Writing to Learn Math: What did the author mean? Put the thought in your own words. Do you agree or disagree? Why?
Do you want your children to develop the ability to reason creatively and figure out things on their own?
Help kids practice slowing down and taking the time to fully comprehend a math topic or problem-solving situation with these classic tools of learning: Notice. Wonder. Create.
“The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would-be solver.”
—I. N. Herstein
Whenever I give a problem or puzzle in an Alexandria Jones story, I’ll try to post the answer soon afterward.
But don’t peek!
In the old days of my snail mail newsletters, the answers always came in the next issue, so students had two months to let the puzzle ruminate without temptation.
After all, if you only read the answer I give, you miss out on the fun of solving the puzzle. Follow the Math Adventurer’s Rule:
Give the problem a good workout on your own. See what you can notice about the puzzle. Wonder about how it connects to the larger world of mathematics.
Play with the ideas and find out where they may lead.
Then check the answer just to prove you got it right, and maybe to see whether we did it the same way. There’s always more than one way to approach any math problem, and each method offers its own insights.
“One factor that has remained constant through all the twists and turns of the history of physical science is the decisive importance of the mathematical imagination.”
—Freeman Dyson
In the previous episode, Alexandria Jones discovered a mysterious treasure: three wooden sticks, like tent pegs, and a long loop of rope with 12 evenly spaced knots. Her father explained that it was an ancient Egyptian surveyor’s tool, used to mark right angles.
And now for something completely different…
The intrepid Quote Investigator played around with math recently:
“You know, people think that mathematics is complicated. Mathematics is the simple bit. It’s the stuff we can understand. It’s cats that are complicated.”
—John Horton Conway
It reminded me of one of my favorite homeschooling exercises:
One of these exercises was a series of short quotations about cats, which my youngest daughter loved.
So in today’s post, I’ve put together an editing exercise you can share with your children, along with several links for playing with mathematical cats.
Enjoy!
“Problems stressing deduction rather than calculation have a special appeal and value. They teach you to analyze, and to seek unorthodox ways of solving a problem.”
—Boris Kordemsky
Today I’m sharing a few treats from The Moscow Puzzles by Boris Kordemsky, which mixes classic brainteasers and original stumpers.
Recreational math expert Martin Gardner called Kordemsky’s book “the outstanding puzzle collection in the history of Russian mathematics.”
Have fun playing logic with your kids!
Welcome to the 184th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.
With all the links, a blog carnival can feel overwhelming. Bookmark this article, so you can take your time reading the posts.
“Living math” means bringing our children face-to-face with the big ideas of mathematics to help them develop their reasoning skills. When the ideas of math come to life for our children, their minds delight in seeing how numbers and shapes connect to each other and exploring these relationships.
Scattered between the playful math links below, you’ll find quotations from my new book Charlotte Mason’s Living Math, along with several paintings of children playing and learning which I considered for the book but ran out of room.
By tradition, we start the carnival with a puzzle/activity in honor of our 184th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.
“The true joy in mathematics, the true hook that compels mathematicians to devote their careers to the subject, comes from a sense of boundless wonder induced by the subject.
“There is transcendental beauty, there are deep and intriguing connections, there are surprises and rewards, and there is play and creativity.
“Mathematics has very little to do with crunching numbers. Mathematics is a landscape of ideas and wonders.”
—James Tanton
James Tanton has a new website. It looks cool, and it’s a great place to discover the things he’s working on these days.
But his wonderful, old-fashioned site full of great insights and interesting problems is gone.
😞 I hate it when some part of the internet that I love disappears. So here’s my attempt to recover one tiny bit of the old site, five tips for creative problem solving through intellectual play.
“You don’t educate people by telling them useful things; you educate people by telling them interesting things.”
— John Conway
If you want help educating your children with interesting things about math, check out Denise Gaskins’ Playful Math store.
We’re currently running a huge back-to-school sale on ALL of my playful math ebooks, problem-solving activities, math journaling task cards, and math art projects.
So many great ways to play with math!
The 20% discount will automatically apply when you check out. No discount code required.
Check it out:
One of the best ways we can help our children learn mathematics (or anything else) is to be lifelong learners ourselves.
Here are a few stories to read as you sip your morning brew. . .
“Play and rigor support each other.
“When students are invited to play with math, they learn more deeply, more robustly, and remember more consistently.
“Play is promoted as something that can engage kids and give them a more positive attitude about school, but it’s easy to assume that it’s not useful for learning, when in reality the opposite is true:
“The student who is playing tends to be the student who is learning most deeply.”
—Dan Finkel, Math for Love newsletter
