Did He Get The Right Answer?

My youngest son is a Second Grade student at Chets Creek Elementary and is being raised in a math learning community that values young mathematicians and works hard to develop their number sense. Since Kindergarten, his learning hasn't consisted of rote procedures and memorization, rather his teachers have cultivated his number sense, stretched him to solve problems using a variety of strategies, and embedded problem solving.

Today, coming home from school, he pulled out his Sunshine Math sheet and got to work. (The Sunshine Math program is run by our PTA and is an optional program that students can sign up for at the beginning of the school year. The weekly sheets offer math challenges for students to complete independently. Students get the sheets on Mondays and turn them in to the PTA on Fridays. PTA volunteers correct the sheets and return them to students. Students are rewarded periodically by PTA for their participation and at the end of the year, the teachers host a Math Challenge Day for students to compete.) Most of the time, the questions are rich contextually based problems which promote my child's problem solving skills. However, today, on the back of the sheet, there were a set of problems that looked very traditional.

The problems themselves didn't give me angst, rather the way the traditional problem pigeon holed my child into solving using a particular strategy-the traditional regrouping algorithm. Notice problem d. Now, humor me, if you will, and write this problem down on a sheet of paper. Then, solve it.

Most of you, like me, probably solved this problem using the traditional algorithm and got the answer easily.

Now, take a few moments to consider how my son solved it.

At quick glance, you may, like the volunteer that will use an answer key to score my son's paper, mark his answer incorrect. However, if you take a closer look, you will see that he is correct. He gave the answer 17 because he did not use the traditional regrouping algorithm, and he did not adhere to the confines of the boxes. He looked at this problem and said, "Six take away nine is negative 3." You can see where he recorded the -3 in the box. Then, he said, "Fifty take away what will give me 20? That must be 30." He recorded the 3 in the tens place box. Next he said, "Twenty take away three is seventeen." He did this all in a matter of seconds and then double checked his work to prove that 56-39=17.

Since I knew that they wanted him to get the answer 27, and I was intrigued by his thinking, I wrote the problem 56-29 on a sticky note and asked him to solve. A second later, he handed me back the correct answer of 27. I said, "Tell me how you solved it." He replied, "I know 50-20 is 30 and 6-9 is negative 3, so the equation is 30-3 which equals 27." He used a left to right strategy to solve and is very comfortable with negative numbers. I said, "How did you know 6-9 is negative 3?" He said, "Do you want me to prove it to you on a number line?" He's eight years old!

I was very intrigued the moment I saw what he'd done with this problem on our car ride home. I've been an intermediate math teacher; I've been a math coach; I've worked as a math consultant. And, I've seen far too many math practice books, websites, and even state adopted textbooks that have this type of problem in them. They look harmless enough, but for kids who think mathematically and even for those in the process of developing their number sense, they can be detrimental.

I am thankful that my son has not had teachers who teach him to solve problems procedurally using only the traditional algorithm. He's been blessed to have an incredibly talented set of teachers that offer instruction to cultivate a students' mathematical thinking. Because of Mrs. Mallon, Mrs. Dillard, Mrs. Ross, and Miss Russell, Carter is a mathematician.