I get a little nervous when I post about something I know is controversial, but what good is a blog if you aren’t willing to share your truth. I saw a funny video on social media today. On one side of the screen was a person solving a 2 digit multiplication problem using an algorithm. It was quick and effective. On the other side was a teacher showing how to solve the problem using a much more complex and time consuming method. The point of the video was to poke fun at “new math.”
I have a different perspective on this than others, even likely in my own family. I was good at school. I am a visual and auditory learner, so traditional instruction worked well for me. I was motivated and engaged, and I always wanted to please my teacher. I took good notes and memorized algorithms, so I rocked my mathematics grade. But I had no idea what any of it meant. I could multiply any number of digits, divide the longest of numbers accurately, convert fractions to decimals and vice versa, all of it. But I had no idea what any of it meant.
I have, by many measures, been successful. (I am, by many measures, still a work in progress.) My lack of depth in mathematics understanding has not held me back from doing what I love. But what more could I have done if anyone had taught me not simply to use an algorithm to get to an answer.
It is not an accident that I taught language arts. My language arts teachers did not only teach me to memorize vocabulary and regurgitate what I wrote in my notes. They taught me to read for meaning, to analyze, to connect ideas, to think. They taught me to use what I read to grow as a thinker and as a person. Yes, they also taught me the foundational skills I needed to read. I learned phonics and decoding and vocabulary. But it didn’t stop there. As they were teaching me those foundational skills, they also taught me the deeper communication skills that have led to my success.
I had many great teachers in mathematics, but none of them taught me the deeper skills, only the algorithms. I don’t think I even knew that what I was learning was an algorithm. I think I thought it was mathematics, but understanding that 37 can be easily be broken down into 30 and 7 which can be faster to manage in your mind is foundational. Understanding that when you divide, the number gets smaller because you are, in fact, dividing the number up is foundational. No one talked to me about those things. “Check your work.” I learned an algorithm for that. Multiply to check your answer in division. Easy. But if I had understood the foundational things, I would have been able to look at the answer and decide if it even made sense.
My father understands this. So do my brother and my sister. They are “good at math.” What that really means is that they knew instinctively, without being explicitly taught, the deeper skills. They sorted it out for themselves. I did not. Again, I got good grades in mathematics, but I remember the frustration when my father would try to help me with my homework. He understood something that I did not. But neither of us knew that at the time.
We know better now.
We must teach foundational skills, in language arts and mathematics and all areas. We must teach phonemic awareness, decoding, vocabulary, fluency, and comprehension. We must teach number sense and procedural and fact fluency through a variety of strategies including, yes, algorithms. No one does lattice math in everyday life. Our teachers are striving to help all students understand not just how they got an answer, but why. So we also teach inquiry and reasoning and communication skills.
Our teachers are working to create the thinkers and inventors and scientists and mathematicians and philosophers of the future.
Nothing is as simple as a social media post makes it…especially not mathematics.