Our family is lucky to live in a small city with great playgrounds. There are at least ten playgrounds in less than 20 square miles, which means that no matter where you live within the city, you’re likely within walking distance of one of them. They’re good playgrounds, too. Each is a little unique, most of them have been updated within the past few years, and all of them are surrounded by a good amount of open, grassy space for running around. As a parent of young children, this is one of the things I like best about where I live.

I wasn’t initially thinking about playgrounds when I first sat down to write this particular blog post. I went through several drafts before I got here. What I wanted to write about initially (and still do) was calculators, and how you should give your kid a calculator, earlier than you think you should give your kid a calculator, just to see what they do with it.

I got this idea from another parent, who had found that a calculator was the perfect toy to keep her kindergartener occupied during hour-long church services. So when my oldest was four, I went out and bought a cheap, solar-powered calculator and handed it to him just to see what he would do with it, and he loved it. A couple weeks ago at the start of the holiday break we were cleaning the house from top to bottom and came across the dusty calculator, languishing underneath a piece of furniture, and my now-7-year-old cried out, “My calculator! I love this!” and immediately jumped back into playing with it. 

Calculators sometimes get a bad rap, partly because most of us adults grew up in math classrooms where we were discouraged from using calculators except in carefully monitored situations. Then we all grew into a world where we basically have a calculator within arms reach 24 hours a day, 7 days a week, and it’s a tool we all use, but that we’ve nevertheless been conditioned to think of as sort of a cheat.

But to my child, the calculator is not a cheat or a shortcut, but a playground. No one has told him how it should or shouldn’t be used, and he can play with it and learn things about numbers and relationships that go well beyond his current numerical reasoning ability. He doesn’t play with it constantly, but each time he rediscovers it, his calculator play has changed a little to reflect his growing mathematical knowledge. His favorite calculator game when he was four was to enter in a randomish string of digits, like 827518271, and ask me to name the number. But now at age 7 he’s doing things like noticing that 8 ✕ 10 and 10 ✕ 8 give the same answer, wondering what other operations this works for, and stumbling across negative numbers when he tries it out on subtraction. A lot of this exploration is certainly stuff he might be able to do without a calculator, but the calculator removes the tedium of hand calculation and allows him to jump straight to the big questions.

I’ve been thinking a lot about playgrounds in my own classes of college students. Years ago when I was a beginning teacher, I would create “explorations” that were really just carefully guided activities where I had a series of pre-planned discoveries I intended my students to make. Unfortunately, I often found that my students could answer every question correctly without ever truly discovering the thing I’d been excited for them to discover. I found that my students were missing out on the wonder and delight of mathematics when I laboriously pre-arranged what they were going to wonder about and delight in.

I don’t think it’s wrong to have a sense of where you want students to end up, and while I’m constantly learning, I am nevertheless a much better lesson writer now than I was twenty years ago. But more and more I’ve been thinking about what it would mean to create and make room for true mathematical playgrounds in my instruction, spaces there’s the bare minimum structure and students can pursue the ideas that spark their curiosity. This is a hard vision for me to realize in practice. College students (most adults, really) often struggle with completely open exploration, and with knowing how to access the curiosity needed to explore. But kids come at this curiosity quite naturally, and don’t feel any compulsion to make their play look productive to an adult.

I wrote a guest post at Everywhere Math a little while ago where I talked about following your child’s agenda rather than your own, and the best mathematical playgrounds give the child agency to follow their own agenda. That’s what I’ve loved about handing my son a calculator.

What makes a tool or a toy or a book or an app or a game a playground? I don’t know that I have a full answer, but here are some questions I thought of:

• Is there more than one way to use it? 
• Do kids have a say in how to use it?
• Can you create your own rules?
• When adults join in, are they playing with the child (as opposed to directing the child’s play)? 
• Is it possible to imagine uses for which it was never intended?

If the answer to these questions is yes, then it might be a playground, and the very last step is to put it into a child’s hand and see what they do with it.