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
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
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
Do you want to help your children master problem-solving skills?
Check out my temporary online store for anyone who missed the Kickstarter.
Through the end of September, you can place a preorder for the early-release edition of Word Problems from Literature, along with the Word Problems Student Workbook and exclusive Audio Commentary (or any of my other books or printable math activity guides).
I’ll lock down the preorder store when I’m ready to send the Kickstarter order to my printer.
Books will be delivered with the Kickstarter orders: Digital items in October, physical books by the end of December.
To wrap up our week of exploring the resources from Word Problems from Literature, let’s talk about getting students to write their own math.
First up, I’m sharing an excerpt from the Word Problems Student Workbook. The “Story Problem Challenge” is one of my favorite math club activities.
Following that, you’ll find an amazing online mathemagical adventure for middle school: The Arithmetiquities. It’s great fun, and a great inspiration for students to create their own math stories.
Have fun writing math with your kids!
What do you get when you cross a library book or favorite movie with a math worksheet? A great alternative to math homework!
The rules are simple:
(1) Choose a worksheet calculation to be the basis for your word problem.
(2) Solve the calculation.
(3) Consider where these numbers could make sense in your book or movie universe. How might the characters use math? What sort of things would they count or measure? Do they use money? Do they build things, or cook meals, or make crafts? Do they need to keep track of how far they have traveled? Or how long it takes to get there?
(4) Write your story problem.
To make the game easier, you may change the numbers to make a more realistic problem. But you must keep the same type of calculation. For example, if your worksheet problem was 18÷3, you could change it to 18÷6 or 24÷3 or even 119÷17 to fit your story, but you can’t make it something like 18−3.
Remember that some quantities are discrete and countable, such as hobbits and fireworks. Other quantities are continuous, such as a barrel of wine or a length of fabric. Be sure to consider both types when you are deciding what to use in your problem.
Then share your problem with friends, and you try their problems. Can you stump each other?
Old books are in the public domain, so you can always use characters like Robin Hood, Sherlock Holmes, or Winnie-the-Pooh (but not the newer Disney version with the red jacket). But most books and movies are the protected intellectual property of their authors or estates, or of the company who bought those rights.
When you write problems for your own private use, feel free to use your favorite characters from any story. That’s like fan fiction, secret, just for your own pleasure.
But if you decide to share your creation beyond your own home or classroom, then be sure to “genericize” it first. Change or remove the proper names, using general descriptions instead.
For example, if you love the Harry Potter series, you might want to use Harry or Hermione in your story problems. Instead, write about “the boy wizard destined to fight an evil sorcerer.” Or “the bright young witch who can master any spell.”
Or if you like the Star Wars movies, you might write about “an interstellar justice warrior with an energy sword.” Or “an alien master of martial arts training a cocky but inexperienced apprentice.”
We’d love to add your story to the Student Math Makers Gallery.
When the world of Sfera is threatened by the machinations of a malevolent sorcerer, it will be up to a band of unlikely heroes to become the brightest light in the darkness.
The adventurers fan out across the land to find and retrieve the Arithmetiquities, a set of ancient mathemagical artifacts.
The Arithmetiquities is a fantasy adventure story told through a sequence of 36 mathematical puzzles.
“Though it is still before sunrise, Lumparland Harbor is already bustling. Sailing ships moor at the misty docks, bringing travelers and goods to the seaside town. Three dwarves disembark from different ships, each adventurer returning home from some faraway locale. The three women gather at the end of the pier.
“The strangers discover that they all live along the main road that leads from the harbor, so they decide to split the cost of a wagon. Egga lives 10 miles away, Floora lives 20 miles away, and Greeta lives 30 miles away. The wagon ride costs $1.50 per mile regardless of the number of passengers.
“How much should each of the adventurers pay so that each one has a fair fare?”
—Jason Ermer, “Lumparland Harbor,” The Arithmetiquities Chapter I
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Which I am going to say right now. Thank you!
“Playful Math: Getting Students To Write Their Own” copyright © 2022 by Denise Gaskins. Image at the top of the post copyright © Hannah Olinger via Unsplash.com.
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