The Fundamental Problem With Common Core MathIntuition relies on skill, not the other way around
In 2010, a bold effort to reform math curriculum was adopted by the majority of the United States. Known as “Common Core Math,” the goal of this endeavor was to establish a common foundation of mathematics education across the country, and to help bolster not only students’ mathematical abilities, but also their mathematical intuition. The goal was to help students think about math more deeply, believing that this will help them work with mathematics better in later years.
Before discussing problems with this approach, I want to say that I appreciate the idea of helping students think more deeply about mathematics. After years and years and years of mathematics education, many students wind up thinking about mathematics as merely a set of formulas that they had to memorize to pass a class, which they will never ever use again in their lives.
In 2005, this was brought to the public’s attention when Jeb Bush was asked by a high school student about trigonometry, and Bush essentially replied that he hasn’t been in high school for a while. While the particular question was ill-posed, this illustrated concerns that students are being made subject to high-stakes tests on questions that they literally don’t need to know.
In other words, students are frustrated because they are being asked to learn formulas and equations for things that have no connection to their present or future, whose sole purpose seems to be jumping through an arbitrary hoop set up to make them fail.
What Common Core is supposed to bring to the table is a deeper understanding of mathematics, so that students recognize how mathematical thinking is part of thinking in general. While this is a worthwhile goal, common core radically misfires on several accounts.
First of all, Common Core tries to teach the concepts first, and to incorrectly-aged students.
Younger students love memorizing and systems. That is what their brains are geared for. They want to learn how to do things. It isn’t that “why” questions aren’t appropriate (in my opinion, it is never too early to start talking about “why”), but the fact is that the “why” questions are not the most important thing, and it isn’t what they are best at learning.
This is why, historically, we taught students straightforward systems for doing mathematics calculation. We taught processes which, once learned, could be applied to any set of numbers. Crucial to this teaching methodology are (a) quick recall of math facts, and (b) a straightforward process that anyone can do. This gives students the skills they need to do problems and to recognize that the size of the problem doesn’t really matter as long as you have the process.
What Common Core advocates don’t like is that (a) the process prevents students from really thinking about what is going on with numbers, and (b) some claim that the high-pressure timed math facts tests cause lifelong student anxiety about mathematics. We will discuss (b) in a later article. In this article, I want to focus on (a).
It is true that younger students learning long forms of addition, subtraction, multiplication, and division don’t spend a lot of time thinking about why the process works. However, the stage of learning that students are at in this time is one where memorizing and learning processes come the easiest. I do think that students should eventually learn why the process works. However, usually students do well to learn a process, and then get curious why it works. This allows them early competence, and a foundation for later reflection.
The fact is, reflecting on why things work is a product of age. Disasters in math education have always come from people interchanging the needs of adults with the needs of children. In the 1950s, a similar attempt was done with “New Math.” It attempted to teach mathematics using set theory, which is the foundation stone most modern mathematicians use. However, while you can build mathematics from set theory, you almost always learn set theory as a reflection on the mathematics you have already done. While Common Core is not as radical as the New Math, both stem from the same basic flaw — they prioritize the thoughts and tendencies of adults over those of the students they are teaching. It is easier to ask why questions when you already understand the process. It is harder to even understand the question being asked when you haven’t learned any process at all.
A second problem with Common Core math is more social. Students often need more help with mathematics than is available in the classroom. Especially in schools with large class sizes, parents wind up being the default tutor when a student doesn’t understand a concept. Any radical shift in methodology, then, immediately strips parents of their ability to act in this capacity.
Educators often complain about the lack of engagement of parents. However, it is difficult to take this seriously when the education establishment goes out of its way to rewrite curriculum in a way that bears no connection to how parents understand the curriculum. If educators want parent engagement, they must consider the ways that their curriculum impacts the ability of parents to engage. If educators don’t want parent engagement, they should be happy when parents don’t engage. Instead, many educators want to have their cake and eat it too — write curriculum which parents don’t have any connection to, and then complain that parents aren’t involved.
Let me say that there is nothing ultimately wrong with the specific things that Common Core wants students to learn. Having more mathematical intuition and recognizing multiple ways to solve a problem are both very good things. However, intuition often develops after repeated exposure to concrete problems, not before. And, before recognizing that there are multiple ways to do something, it helps to learn one of them well.