider volunteering to host sometime this year? Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn, please speak up!
And now, let the mathematical fun begin!
When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade.
Help inspire your kids to try writing their own unique problems. Includes a wide range of math topics and concepts: money and time, fractions, percentages, geometry, logic, and multi-step problem solving.
“I’m so tired of being ignorant about math. I can memorize rules and do calculations, but if I miss a step the numbers make no sense at all, and I can’t spot what went wrong. Another struggle I have is keeping everything organized in my mind. When I learn a new concept or strategy, I easily forget it. My son is only a toddler now, but as he grows up, I don’t want to burden him with my own failures. Where should I start?”
As a first step, convince yourself that math is interesting enough to learn on its own merits, because parental guilt will only carry you so far. Start with Steven Strogatz’s “Elements of Math” series from The New York Times, or pick up his book The Joy of x.
Denise Gaskins' Let's Play Math 