I’ve tried out a bunch of parenting podcasts, but the only one I listen to consistently is the Your Parenting Mojo podcast. I like the variety of topics and the focus on actual research, as well as the discussion of how parenting in other parts of the world differs. I find many of the episodes thought provoking, but so far most of them haven’t actually changed the way I parent. There’s one notable exception: Episode 31 on “Parenting beyond pink and blue.” It covers a lot of interesting ground, but the part that really hit home was the discussion of gender and math. In particular, I was quite shocked by this discussion of gender differences in “casual number use.” (The discussion is at minute 8:35 if you want to hear it for yourself.)
“We did this really cool study …. And it looked at how much parents of toddlers talked to their kids, using just like the kind of numbers you use when you have toddlers, like ‘Oh look, you have four apple slices left. Oh, there’s three blue cars in a row. Look, there’s five trees.’ That kind of thing. ‘Let’s count the stairs as we walk up them.’ That, just kind of everyday casual number use. What we found was that, parents of toddlers, parents of boys used numbers three times more than parents of daughters. So it’s like… In the world of psychology, that’s a huge difference. You know I mean three times the amount is a lot.”
Whoa. That’s crazy. American mothers talk about numbers three times as often with little boys than with little girls? I went and looked at the original study and most of the kids were around 2 years old, and the mothers were middle- or upper-middle class. The mothers of boys mentioned numbers twice as often as those of girls, and used “cardinal” numbers almost three times as often.
The full text of the study is available here Chang, A., Sandhofer, C., & Brown, C. S. (2011). Gender biases in early number exposure to preschool-aged children. Journal of Language and Social Psychology, 30, 440-450.
After reading this study, I tried to start bringing more everyday math conversation into our daily life. When Chickpea was a toddler, we talked about how many feet she had, and how many fingers. We counted the wheels on the car, or the number of oranges that the very Hungry Caterpillar ate. We also read lots of counting books. (Her favorites were two very tactile books: Ten Little Ladybugs and the TouchThinkLearn Numbers book.)
Now that she’s a preschooler, we continue to incorporate lots of number talk. We count by twos or threes or fives when we go up the stairs (and we live in a fourth-floor walkup, so we get lots of practice). I recently learned that this sort of “skip counting” is a very helpful skill for learning multiplication. We also count the stairs in other ways—sometimes we go up the stairs backwards and count down instead of up. We also do a lot of basic math when discussing time, weather, and cooking, as well as when playing board games. (See below for more details.)
Maybe I would have engaged in all of this everyday math talk even without listening to the podcast episode, but I’ll never know. My guess is that I would have done it anyway, but maybe not to the same extent. Of course, in the back of my head I always worry that I’ll overdo it and totally turn Chickpea off math. I try to keep it fun and light and somewhat child led. So far (at least) she seems to enjoy it.
And I think it’s working. I’m not sure what’s “typical” for a four year old, but Chickpea seems quite comfortable with numbers and basic mathematical concepts. I guess it’s possible she’s learned most of it not from me but from her Montessori preschool, but somehow I doubt it. I get the feeling she spends most of her preschool time coloring and running around with her friends exchanging house shoes, trading necklaces, competing for who can wear the most layers of clothes, playing Mutter-Vater-Kind, making mud pies, and fighting off monsters and foxes.
Whatever the reason—whether it’s due to preschool, my efforts, or just her own personality and interests—Chickpea seems quite comfortable with numbers. She can count at least up to 60. (I know because I told her I would do something in one minute today, and she held me to it.) She can count by 10s up to 100. (Thanks to our stairs!) She can read and understand one and two digit numbers. And she can do some basic addition and subtraction. She knows if we are having two friends over for dinner that she needs to set the table with five plates. She knows that if it’s Wednesday then there are two more days until Friday.
I think the reason this whole topic struck such a chord with me is that math competency is something that’s been an issue in my own life. As a kid I always liked math and considered myself reasonably good at it, but then towards the end of high school I suddenly felt like I wasn’t keeping up. I struggled in my high school precalculus class, and then again my senior year in my number theory and advanced physics classes. In college I took the minimal number of math courses necessary to get my bachelor’s degree, but then when I started doing a PhD in computer science it turned out I didn’t have the math skills I needed to do the research I wanted to do. But rather than go back and gain those skills I just avoided it and tried to work around my deficiencies, which eventually (I believe) led me to give up on research.
I want Chickpea to have the math skills and confidence to do whatever it is that she wants to do in her career. I hope by bringing a lot of number talk into her toddler and preschool years, we’ll set the groundwork she’ll need—no matter what career she ultimately chooses.
Math activities at 4 year old
We still read lots of number and counting books. Her current favorite is Curious George Learns to Count from 1 to 100. But I just ordered Richard Scarry’s Counting Book, and Chickpea worships Richard Scarry, so I’m guessing it might soon overtake the Curious George book. I’m also planning to check out some of the books on this “Ultimate list of Counting Books.”
We do a lot of math practice related to time. We figure out what time it will be in Germany when Nana wakes up at 6am in Texas. We figure out how many hours until Daddy comes home, or how many minutes until the cookies are done baking.
She is still working on learning to read an analog clock, but she can read and understand a digital clock quite well. She knows that Daddy gets home at 5:20, and will look at my phone at 5:15 and say “Daddy will be home soon” or look at my phone at 5:25 and say “Daddy is running late.” She knows 5:50 is 10 minutes before 6:00. She chided Derek for getting her to daycare too late the other day. She told him she didn’t want to get there at 10:00 anymore, or “even close to 10:00, like at 9:59.” She knows that when our digital clock says 19:30 it’s seven thirty p.m. and I’m pretty sure she’s figured out that 20:00 is 8pm. Luckily she doesn’t yet know that 22:00 is ten o’clock, or she would chide me for going to bed too late. (She thinks my bedtime is 10pm, and would be disappointed to learn that I rarely get to bed on time.)
