Doing Math with Kids

If You Give a Kid a Calculator, Part II

/ Amy / 2 Comments

I have a confession: I gave my oldest a calculator when he was four. But I did not give my second child a calculator when she was four. In fact, she is now almost 6 and it was only when her older brother found the calculator the other day that it occurred to me that I should give her a chance to play with it, too.

This is partly a first child/second child matter. I didn’t think to get her a calculator because I had already thought to give a child of mine a calculator, and my brain had checked the “done” box on that one.

But it’s also because my oldest has always shown a very obvious interest in numbers and patterns and is therefore very easy to give a calculator to, or a math problem, or a math game. My youngest is…not. At least, not always. My son has already been identified by his teachers as a “math person”, but my daughter is very different from her older brother and I worry that she will be identified just as early as someone who is not a math person. I am especially aware of this because I see how easy it is for me, a parent who believes deep within my soul that every child is a math person, to nevertheless give different math opportunities to my older child (who is practically begging me to do math with him) than to my younger child (who would rather just do her own thing, thank you very much).

“Do you want to play a math game with me?” I ask my older child, and he says, “Yes!” and drops whatever he is doing, and we play the math game.

“Do you want to do play a math game with me?” I ask my younger child, and she doesn’t even look up, but just smiles knowingly into the pages of her sticker book, confident that I cannot make her play anything she does not want to play, and we don’t play the math game.

The problem is that if a child is particularly interested in or receptive to mathematics activities early on, they will likely get more opportunities to do math, to do more interesting and open-ended math, and to experience more positive feelings around mathematics. If a child tends to show less interest in math over other activities at an early age, or takes longer to learn some of the skills we think of as foundational, that child will probably be given fewer opportunities, more basic skills practice, and a less interesting mathematics experience overall. 

I can’t (and shouldn’t) force my daughter to do math with me. But I’ve also learned that with the right approach she’s really receptive to doing math and talking about math and exploring what it means to do math. She actually loves to play math games when she’s in the mood (Tiny Polka Dot is our current favorite), and she solves problems in interesting ways. Doing math with her just looks different than doing math with my son, and it requires me to be more a little more conscious about looking for opportunities and helping her build a positive view of mathematics and her own ability to do math. 

So here’s my advice (and it’s advice for myself, too):

Give your kid a calculator. Give one to the kid you know will love playing with it, and give one to the kid you’re not so sure will love it. You may be surprised to see what they do.

Show interest in how your child thinks about math. Show as much interest in the child who is using the commutative property to solve a complex multiplication problem, as you do in the child who is counting on their fingers, because all children’s thinking is interesting when you really stop and listen.

Find math activities that encourage creativity and multiple approaches. These types of activities allow any kid to shine by sharing their unique ideas. Right now my son is enjoying the game Proof!, which gives us a chance to combine numbers in interesting ways. My daughter loves the activity “Foot Parade” (we’ve also created our own version called “Alien Parade” where there’s no limit on the number of feet you can create). And both my kids love the book How Many? by Christopher Danielson, which is an open-ended and interactive counting book that we never get tired of looking at.

My own children may or may not decide that math is their thing, but as a parent I hope to give them the gift of knowing that it can be if they want it to, and to share ideas with other grownups who want to do the same thing for the children in their lives.

Sharing Brownies

/ Amy / 2 Comments

The other night at dinner as we all debriefed our days, I mentioned that I’d given my college students a problem about sharing brownies. “I should give the problem to you and see how you would solve it,” I mused to my kids, and my husband immediately said, “Let’s make brownies and solve the problem in real life!”

So we did. We threw together a pan of brownies from a mix we had sitting in our cupboard, and when they had cooled I cut and plated three square brownies for each kid. Then I handed them each a plate and a dinner knife and told them to figure out how to give every member of our 4-person family the same amount of brownie.

We like to ask sharing problems about food (“If there are 8 pancakes, how many can everyone have?”), because our kids, like all kids, are highly motivated by food and by fairness. But this is a challenging problem, without a clear, immediate solution.

Still, my kindergartener dove right in, deftly cutting all three brownies in half. She then paused for a moment with the two extra pieces before cutting them in half too and stacking a quarter brownie on top of each half-brownie portion. “Everyone gets a half and a piece,” she said when I asked her about her solution.

(Surprisingly, very few of my college-age students come up with this particular method initially, although once they have seen it they tend to prefer it. This semester one student commented on how surprised he was that a kindergartener would come up with this method right away when he, a math education major, didn’t think of it on his own.)

