I grew up in France, and went to college there. Since I was majoring in Biology, I had to take a fair amount of courses related to Statistics and Probability. And a fair amount of 2-3 hour exams, mostly essays. So I studied, studied, and studied all of the equations, and rules. Then the final exam came, and I got to the last question with just a few minutes left. I jumped into equations, got lost, started over, got lost again, spent too much time, and ran out of time. When I got home, I shared my frustration with my brother, an English major, who looked at me and said “Well, it is 3 socks”, explaining me his reasoning in a couple of sentences. The question was:
“You are in the dark. In your drawer, there are 10 white socks, and 10 black socks. How many socks do you need to draw to make sure you have two of the same color?”.
It IS 3 ! Of course, it is 3 ! But because it was at the end of a 3 hour exam full of probability problems, I just kept using equations. I stopped thinking, forgot to visualize the problem, and wasted precious time that I could have used to edit my paper. Now, I ended up passing the exam, and 20+ years later, I wish I could thank my professor for his eye-opening question.
As a parent, I am wondering when it is going to happen to my kids, you know, when you are so focused on the abstract that you start forgetting to step back and see the concrete associated to it. Maybe not in Elementary School, but in Middle School? High School? When it happens, I hope they see the step of going back to modeling and representation, as a progression rather than a regression.
So this is one of the goals I am trying to accomplish with my children, with this blog. Make sure they take the time to explore, model, draw, step back and think. So it becomes natural for them to keep doing it when they get older. May look silly to spend 20 min on discussing 2 + 3 = 5 with a rising 1st grader (here), but it is my way as a parent to strengthen my kids’ foundation in math. At home. Peacefully. So when they get lost in a drawer full of socks, they can find their way out. With 3 socks in their hands.