Over the past few weeks, I have had the privilege of working with some fourth- and fifth-grade students to learn more about their mathematical thinking. It has been fun and informative. I am an “old dog” and resort to my “old tricks,” so hearing some of their approaches to solving a math problem was nothing short of enlightening.

As we looked at various problems, I learned so many ways to solve them. For example, when given the problem 1000-998, one student did the following: 1000-900=100; 100-90=10; 10-8=2. Another approached it in a similar fashion, saying 900+100=1000; 100-98 =2. And yet another student counted up from 998 to 1000, realizing that they only had to count up 2 numbers. Each student arrived at the correct answer; each answer was the result of a different approach. They explained their thinking, and it was as varied as they are.

The thing that fascinates me about this is that when I was a student in upper elementary school, there was only one way to approach that problem: you set it up vertically, canceled the zeroes, borrowing from each previous digit and arrived at the solution of 2. There you have it! There was one way to do it and one correct answer. For everyone. No leeway allowed. And, boy, could those zeroes be tricky. Continue reading →