My 7-year-old stared and stared and stared at the brownies and I could see the gears turning in his head. Finally, several minutes after my daughter had confidently offered up her half and a piece, he said, “Okay, I think this will work,” and embarked upon a complicated cutting exercise that I would call “split the brownies into smaller and smaller pieces and hope it will all work out eventually.” First he cut one brownie into thirds, cut another brownie into fourths, cut a fourth in half, and put the half-quarter together with a full quarter to make another “third”. He then cut the last brownie into fourths, and proceeded to cut and re-cut any odd pieces out until he felt confident that he had a workable number of pieces.

He explained that everyone got a third and a quarter and a half quarter and a “small quarter” (half of half of a quarter). But when he actually distributed the pieces onto each of our plates, there were a few extra bits left behind. “Hmm, I don’t know if that really worked,” he said, and then shrugged and popped the extra pieces into his own mouth.

It was obviously interesting and fun to watch how my kids approached this problem on the very same day I watched my college students approach the same problem. But it was also interesting to listen to the informal language they used to talk about their solutions. They both already had some language for talking about fractions, and they both ran up against limits. The kindergartener could talk about halves, but once she got to quarters they became “pieces”. Nevertheless, with the motivation of actually getting to eat the brownies at the end, she was remarkably accurate at splitting the brownies into equal parts. The second grader could talk about halves and thirds and quarters, but then began talking about half-quarters and “smaller quarters” when he got down to eighths and sixteenths. And he made an interesting approximation of 1/3 by combining 1/8 and 1/4. This was not precisely equal to 1/3, but it was certainly close enough to feel fair.

My college students like to ask me questions like: “When would you start teaching this to students?” My answer is often: “Much earlier than you’d think!” When can kids start understanding fractions? Much earlier than you’d think! When can kids begin making sense of probability? Much earlier than you’d think! When can you give kids multiplication problems? Much earlier than you’d think! When can kids understand that a square is a type of rectangle? Much earlier than you’d think!

This particular problem involves both division and fractions, and while I had no idea what my 5- and 7-year-old children would do with it, I knew they would be able to do something. Kids have great ideas, and they have great ideas much earlier than you’d think!

Finger Counting

/ Amy / 1 Comment

How do you count on your fingers?

Here’s how I do it:

I think it’s a pretty normal way to count on fingers, and when I asked a group of adults to count on their fingers, most of them did either this, or started with their thumb.

But then I asked my 6-year-old how he counts on his fingers and this is what he showed me:

I had to have him do it for me a few times because it was so strange! It starts off normal enough, but then when he moves from two to three, instead of just holding up the next finger, he puts down his first finger and holds up a completely different set of fingers!

I have lots and lots of thoughts about this, but for now I’ll just leave this here as an example of the weird and wonderful things that happen when you ask kids to show you how they think.

Scavenge for Quantity

/ Amy / Leave a comment

The beginning of the college semester has kept me extra busy for a couple weeks, but I’m back. And I have a game this time that can be adapted for a very wide variety of ages – a scavenger hunt!

One way to help your child to internalize mathematical thinking is to open their eyes to the quantities around them. As parents, we help provide our children ways to see the world from an early age. We name objects, identify colors, describe what we’re doing. A child doesn’t necessarily see the color blue on their own – they see blue because adults point blue out to them (listen to this totally fascinating Radiolab podcast about the color blue). We point out big and little, noisy and quiet, dark and bright – we help show them which characteristics are worth noticing.

Quantity is also a characteristic. So many things in our world come in quantities, but since kids don’t tune in naturally to the characteristic “how many,” adults can help by pointing it out. I’m not talking about learning to count – I’m talking about learning to see quantity as an attribute, something we can recognize, describe, and use to characterize parts of our world, just like color. Just as Monkey’s t-shirt and the playground equipment in the picture below, although entirely different in other ways, share the attribute “gray,” the flower petals and the dots on the dice below the photograph share the attribute “five.”

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flower dice

A scavenger hunt for quantities can help your child become accustomed to seeing quantity as an attribute. There are all sorts of ways to do a quantity scavenger hunt. Here are three:

  1. Open Scavenge: Pick a room in the house and work together to find as many quantities as possible. You might choose the kitchen and find that there are two salt/pepper shakers, six chairs around the table, four drawers beneath the counter, three slats on the back of the chair, two towels on the front of the oven, and so on and so on. This can be played one-on-one with a single child or cooperatively with two or more children. Some children may enjoy labeling quantities with sticky notes or a label maker.
  2. Number Challenge: Give your child (or children) a paper labeled with the numbers 1-12, or a set of sticky notes labeled 1-12. Then roam throughout the house and try to find a quantity for every number. With multiple players, everyone can have their own set, the rule being that no two people can choose the same set of objects for their number. Because some numbers will be much harder than others (how many things come in sets of 11?*), you may wish to eliminate hard numbers, set a time limit, or simply play for fun with the expectation that you might not find everything.
  3. Quantity Match: Can be played with a parent and child, or with two children. Have one player find a quantity (four shelves, for example). The other player then has to find something different, but with the same quantity (four pillows on the couch!). Then switch places. Repeating quantities is okay (and even repeating sets of objects for very young children).

