As a high school math teacher, I never really thought very much about how numeracy and number sense develops in young children. Like many secondary teachers, I lamented the fact that many of my students struggled with basic fact fluency and had an irrational fear of fractions, but I never thought much about why they did, or what I could do about it. Though I think I was well prepared for the classroom by an excellent pre-service program, this was not part of my teacher preparation program either. We talked a lot about how to teach math, but not as much about how students learn it.
When I became a parent, I started thinking about it a little more, but not from an educator’s point-of-view. I’ve always “talked math” with my kids, but since becoming the K-12 math coordinator for our school district, and coming across Christopher Danielson’s (@trianglemancsd) blog Talking Math with Your Kids, I’m much more intentional about the questions I ask them to try to probe their thinking. I’ve also read a lot about Number Talks and the importance of helping kids developing mental math strategies and deconstructing numbers so I try to focus on those things when we’re talking math.
Despite having a house full of Girl Scout cookies, my husband has been asking me to bake chocolate chip cookies for the last few weeks. Tonight I finally caved. As I was beginning to scoop the dough out on to the cookie sheets my 8 year old son came out into the kitchen. I had scooped 5 cookies on to the tray – 3 in the first row and 2 in the next. Ian asked right away, “Are you going to put three in the next row?” Yep. “And then two in the last row?” Yep.
Before I slid the tray in the oven, I asked him “How many cookies are on the tray?” “10” he quickly replied.
“How do you know that?” “Three plus three is six, and two plus two is four, and six plus four is ten.” Hmm….my brain immediately puts the three and two together to make 5 and then adds the 5s together.
We didn’t stop there. “The recipe days it makes 5 dozen cookies. How many is that?” Ian confirmed “So that’s 5 12’s?” Yes. “36?” “No…” He started to think out loud “24 plus… No, wait. 60”
“Ok, I made a double batch, so how many is that?” “120”
“And if there’s 10 on a tray, how many trays of cookies will that be?” “12”
“I have three cookie sheets, so how many times will I have to put each tray in the oven?” “12 divided by 3 is 4 – four times”
I was pretty impressed. Granted, Ian has been identified as intellectually gifted, and takes after his mother in the math department, but for a second-grader, this is pretty sophisticated thinking. The rest of the kids were really excited when they heard I was making 120 cookies.
Two questions that I didn’t ask but should have:
If each tray takes 11 minutes to bake, how long will it take me to bake all the cookies? Ugh..way too long!
There are 7 people in our family, and I’d really like the cookies to last until the weekend. How many cookies can each person eat per day? Maybe I’ll ask that question tomorrow when half of them are gone.
In retrospect, I could have asked a lot more “how do you know that” questions, but I’m cautious about doing that too much
so that I don’t turn them off or frustrate them.
I love talking math with my kids.