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 read with your Monday morning coffee:

- David Butler invented a challenging new game that can spark plenty of mathematical thinking: Digit Disguises.

- Which led me on a delightful rabbit trail through David’s archives, rediscovering old delights like his Seven Sticks post and The Arts students’ maths brain.

- If you liked James Tanton’s video on the area model in last week’s post, you may enjoy his in-depth discussion of The Astounding Power of Area.

- And a (broken) link on that page sent me along another rabbit trail to find Geri Lorway’s blog. I love her post on multiplication: Teaching division?… Do you know the “basics”?

- On a lighter note, I’m sure any classroom or homeschool teacher can think of several ways to use Sara VanDerWerf’s collection of Math Fails. Scroll down for links to earlier collections, too.

“I told them that actually what they did was exactly what maths is — reasoning things out using the information you have and being able to be sure of your method and your answer. Just because there’s no symbols, it doesn’t mean it’s not maths.”

—David Butler

The Seven Sticks and what mathematics is

“I am not willing to teach mindless math. It leads to mindless adults. Thinking is not an add-on once they have memorized.

Thinking is the basic toolto negotiate the world.”—Geri Lorway

Teaching division?… Do you know the “basics”?

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

Hi Denise,

Regarding the “Teaching Division, do you know the ‘basics’? ”

I’m curious to hear your thoughts on this particular post from Geri Lorway.

I’m always surprised when a teacher gets that upset about a student getting something wrong. Do they hide it from the student and start where they are?

Her comments under the student notes are snarky, I agree. I doubt she would actually talk to students that way in person. But this article is aimed at teachers, and I think she’s trying to shock us into listening to her point.

I liked her overall emphasis on making sure students have a robust understanding of multiplication (one that will not “expire” when they work with decimals or fractions) before trying to teach division. Division depends on multiplication to make sense.

And I agree with her comment: “When we focus on memorizing facts and multi-step algorithms before we develop how multiplication and division are related both visually and spatially, students do not come to understand. That is what makes teaching division so difficult. They have no way to make sense of what they are doing or why.”

Hi Denise,

Ok. I got past the snarky(rude) comments under the students papers which didn’t strike me as useful, and read the rest of the post. Also, I just read Ben Orlin’s post on multiplication and found it very useful.

The point to come away with from Lorway that I thought she could have started with, was that multiplication and division are inverse functions. You can’t seperate them when you present them; teach and learn them together.

I see she has some set of cards, a learning system she has developed.

I’m like Ben Orlin, in that I love math and I’m terrible at drawing.

I read Lorway’s post because I wanted to hear how division is presented in elementary school, especially since core curriculum has generated so many new approaches to curriculum. I have empathy for the students and teachers who were the object of her scorn, though. A simple ” Here’s a couple of enthusiastic but unfortunate students who do not understand what multiplication is”

🙂 Kim

Do you mean this post by Ben Orlin? The Sixth Sense for Multiplication. He covers a lot of good information — some of what Lorway was talking about, plus more.

Yes, I think that’s the post. I’m going to try reading his books, and I’m following his blog.

Thank you for sharing what you read.