Again, this is really easy to adapt, and it’s easy to involve multiple members of the family – including younger and older children. Have fun with it!

scavenge

And as a side note, it’s never to early to start helping your child notice quantity. With very young children, you can point out any quantity but especially two – there are all sorts of twos in a baby or toddler’s life! Two ears, two hands, two feet… This morning as I was changing 16-month-old Monkey out of his pajamas, I counted “one…” as I pulled one foot out of the footie, and as I reached for his second foot he responded with, “dooh!” A few more repetitions convinced me that it wasn’t just coincidence – he’s picked up on the “one…two!” count he’s been hearing from me, and I wasn’t even really thinking about it. Way to make your math mama proud, Monkey!

 

* Look! 11 slats on the shoe rack!

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Reading Share: 5 Ways To Help Your Kid Not Stink At Math (NY Times)

/ Amy / Leave a comment

Recently the New York Times magazine published an article on the recent history of math education in the U.S., written by Elizabeth Green. It’s a fantastic read for anyone who is at all invested in the education of children (which, of course, includes all parents!). I highly recommend it, and I’m looking forward to reading her new book, Building a Better Teacher.

But the article, while very readable, is also quite long. As a parent, and a parent who loves to read, I still may not have made it through if it wasn’t exactly up my alley. So if you’re looking for something shorter and directly relevant to how you interact with your kids around math, I’d like to point you to Elizabeth Green’s accompanying blog post on the New York Times parenting blog, Motherlode: 5 Ways To Help Your Kid Not Stink At Math. It contains excellent advice, and it’s solid – these are things that really work, no matter what math curriculum your child might be using.

While all 5 of her main points are good, my favorite is the first:

1. Listen to What’s Going Wrong

Teaching children math requires first figuring out what they don’t understand. Instead of getting to the heart of a misunderstanding, we are far more likely to tell children something like, “No, that’s not right, try it this way instead.” The better response to a wrong answer begins with asking the child to explain her thinking.

You’ll hear this from me over and over again, but the very best thing you can do to help your child, whether you’re encouraging a preschooler’s interest in numbers, or helping a high schooler with their math homework, is to make an effort to find out what they’re thinking.

Click over and take a look. And if you have other resources (books, articles – anything!) that have helped you as a parent to help your child with math, please share!

That’s Math!

/ Amy / Leave a comment

The word “math” has a lot of baggage behind it. I find this unfortunate, but I also totally get it. A lot of people have experienced math that was hard, or boring, or didn’t make much sense. A lot of people watched as other students seemed to “get it” effortlessly, while they struggled along. Some people didn’t have great teachers; some people had great teachers and wondered why they still couldn’t understand.

And while there are still plenty of people who love math, or at least don’t dislike it, there are so, so many people for whom the word “math” rings lots of scary bells. But my experience is that when those people are parents, they really, truly want their children to feel differently.

One possible solution is for a parent to think, “I didn’t like math, and so I’ll sneak math in without telling them. That way they won’t be scared off by knowing that they’re doing math.” I think of this as the “hidden vegetables” approach to doing mathematics, akin to adding squash to macaroni and cheese or sneaking zucchini into a chocolate cake. It might get kids to eat their squash and zucchini, but it won’t help them learn to love it. (But seriously, give these recipes a try. Yum!)

So I recommend a completely different approach. Instead of hiding math, showcase it! Let kids know they’re doing math! I don’t mean you should surround every math experience with bells and whistles and confetti, because some kids are going to get suspicious. A lot of young children will find natural pleasure in learning about numbers, identifying shapes, measuring, counting, adding— just as they naturally want to learn language. Build on that natural interest and tell them exactly what they’re doing—they’re doing math! Say, “Do you know what we just did? We did math!” Or even just, “That’s math!” Labeling mathematics for what it is while they are having positive experiences with it will help children develop an early positive association with the word math.

I like this blog to be positive, to tell you what you can or should do rather than what you shouldn’t do. But there is one thing that I warn parents against without hesitation, and that is putting your own fear or dislike of mathematics on display for your children.

Don’t tell your kids, “I’m bad at math,” even if you think you are. Don’t tell your kids, “Math isn’t much fun, but you’ve got to do it,” even though math sometimes does require hard work. That’s true of everything, but somehow the “not fun” label and the “hard” label snap on to mathematics like magnets.

Rather than telling your kids that you aren’t good at mathematics, show them that you are willing to learn this stuff right along with them. Empower your children with a belief that mathematics (like everything) is not a natural ability, but something that they can access through persistence and effort. I believe that hearing that message, early and often, will do far more for your child than any mathematics instruction you give them.