I love it when a plan — or rather, a series of math thoughts — comes together.
On Monday, Emily Grosvenor (author of the Tessalation! picture book) asked me how parents who are insecure in math could help their children learn through play, and I responded with this quote from my Let’s Play Math book:
If you are intimidated by numbers, you can look for patterns of shape and color. Pay attention to how they grow. Talk about what your children notice.
But I wasn’t entirely satisfied with that answer. So many adults have come away from their own school experience thinking math is only numbers. Even with shapes, isn’t it the numbers about them — how many sides, what size of angles, calculate the the area or perimeter — that are important? That’s what school math tends to focus on.
Those of us who are comfortable with math know that there are many more things to notice and think about than just numbers. We know that it’s this noticing, thinking, and wondering that is at the heart of math. And that just playing with shapes can build a powerful foundation for future math learning.
The ability to create, and maintain, and manipulate shapes mentally — that’s the goal. Just like kids who can put numbers together in their heads, kids who can rotate, flip, and think of how shapes fit together in their heads have a powerful tool to analyze not only simple shape puzzles, but dividing up an area that’s a more complex room shape … to look at a piece of artwork … or look at a building … For these kids, all the world around becomes a playground to use mathematical ideas.
Of course, pattern blocks are good for much more than just filling in worksheet pictures. But I love this peek into how a child’s understanding grows, in bits and spurts — without any numbers at all — until the world itself becomes a playground for mathematical ideas.
You know what? Children like mathematics. Children see the world mathematically … When we do a puzzle, when we count things, when we see who’s got more, or who’s taller … Play and mathematics are not on opposite sides of the stage.
Tova Brown concludes her exploration of the Hilbert’s Hotel Paradox with a look at the cardinality of the real numbers.
You run a hotel with an infinite number of rooms. You pride yourself on accommodating everyone, even guests arriving in infinitely large groups — but some infinities are more infinite than others, as it turns out.
Welcome to the 92nd edition of the Math Teachers At Play math education blog carnival—a monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.
Let the mathematical fun begin!
By tradition, we start the carnival with a couple of puzzles in honor of our 92nd edition…
What is the maximum number of queens that can be placed on an chessboard such that no two attack one another?
Spoiler: Don’t peek! But the answer is here—and the cool thing is that there are 92 different ways to do it.
Table Of Contents
And now, on to the main attraction: the blog posts. Many articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.
Joshua Greene (@JoshuaGreene19) offers some great ways to tweak an already-wonderful multiplication game in Times square variations. “It was really interesting to see the different strategies that the students took to determining what would go on their boards.”
Tina Cardone (@crstn85) experiments with Bar Models in Algebra to help her students think about linear equations. “I did not require students to draw a model, but I refused to discuss an incorrect equation with them until they had a model. Kids would tell me ‘I don’t know how to do fractions or percents’ but when I told them to draw a bar, and then draw 4/5, they could do that without assistance…”
How can we get a peek at how our children are thinking? Kristin Gray (@mathminds) starts with a typical set of 1st Grade Story Problems and tweaks them into a lively Notice/Wonder Lesson. “When I told them they would get to choose how many students were at each stop, they were so excited! I gave them a paper with the sentence at the top, let them choose a partner and sent them on their way…”
Tracy Zager (@tracyzager) talks about her own mathematical journey in The Steep Part of the Learning Curve: “The more math I learn, the better math teacher I am. I keep growing as a learner; I know more about where my kids are headed; and I understand more about what building is going on top of the foundation we construct in elementary school.”
And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.
The December 2015 installment of our carnival will open sometime during the week of December 21-25 at Math Misery? blog. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.
We need more volunteers. Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself)—if you would like to take a turn hosting the Math Teachers at Play blog carnival, please speak up!