## Morning Coffee – 31 August 2020

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 morning coffee this week:

• David Butler’s post Twelve matchsticks: focus or funnel presents an interesting puzzle. But even better, it opened up a rabbit hole of thought-provoking posts about how to talk with children — or anyone.

“The approach where you have an idea in your head of how it should be done and you try to get the student to fill in the blanks is called funnelling. It’s actually a rather unpleasant experience as a student to be funnelled by a teacher. You don’t know what the teacher is getting at, and often you feel like there is a key piece of information they are withholding from you, and when it comes, the punchline feels rather flat.”

—David Butler
Twelve matchsticks: focus or funnel

## Morning Coffee – 24 August 2020

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 morning coffee this week…

“We are all mathematicians. We all have the power to notice, describe, and generalize patterns. You have all had this ability since birth. If we believe this then every day we must plan lessons that allow students to act as mathematicians. We must put something in front of our students to notice. We must put something in front of our students to describe, to generalize.”

—Sara VanDerWerf
What is Math? What do Mathematicians do?

## Morning Coffee – 17 August 2020

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 morning coffee this week:

“A strategy is how you mess with the numbers, how you use relationships and connections between numbers to solve a problem. A model is a representation of your strategy, the way the strategy looks visibly. Modeling your strategy makes your thinking more clear to others because they can see the thinking and the relationships that went into your process.”

—Pam Harris
Strategies vs. Models

• Do you have preschool or elementary students? Michael Minas has a great collection of games on his blog. Easy to learn and full of mathematical thinking.

“Doing mathematics like this deprives students of, well, let’s be honest, mathematics itself. We need to get to the answer faster. We need to move on. No time to stumble around rabbit holes. There is a curriculum to cover.”

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

## Morning Coffee – 10 August 2020

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 morning coffee this week:

“The happy truth about doing math with your kids is that it’s way more fun than you’re expecting it to be. It’s not about right answers, and it’s not about speed. It’s about playing, counting, building, sorting, and studying the wonderful, colorful world around us.”

—Dan Finkel and Katherine Cook

## Morning Coffee – 4 November 2019

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:

“Games aren’t just about practice and fluency. My favorite games create opportunities for learning, too. They spark discourse, promote the use of strategies, and allow students to dig into the mathematics.”

• Have you read Pam Harris’s Development of Mathematical Reasoning series? Check out Part 1, Part 2, and Part 3. Well worth your time!

“The teacher’s role is to help students change the way they think, in increasingly sophisticated ways. The goal is not answers. The goal is development. We don’t need students who can just answer a multiplication question, we need students who can reason multiplicatively.”

—Pam Harris
The Development of Mathematical Reasoning

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

## Morning Coffee – 28 October 2019

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.’”

• 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.”

“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.

## Morning Coffee – 4 October 2019

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 Friday morning coffee:

• In the spirit of cracking eggs to make omelets, Michael Pershan cracks open some of the ideas around Equations and Equivalence and relational thinking.

“My experience is that when I have vague hope that children will learn something from an activity that is related to the mathematics I want them to learn, they usually don’t.”

—David Wees
Hands on or minds on?

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

## Morning Coffee – 30 September 2019

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:

• Kathy Iwanicki’s students explore an unsolved math puzzle: the Hailstone Sequence. I think my co-op class might enjoy this activity, too.
• If you want to understand how number concepts develop through the school years, Graham Fletcher’s Progression Videos are a great place to start. Watch, re-watch, and learn.

“Learning occurs when we get something wrong and have to correct it. This is analogous to the much better known fact that when we subject our bodies to physical strain, say by walking, jogging, or lifting weights, the muscles we strain become stronger — we gain greater fitness.

“Indeed, the learning is better if the correction occurs some time after the error is made. Stewing for a while in frustration at being wrong, and not seeing how to fix it, turns out to be a good thing. Cracking your ego is an unavoidable part of learning.”

—Keith Devlin
On making omelets and learning math

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

## Morning Coffee – 27 September 2019

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 Friday morning coffee:

• Do you have early learners? Christina Tondevold explains the building blocks of Number Sense for Pre-K to 2nd grade children.
• If it’s time to teach your kids about the order of operations, consider using David Butler’s graphic version The Operation Tower. But don’t let yourself be drawn into those “gotcha!” memes on social media. As Dave Peterson points out (using trig functions), Order of Operations flows from basic common sense. If you need parentheses to make your meaning clear, then use them.

“What do we need to know in order to accomplish the goal? Well, start asking questions. And remember, one unasked question could put the entire enterprise in jeopardy…”

—Joe Schwartz
Houston, 1964

“It’s a little weird, isn’t it, that prime means first, and yet the first number isn’t prime?”

—Ben Orlin
Why Isn’t 1 a Prime Number?

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

## Morning Coffee – 23 September 2019

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.
• 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.
• 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 tool to 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.