I have a new podcast interview, and I think you’ll enjoy it!
Check out Pam Barnhill’s 10 Minutes to a Better Homeschool on your favorite podcast app, or listen on the website:
Here’s a couple of excerpts…
Continue reading Podcast: How to Transform Math Lessons without Changing your Curriculum
Last week, I quoted Pam Harris calling out a foundational myth of math education, the idea that we need to teach kids the methods that work on even the most difficult math problems.
“We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.
“We would be far better served to teach kids to think about the most common kinds of questions WELL, and let technology handle the crankiest.”
—Pam Harris
Since many of us grew up in schools that taught these methods, they may feel like the only sensible approach to math. Without the standard procedures, how will our kids learn to do math?
If we don’t teach subtraction with borrowing/renaming, how can students figure out calculations like 431 − 86? If we don’t teach fraction rules, how will they handle problems like 1 1/2 ÷ 3/8?
Welcome to the 172nd edition of the Playful Math Blog Carnival, a buffet 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.
The carnival went on hiatus for a couple of months due to unexpected life issues facing our volunteer hosts. But we’re back now, and ready to celebrate!
By tradition, we start the carnival with a puzzle in honor of our 172nd edition. But if you’d rather jump straight to our featured blog posts, click here for the Table of Contents.
One of my favorite podcasts to listen to is Pam Harris’s Math Is Figure-Out-Able because she puts so many of my thoughts into words.
For example:
“We have a misconception in math education that we think we need to teach methods so that kids can answer the craziest kind of a particular problem.
“We would be far better served to teach kids to think about the most common kinds of questions WELL, and let the cranky ones go to ChatGPT. Because they’ll recognize the sense of the answer.
“Let technology handle the crankiest, and REASON about the rest of them.”
—Pam Harris,
the Math is Figure-out-able Fractions Challenge
Well, I do think she’s wrong about the AI chatbot, because ChatGPT comes up with the strangest bald-faced nonsense about math problems. Wolfram Alpha is a much more reliable resource.
But Harris’s main point stands. This misconception, this math-education myth, drives much of what happens in our classrooms and home schools today.
I’ve tried a few times over the years to express my philosophy of teaching math. Back when I first started doing workshops for homeschooling parents, I told them:
“Instead of drudgery, mathematics should be a game of discovery. It should give children the same ‘Eureka!’ thrill that sent Archimedes running through town in his birthday suit. I call this the ‘Aha!’ factor, the delight in solving a challenging puzzle.”
I’ve just launched the Denise Gaskins’ Playful Math Store!
There’s a new math journaling prompt this week.
Have your kids tried it yet?
This week’s prompt features one of my favorite quotations to get kids thinking (and writing) about the value of mistakes in learning. Or you might prefer last week’s prompt, featuring a classic math brainteaser and encouraging students to create their own related puzzles.
Or, if you’re reading this post later and missed those, there’s another great new prompt this week for you to explore.
Check it out:
Kitten (my daughter) and I sat on the couch sharing a whiteboard, passing it back and forth as we took turns working through our prealgebra book together.
The chapter on number theory began with some puzzles about multiples and divisibility rules.
Games are fun, building a positive attitude toward math. They give students a refreshing break from textbook work and make kids willing to practice their math. Games make math practice enjoyable, something children want to do. We can happily work through many more calculations during a game than anyone would ever want to do on a homework page.
But more important than the fun, math games push children to think about what numbers mean and how they work. The numbers in a math game are not just meaningless abstractions, but tools that players can use to gain an advantage over their opponent.
A good math game reinforces the idea that math is about reasoning, using the things you know to figure out what you need. Math is not just about getting the right answer. It’s about what goes on in your head on the way to that answer. The answer itself is merely a side-effect. of what really matters, your thinking.
A good math game helps students develop flexibility, the ability to adapt, applying what they have learned to new situations, finding a way to work out the things they haven’t mastered yet. All these add up to a more robust type of mathematical fluency than what many people imagine possible.
Having knowledge in long-term memory can be very helpful in solving problems.
But master problem-solver Sherlock Holmes was concerned that if he had too much knowledge in his mind, new facts would crowd out the old and cause him to forget something important:
Continue reading Math Musings: When Should We Work on Memorization?
