The Rookery

Some recent conversations with students have gotten me thinking.  One shared that a video they'd watched in spanish was 2 1/2 minutes long.  "So I started doing the math and figured out that 8.3% of our class was the video…I think," she said.  Another shared that he'd been bored on a car drive the past weekend and had been trying to figure out how many ounces were in a gallon.  I shared with the students that I often pass time when I'm at stop lights behind people with 26.2 or 13.1 stickers (the lengths marathons and half marathons, respectively).  What's a quarter marathon?  6.55.  An eight?  3.275.  What if I just wanted to walk 10 steps?  (That's usually about the time the light turns green.) 

When I brought these situations up in class, other students chimed in with times they'd passed time with math:

"I gave letters their number value and added up license plates on a trip."  "I tried to figure out how many pours of the soy sauce bottle it would take to empty it." "I was waiting for my mom to come out of a store and tried to figure out how much money all of the cars in the parking lot cost."  "I count by 3s to see how high I can get."  "I kept track of how many men vs. women I saw at the airport." "I counted by 5s for the whole flight to Baltimore."  "I see if I can finish my water before the waiter comes again…and then try to figure out how much time I have to drink the new glass." "I figured out how many lures I'd lose in three hours."  "I figured out the average age at our family gathering."  "I swiped my finger on frost on the window and tried to figure out how many swipes it would take to clear the window."  "I figured out the speed of the car based on trees we were passing." "I counted the panes of glass at church and multiplied it by the number of ceiling panels."  "I used the mileage signs and our speed to figure out how long it would take us to get there."  "I counted people in cars and figured out the average."  "I'm figuring out how long this conversation will be if everyone shares something." 

I realized that an important step in math development was staring me in the face — when children learn how to read there is a tipping point of sorts where they start to read all of the text around them.  Suddenly signs and cereal boxes and magazines lying on the table come into focus and the child registers that there are words there and he or she tries to read those words.  One can no longer give the child a menu and skip the undesirable items.  The amount of decoding the child is doing increases tremendously (and there is almost always a big leap in reading level and confidence because of all of that extra practice.)  The words that surround us are called "environmental print."

So what is the equivalent in numeracy?  Whatever it is, these kids had made that leap (and then some.)  They were playing with number constantly and getting so much practice with math concepts.  "Math class" is five or so hours a week.  A lot of these kids might be thinking about math three or four times that much — it's no wonder some kids seem to "get math" more easily.  They're working at it a lot more and that work is mostly invisible.

I didn't even recognize the point in time when my own children started to notice number around them.  It could be that it happened multiple times for different kinds of math.  Early reading development follows a somewhat linear trajectory (that's a simplification but not untrue) and the moment when environmental print appears to a child is just that, a moment.  Number, on the other hand, has a lot of different forms – noticing a clock, counting objects, comparing quantities, seeing shapes.  Just today, my daughter Hazel was looking at a floor grate and noting how many squares she could see in the design.  It's my guess that the "environmental number" stage of numeracy happens repeatedly for different kinds of ideas.

And of course, what my students reported (finding the percentage of class time spent on a video, for instance) is not analogous to that first recognition of environmental print.  It's more like finding anagrams in the words you see around you, trying to make new words out the letters of another word.  They have continued to build on those initial moments of number awareness.  All of the examples my students shared with me were playful; they were challenging themselves to solve puzzles they were creating.

So if environmental number is a numeracy developmental stage, how could we encourage it?  For environmental print, primary teachers label everything with its name.  What is the equivalent in our classroom and homes?  Class data posters?  Clocks?  Charts with fractions? Number lines? Those are all visual prompts.  Could we be modeling number awareness?  We make a point of talking to young children and asking them questions to encourage language development.  What conversations can we start about number?  Comparing bedtimes…timing table setting…cooking with fractions…labeling shapes…

And what about the next step — playing with the numbers you come across?  I suspect that, like literacy and fitness, we need to model it for our kids.  Asking ourselves questions from the mundane:  How many steps is it across the room? How long does it take to clean out the dishwasher?  To the ridiculous:  How many kids end to end would it take to get downtown?  How many scoops of ice cream would fill the fountain? At first you may be pondering the mathematical universe by yourself…but with time, that world of number play will open up for your child as well.

What do you think?  Is this a stage of development you've noticed in your child?  Do you play with number this way?  What are some ways you encourage numeracy in your home?