Lately I’ve seen many parents, both in the media and in my own life, railing against Common Core, particularly math. There’s a great deal about the Common Core I don’t care for, but math is not one of them.
One of the main objections I see to “new” math, such as Everyday Mathematics or Investigations, is the emphasis on writing about math to explain who the student solved the problem. In the case of Common Core, it’s part of the “evidence” that the student has to build to explain why they did something. This evidence is used not to put pressure on students, but to help them develop critical thinking about why math works. As a teacher, when I see a child work through a problem and describe it to me, I can confirm if they understand why it works.
I have many parents bring me a student and say, “Oh, my child needs accelerated math! He’s so good at math!” And yes, the student can crank out correct answers to an addition worksheet in under a minute. However, frequently the child has no practical application of those skills. One of my students was amazing at worksheets and learning algorithms, but one day he was in charge of snacks, and needed to know how many to get. I told him, “Well, you’ve got eight boys and ten girls, so how many snacks do you need?” The boy gave me a blank stare and proceeded to do a headcount. So, he knew that 10+8=18 on paper, but when asked to apply that knowledge, had no idea what to do. It’s far more common than you’d think, which is why the newer methods were developed.
The other thing that I love about the new math books is that it provides the teacher with about 5-7 different methods of approaching the problem. If as student doesn’t understand it the first way, I can attempt the second, and so on until I find the method that reaches that student. When I was in school as a child, I couldn’t understand math at all, and my teacher told me I had to do it as it was written in the book. Like many learning-disabled children, I was able to memorize patterns well enough to work through an algorithm, but it might as well have been hieroglyphics for all that I understood. So, when I reached higher level mathematics, I was unable to understand how the lower level algorithms fit into the higher ones, because I had no base. Proofs were a complete disaster, because I had no concept of why the math worked, or any form of number sense. I could memorize long strings of facts, but what good are they without application skills?
As teachers, it is our job to ensure that students have both a solid base in facts and the understanding to apply them. Memorizing multiplication tables and fractions is a useless exercise unless the child understands what the purpose is. I, as a child, memorized long strings of fractions, but it wasn’t until I began cooking as a teenager that I understood that fractions simply meant dividing a whole into measurable units. With the new math, I can demonstrate to the students that if I have a candy bar, I can break it into equal parts and place it back together. Then, if they write about the question, “Jane, John and Stacy want to share a brownie. How should they divide it so it’s fair, and why?” I can see both the mathematics portion (drawing the division of the brownie) and the reasoning behind it. If the child can draw the division but writes, “I don’t know,” then the child does not actually understand what has happened. Then, I know to go back and reteach a new method to ensure understanding. It helps to catch those children, like me, who may be able to memorize but not realize what it means.
I saw a parent say, “There are always slow kids, but why should the kids who get it have to put up with them?” First of all, quit calling them “slow kids.” Those kids typically have a disability, even if it isn’t visible. And they have just as much of a right to learn as any child. Second, the other children should not be held back. A teacher who understands how to balance curriculum should be able to accelerate the child if he or she requires it. I had one child doing fifth grade math in first grade–so, I went to the fifth grade teacher and got the materials for him, as well as some accelerated computer programs, and he was happy as a clam. But before I am willing to accelerate a student, I must see that they have both the factual base and the ability to apply it. Being able to churn out worksheets is not “getting it.”
For those who say, “Well, those kids that need remediation should be in a different class!” That could work, sure, but it requires money. If you want that, vote for education bills and bond issues, and cough up the tax money for more teachers and aides. I know that there’s a magical idea that teachers should be able to reach every child perfectly,with only their love of students and learning to sustain them, but it doesn’t work without resources. The more students I have, the less time I can spend on each one, no matter how much I want to make it work. The strongest students will be the ones whose parents help them at home, who show them how the world works and how to use math in it.
Some of the parents write to me and say, “I don’t understand the math program or this algorithm.” It’s my job to explain it, and I’m happy to do so. Your child doesn’t have to master that particular method if it doesn’t make sense to them–as long as they have a way to explain how they got their answer, the method doesn’t matter. I do want them to be aware that the method exists, because what works for one may not work for the other. Every child deserves to understand what they learn, and that is what those questions are about.