HOW DO YOU KNOW?
This week's contribution is from Christopher Danielson, whose work is worth diving into. Christopher has taught middle school and community college—everything from introductory fraction ideas through Calculus 2. He spent much of the last school year playing math with kindergartners. Presently on leave from Normandale Community College in Minnesota, he is a member of the teaching faculty at Desmos. He is the author of two books--Common Core Math for Parents For Dummies, and Which One Doesn't Belong? A Shapes Book. He developed and directs Math On-A-Stick, an annual large-scale family math event at the Minnesota State Fair. You can find more of his writing at his websites: Talking Math with Your Kids, and Overthinking My Teaching.
I write a blog called Talking Math with Your Kids where I help parents support their children's math learning. For reading, we know to read out loud with our children every day. What can we do for math? Exploring answers to that question—through examples and research—is the goal of the blog.
In that work, one of my favorite moves is to ask How do you know? I make how do you know? a regular part of conversations that involve numbers, shapes, and patterns. You can too, and both you and the children you're talking with will learn things as a result.
Here are some examples from the blog:
My nine-year old son and I were talking about baking cookies. If we needed 3/4 cup of sugar, but only had a 1/2 cup measure, how could we get what we needed? He said, You fill the measure and dump it into the bowl, then you fill the cup halfway and put that in.
That's a correct answer. I asked, How do you know? and got a really lovely response. He said that he visualized it as a square. Shade half the square in, then shade half of the unshaded part, and that looks exactly like a 3/4 shaded square.
My seven-year-old daughter was eating pistachios. She said that she threw out eight shells, and that this meant she had eaten four pistachios. I asked how do you know? and that opened a conversation about even and odd numbers that continued over the course of several days.
A parent once reported this story to me: [My daughter] A. was making a giraffe and wanted each leg to be two wooden spools long. At first she wasn’t sure how many total she’d need, but when I asked how many a giraffe has, she quickly figured out the total was 8.
Before reading the talk math with our kids stuff I would’ve probably just said yep, you got it- but we ended up having a great conversation about all the different ways you could figure that problem out.
Adding this simple question: How do you know? turns out to be a powerful way to deepen and extend your mathematical table talk. Try it out and share your stories through the blog, or on Twitter (I'm @Trianglemancsd).
Hopefully this week's Table Talk Math has your dinner table sharing ways in which math can serve a conversation.
If you have any questions, please feel free to contact us on Twitter (@TableTalkMath) or add a comment to the blog. Also, I would love to hear what you and the family came up with. Tweet, email me, or comment on the blog with the family's stories; I'll post some of my favorites.
Thank you for taking the time to improve math fluency for children, one table talk conversation at a time. For previous newsletters, check out the archive each week.
Header photo credit: Mads Bødker, Flickr CC BY 2.0