Raising mathematicians

I read a recent article about the importance of early number talk with children and was pleased that this issue was being brought up. The article shares research on a few of the stark differences in how parents talk with their children about numbers. For example, parents tend to talk to their daughters about half as much about numbers as their sons. Parents also range in how much they use number words around their children from about a dozen times a week, to as much as 1800 times per week.

However, I felt that the list of suggestions the article had at the bottom was incomplete. The article’s author essentially makes suggestions which I feel will only help children develop an instrumental understanding of mathematics, as opposed to a more useful, interesting, relational understanding.

Here are some more things my wife and I do with our children from a very young age to help them develop a deeper understanding of numbers.

• We play games with our children that involve numbers. We roll dice, we play cards, we solve puzzles together, and we play hopscotch. Through these games, my children gain an understanding of the relationship between numbers and actions we take in the games themselves. We ask questions like "how many ways can you get a 10?" My son recently answered that question with this sequence of answers: 20 – 10, 30 – 20, 40 – 30, 50 – 40, etc…
   
• We talk about how we use numbers in our day to day life. We talk about fractions of food (that are physically present in front of us), and talk about the relationships between these different fractions. We cook, do our finances, and share as many uses of numbers as we can with our children.
   
• We look for patterns in numbers. We play with relationships between different numbers. We celebrate discoveries our children make. For example, my eldest son noticed that he only needed to remember the very last digit in a large number to figure out if a number was odd or even. Now, he delights in asking people to give him gigantic numbers like 30,938,309,830,983 and being able to tell right away if the number is odd or even. As a mathematician father, I try hard to balance between giving my sons space to come up with their own discoveries, and expanding where their explorations might go.
   
• I also try very hard to remember that when my son makes a mistake, with further experiences, it is likely that he will discover these mistakes later for himself. For example, my son was convinced for a long time that numbers went 90, 100, 110, 200. He did not understand place value well enough, but over time, and with further exposure to our use of numbers, this misconception of his has disappeared. He now has a very good understanding of place value up to 1000, although he still does not understand larger numbers (he will say things like 233 hundred thousand, 293 million, 389 billion, and 43), but I am confident that as he continues to be exposed to numbers in his day to day experience, he will understand these numbers better.
   
• We balance our discussion of patterns in numbers with other types of patterns. We look for patterns in art work, in sidewalks, in tiled floors, and wherever else they may form. We create patterns ourselves in our art work and notice where they came from. We doodle, we draw shapes, we watch clouds, and we look at maps, all of which help my son develop a sense of shape and space.
   
• We ask for evidence from our sons about why they think something is true, whether or not what they are saying is accurate or not. When they have discovered something, and provided solid evidence for why they think it is true, we celebrate it. We might ask questions like, "How did you discover that?" or "Wow, that’s neat. Does it work all the time?"
   
• We give our children plenty of creative time to explore the world through art work, Lego, blocks, reading, playing games, and other self-exploration activities.
   
• We see the development of our children’s numeracy as a process, rather than a race. I have no interest in accelerating my sons through the elementary school curriculum, instead I focus more on providing opportunities for enrichment.

The key to all of these activities is that we view numbers and quantities as ways of exploring, and we nurture our children’s sense of wonder about the world.