FACT: I love math. I love it so much that when teachers assigned just the odd problems, I did the even ones too. (Yes, I was that freak in school). I took Calculus 1 and 2 in college for fun. I also took a computer science class in college, again for fun. I actually delight in teaching my kids math!!!
So when the whole 5 X 3 controversy erupted, it immediately peaked my interest. As I began to read differing views such as “Why 5 X 3 = 5+5+5 Was Marked Wrong.” I immediately thought that the teacher was on drugs because multiplication is commutative meaning that 5 X 3 = 3 X 5 = 15.
I also thought 5 X 3 = Five three times. And for everyone who says it is five groups of three, I would argue, that the X means times, not groups. And for every mathematician that says it is 3 Five times, I can find you one that says the opposite. Because you see, it really isn’t important how you word the problem if you understand the commutative property. If I have 3 people and want to give each 5 bananas, I need 15 bananas. If I have 5 people and want to give each one 3 bananas, I need 15 bananas. If I understand the commutative property, I can get the correct number of bananas and give out the correct number to each person.
I have consulted numerous math textbooks, and many of them agree with me. I consulted the Khan Academy. You can watch the lesson here. In one lesson, the teacher (Sal) offers several explanations that shows that multiplication is commutative. He gives the problem 2 X 3 and says, “The easy way to think about multiplication . . . is that it is just a simple way of doing addition over and over again. You are going to add 2 to itself 3 times.” Meaning 2 + 2 + 2. He later goes on to explain that you get the same result by saying 3 + 3.
Here is another website that explains 5 X 3 (ironically, it is the same problem). The bottom line is that any good mathematician knows that math is fun, and we never argue about how we got to the end result if it works for you. Only teachers that don’t love math argue how we get to the end result.
However, the more important issue at hand is the love of learning. Children are little sponges, and they love to learn. We see this in children from infancy. Even the smallest babies observe their surroundings. Before they can talk, they are little scientists dropping spoons from their high chair to see if they get the same results over and over. Take a 1 year old over to the light switch and turn it on. The child will continue to flip the switch over and over to see if they get the same results. Children continue this love of learning even in school until they have a teacher that ruins it for them. And we all know when that happened to each of us. For me it was first grade. I loved every day of kindergarten, but I cried every morning of first grade. The teacher I had was mean and nasty. She called us names, and clearly she hated children. She wanted order and quiet. Quite frankly, I hated that I never got to play the cymbals or the drum!
So when I saw that math problem I thought back to my days of my schooling. I thought about that teacher that robbed a bright-eyed little girl of her childhood. I thought about how we are robbing children of so much by the way we instruct. We take away the love of learning, and replace it with the teacher is right and the student is wrong. We tell that child that even though you might understand a concept, we haven’t taught it yet, so you can’t use it. We tell children not to work ahead or even look ahead in their books.
What do you “see” or “hear” when you see the problem 5 X 3? I would love to hear your thoughts.