We’ve talked about several types of math manipulative that homeschooling parents might use to help their children learn math (see part 1 and part 2), but we never stopped to ask the most basic question:
Why use math manipulatives at all?
Math manipulatives are a tool for solving educational problems, so we should first decide what problem we are trying to solve. That will help us know which tool to use.
Continue reading Homeschool Musings: Math Manipulatives Part 3
In my previous post, I examined fingers and found items (beans, buttons, leaves, and so on) as tools that can help our children learn math. This time, we move on to the kinds of math manipulatives you’ll find in stores or packaged with your favorite curriculum.
The standard base ten blocks consist of plastic or wooden cubes, a rod with the length of ten cubes, a flat shape the size of ten rods side-by-side, and a large cube equivalent to ten of the flat shapes stacked atop each other.
These are used primarily for modeling place value as a means of developing the standard arithmetic algorithms for addition and subtraction.
They can also be used for modeling decimals as a place value notation, without relying on fraction concepts. And with a bit of imagination (“Pretend the rods are stretchy, so we don’t know how long they really are”) they can model simple algebraic expressions.
Continue reading Homeschool Musings: Math Manipulatives Part 2
I stumbled across another blogger’s post on the common question, “What are the best math manipulatives for homeschooling?”
My answer to this question has changed over the years, as I’ve grown in my understanding of math and of education. As my current stance is far different from much of what I read from other homeschoolers, I’m going to lay out my reasoning below.
I’d love to hear your thoughts, especially if you disagree, because comparing ideas with one another is a great way to learn.
Continue reading Homeschool Musings: Math Manipulatives Part 1
What is a “living book”? English education reformer Charlotte Mason introduced this term for any book that brings the reader directly into contact with the major ideas that have fascinated humans across the ages.
We know that reading aloud helps build our children’s love for books. But did you know it works for math as well?
And that it can transform the parent’s attitude as well as the child’s?
A playful math book fleshes out the bones of abstract math,
brings it alive,
makes it human, relatable,
interesting to readers of all ages,
opening our eyes to the wonderful world of big ideas,
where concepts meet and topics intertwine
in a beautifully intricate dance
of understanding.
We live in an age of abundance, with more new creative math books being published every year, so many that I can’t keep track of them all, not to mention the older classics, some out of print, that can still be found in public libraries.
Here are a few of my favorite books of playful, living math, both old and new:
I was asked to do an interview for a new podcast called Learning is Disruptable, and that got me thinking…
Math education is not working. Too many people come out of school with math avoidance, math anxiety or even phobia, a profound conviction that math is not for them.
Generally, humans enjoy success, the feeling that things make sense, that they are capable of understanding big ideas. People like subjects that give them this type of success, where they are meeting and making sense of new ideas, growing in mastery.
But they hate subjects that make them feel like a failure, where things don’t make sense and there seems to be no real chance of success.
Therefore, understanding our students’ attitude toward math gives us a solid indication of how well they are learning.
There’s a great new homeschool math program that can radically transform your children’s experience of math, building understanding through creative exploration.
First, a bit of history…
Back when I was still homeschooling, I read a couple of articles by Keith Devlin about the benefits of teaching children algebra, even before they study numbers.
As a homeschooler leaning toward Charlotte Mason-style education, I found the notion of algebra-first math intriguing. What if we could introduce students to the big ideas of math, the foundational concepts that explain how numbers relate, before they get distracted by details like math facts and memorized rules?
Continue reading A Revolutionary New Approach to Homeschool Math
I have a new podcast interview, and I think you’ll enjoy it!
Check out Learning Is Disruptable on your favorite podcast app, or listen on the website:
Here’s an excerpt…
“I think the most important thing that we need to change…we need to radically change what our idea is of what it means to learn math.
“Our biggest failure, both in the classroom and in homeschool settings, is that we’ve given our children a totally wrong idea of what math is all about.
Continue reading Podcast: Cultivating Math Curiosity and Reasoning in Kids
Do you have good intentions to play math with your children, but never seem to follow through?
When I was homeschooling, I found it easy to fall into a rut.
Do the next lesson in our workbook, and then the one after that, day after day.
Math became just another chore.
Yes, I knew better! But it’s so easy to just follow what’s in front of you. And searching out new ways to play with math takes time.
So now I’m offering something new to help you jump out of your math rut, the Playful Math Activities Subscription on Patreon.
Continue reading Introducing the Playful Math Subscription Plan
Welcome to the 162nd 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.
Bookmark this post, so you can take your time browsing.
There’s so much playful math to enjoy!
By tradition, we start the carnival with a puzzle/activity in honor of our 162nd edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.
The number 162 is a palindromic product:
162 = 3 x 3 x 2 x 3 x 3
and 162 = 9 x 2 x 9
Make a conjecture about palindromic products. (A conjecture is a statement you think might be true.)
Make another conjecture. How many can you make? Can you think of a way to investigate whether your conjectures are true or false?
Welcome to the 160th 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.
Bookmark this post, so you can take your time browsing.
There’s so much playful math to enjoy!
By tradition, we start the carnival with a puzzle/activity in honor of our 160th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.
Appropriately for an October carnival, 160 is an evil number.
A number is evil if it has an even number of ones in binary form. Can you find the binary version of 160? (Hint: Exploding Dots.)
160 is also a polyiamond number. If you connect 9 equilateral triangles side-to-side, a complete set of 9-iamond shapes would have 160 pieces.
But sets that large can be overwhelming. Try playing with smaller sets of polyiamonds. Download some triangle-dot graph paper and see how many different polyiamond shapes you can make.
What do you notice? Does it make you wonder?
What designs can you create with your polyiamonds?
Photo by Daiga Ellaby on Unsplash
Denise Gaskins' Let's Play Math 