Chickpea is also very interested in the weather app on my phone, and that interest has also been great for developing her math skills. Chickpea loves to check the weather in Saarbrücken and compare it to Austin and New York (where her grandparents live), as well as places we’ve visited recently (Barcelona, Tel Aviv, …) or places Derek has travelled to recently. I had Montreal listed on my phone, and she very quickly picked up the idea of negative numbers. “Whoa,” she said a few weeks ago. “It’s so warm in Montreal. It’s gonna be -2! That’s warm for Montreal!”
The weather app is also good for understanding relative size. I am pretty sure Chickpea understands that 6 is more than 5, since she likes to compare weather reports in different cities and find the warmest or the coldest city each day. She’s always excited if an unusual city is on the top or the bottom. It’s usually Anchorage or Montreal that’s the coldest, but one day New York (at -17!) was even colder, and she was impressed. She’s also excited when Saarbrücken is warmer than Austin. Or when two cities that have different climates are the same temperature: “Saarbrücken and Tel Aviv are both going to have a high of 17 today. Isn’t that cool Mom?”
Weather also led Chickpea to practice some basic addition. We were struggling with Chickpea not wanting to wear appropriate clothing this winter. It seemed like part of the problem was that she just didn’t want to be told what to wear, so after discussing it I made her a chart that shows appropriate clothing for each temperature. That way she could look at it and decide herself what to wear. But we quickly realized that the temperature is not the only factor. If it’s 8 degrees and very sunny then that’s quite different than 8 degrees, overcast, and windy. So now Chickpea knows to add about 3 degrees if it’s a sunny day, and then check the chart with the modified temperature.
Another way we build math skills in a fun way is through board games and card games. Chickpea has recently really gotten into board games, and I try to bring math into those games frequently. I’ll write a separate blog post about that when I get a chance. (Update: It’s finally up! Preschooler Games That Encourage Math Skills)
Cooking is also great for building math skills, especially addition and subtraction. We need 5 eggs and we’ve put in 2, so how many more do we need? We’ve also just started doing some basic division, e.g., figuring out how many cookies everyone will get if we split 6 cookies evenly between the three of us. Another not-quite-math game we like to play is guessing how many of one cup it will take to fill another cup. Does a short fat cup hold more or less water than a narrow tall cup? How much more? Will it take one or two of the purple cup to fill the green cup?
Recently we’ve even been using cooking to explore fractions. Chickpea got interested in fractions when I told her it was going to be her quarter birthday soon. (She loves birthdays!) But she didn’t really understand what quarter meant, so we started exploring the concept with measuring cups. We use a 1/4 cup measure to measure out flour, because it’s small and fits in our flour jar. But we actually need 1 cup of flour, so we have to figure out how many 1/4 cups it will take. We also talk about fractions with time (“It’s a quarter past five.” “It’s a quarter to two.”) So far Chickpea doesn’t really seem to have a sense for fractions, but I think if we keep talking about them she’ll understand them eventually.
Other household activities like setting the table or emptying the dishwasher are also good for building math skills. Last year sometime (maybe in the summer?) Chickpea was distributing little post-it notes between the two of us. She was frustrated that she couldn’t give each of us the same number. There was always one left over. So we talked about odd and even numbers. Then the next week when Chickpea was emptying the dishwasher she pointed out that there was an even number of plates but an odd number of bowls. Huh? How did she know? She showed me that she always emptied them two at a time, with one dish in each hand. And for the plates she could empty them all, but when she emptied the bowls there was one left over. Wow. I was amazed that she got that from one brief discussion of post-it note fairness!
I haven’t tried this yet, but on one of Jen’s podcast on All Joy and No Fun she talked about incorporating math into grocery shopping by weighing produce and guessing how many more apples you need to make a kilo, or what weighs more, the eggplant or the leek. I could imagine also discussing prices and figuring out which brand of almonds costs more, and eventually comparing prices of different package sizes.
Update Apr 10, 2019:
Jen Lumanlan has a free infographic titled “11 Ways to Support Your Child in Learning Mathematics,” which offers lots of other ways to introduce math skills to a preschooler. Just enter your name and email address about a third of the way down this page. (I assume you’ll get added to her mailing list, but that’s a good thing! She doesn’t send a lot of emails and they are generally very interesting.)
After looking at the infographic, I want to try working with Chickpea on subitization, the ability to quantify small numbers without counting. I know Chickpea can distinguish a die with 1 or 2 from 3 dots, but I haven’t yet noticed if she can tell whether a die has 5 or 6 dots showing. The board game Outfoxed has three dice, and now she adds up the dots on the dice just by looking at them. At first she had to count them up, but now she knows for example that 2 plus 2 plus 1 is 5. But I’m not sure that’s the same as recognizing one die with five dots. We’ve played dominoes before, but our dominoes have different kinds of trucks on them. I’m going to try to borrow her best friend’s triominoes set (like dominoes but triangular, so with 3 sides not just 2.) Or maybe we’ll try making patterns with nuts or raisins and seeing if she can tell how many there are without counting.
Chickpea woke up last night at 10:30pm with a hacking cough. She asked me for some mint tea, and she was still awake at 11pm. The clocked turned to 23:00. She immediately noticed it and announced gleefully “It’s 11:01 Mama, it’s past your bedtime!” (She knows that the clock runs slow, and added the minute for additional accuracy.) So I guess I was wrong above, and she has figured out that 22:00 is the same as 10pm.