When my kid was born, I went on a shopping spree for toys that are both engaging and educational. I spent hours combing through Amazon, looking for 5-star-rated, BPA-free, lead-free toys—the stacking blocks with numbers on the sides, the beads on rods, the hand-made wooden toys, the little "LeapTop" that spoke the letters when you pressed the buttons on the keyboard, another toddler tool for teaching him to write. My house was a veritable LeapFrog shrine.
I admit it: a part of me hoped my child would learn the alphabet, numbers, reading, counting, higher-order thinking skills, and classical music through osmosis while playing with his curated collection of books and toys.
Of course, that was sleep-deprived, wishful thinking. And I knew better. Sure, my kid played with the toys. And kids do learn many things through play. But in retrospect, I’m pretty sure he didn’t absorb many math or language skills simply by having these educational toys around.
Over the years, Math Education has also wrestled with how much or how little freedom students should be given to “discover” mathematical concepts. Ever since Jean Piaget sensitized us to the idea that we learn by constructing our own knowledge through experience, we've tried to come up with with how best to infuse creativity and deep understanding into math instruction. I’ll spare you all the gory details of how we arrived at where we stand on this today, but here is what we now know: when kids are left to themselves to discover things entirely on their own, it is not as effective as presenting them with new ideas to consider.
A great way to suggest new ideas is by using a think aloud. A think aloud is a technique used by teachers to show students how to think through a problem. The teacher describes what she is doing and why she is doing it--including all the messy thoughts that come about when actually thinking. This is a technique used to teach reading strategies; in math, it is employed by students so that we know how they are solving problems and is a precursor to writing what they were thinking. This is why I like this technique so much--by doing a think aloud, I am simultaneously showing how I think about a problem, AND how I explain my thinking.
I find that using this technique as a parent is much more effective than when I do it as a teacher. As a teacher, you have to start it off by saying, “I’m going to tell you what I’m thinking, and I want you to notice what I am thinking and doing. I'll ask you to describe it afterwards.” This is because the whole rest of the time, students aren’t really listening that carefully. But at home, children are always learning behaviors through imitating parents.
This is how a think-aloud could go, as a parent:
- Notice. You notice a strategy or behavior that you wish your child were using.
- Slow it down and model. The next time you are faced with that same situation yourself, slow down your actions in front of your child.
- Think aloud. While performing that action, speak your thoughts aloud, describing the problem, what you’re doing about it, and why.
This technique can be used to model all sorts of things, both mathematical and behavioral. Here are some examples.
When your kid loses track of counting.
Let’s say that your child is just learning how to count. While he says the numbers in order and points to the objects one at a time, he loses track: he skips over objects or re-counts them. You want him to notice that he has to pay attention.
You might be tempted at that point to correct him. But don’t. That will most likely confuse him--or worse--make him anxious about making mistakes. Instead, model. The next time you have to count, recreate the problem, slow it down, and think aloud. It might sound like this, as you point to each object that you count: "One, two, three, four, five… Oh wait, I think I skipped one. Let me try again. One, two, three…." When you count again, slow down even more to show that you are paying more attention.
When helping with homework.
One characteristic of good problem-solvers is that they can solve problems in a variety of ways. The more ways they can think about numbers, the more likely they’ll be able to solve problems. You can do a lot to help your child develop this practice.
Let’s say your child is trying to figure out that 4x6 is 24. While you might believe that it would be better for your child to have memorized this basic fact, it may take a while before your child has seen 4x6 enough times for her to recall it. In the meantime, you might model a different way to solve it:
“Hm, well, if I don’t know what it is, what I do know is that this means 4 groups of 6. I know that 2 groups of 6 is 12, and I know that 12 plus 12 is 24.”
Later, you might use the same think aloud technique to plant the idea that knowing facts by rote is useful: "Wow, I keep seeing 6x4 over and over again. Maybe I can try to remember that 6 times 4 is 24." (As a bonus, throw in, "Can you help me remember that?") In my experience, this type of suggestion is especially effective when I make it repeatedly long before my child is asked to do it in school.
When your child is frustrated.
Along with knowing multiple ways of doing problems, good problem-solvers need to be able to solve problems without giving up. These two characteristics naturally feed each other, so it is important to model strategies for staying engaged with the problem.
Even though my child is good at math, he has a tendency of becoming frustrated if something doesn't come easily--especially if it is preventing him from playing with electronics. When this becomes problematic, I make it a point to model problem-solving strategies, such as ensuring that I understand what the question is asking. I might say, "Wow, I can see why this might be challenging! I'm going to re-read this to make sure I understand what is happening."
When playing with toys or games.
Having educational toys and games around is great, but children often need a little suggestion here and there to realize the potential of what they can do with their toys. Regardless of how much or how little your child spontaneously notices letters on blocks, or know what to do with the awesome electronics kit that you would love to play with yourself, you can help your child by modeling strategies.
Don’t me wrong—I’m not saying to replace free play with structured lessons. I’m saying that you can sneak lessons into your child’s play. Here are some toy/game-specific tips for kids ages 0-3, for kids ages 3-6, and kids ages 7-9 to help develop math skills.