Common-core math aims to have students do less memorizing—but it’s being misinterpreted to have students do more, argues Kathy Liu Sun, an assistant professor of math education at Santa Clara University.
In my research and work with math teachers, I’ve observed that educators are trying to fit the standards into an old system of teaching math. We used to learn math by memorizing a “rule” and then repeating it to solve a series of similar problems. ... Under the guise of Common Core, rather than learning one rule, students are now memorizing and executing three or more different rules for the same set of problems.
She shows how this is happening with subtraction. In the past, students have memorized the traditional algorithm for double-digit subtraction. (Line the numbers up vertically and “borrow” or “regroup” as needed). But the common core notes there are many other ways to subtract two numbers. And some teachers are having students memorize them all.
Here’s the exact language from the 1st grade common-core standard for subtraction:
(I’ve written before about the many methods for subtraction, if you’re looking for more examples.)
Notice the words “Use strategies such as” in the second part of the standard (under No. 6). There’s no actual requirement that students learn all of those strategies. In fact, Jason Zimba, a lead writer for the common-core math standards, has argued that it’s possible to only teach the traditional algorithm, and still technically be following the standards. (Though that doesn’t appear to be the intent of the standards either.)
Leaving “Sensemaking” to Students
In an interview, Sun said that the benefit of exposing students to various strategies is to help them understand what subtraction really means—and in a way that makes sense to them personally. When given a chance to play with numbers, she says, students will come up with many of these strategies on their own.
She recommends introducing the concept of subtraction with an open-ended word problem, and letting students use manipulatives or whatever they want to try to solve it. (For instance, David has 12 goldfish and he gives 7 to his friend. How many does David have left?) The teacher can watch how individual students solve the problem, and show the class that there are several different ways. “I think the algorithm should always be taught after the sensemaking happens,” she said.
Having students explore subtraction before they learn it formally helps them build context, she explains. “I think the beauty of it is it frees the teacher to say I’m open to other strategies,” she said. “You’re not ever going to predict everything kids are going to do. Kids will surprise you.”
Much of the common-core misinterpretation is not a teacher issue, but “a curriculum issue,” Sun said. Some curricula include an entire lesson on each strategy mentioned in the standards. “Just because it’s the official [curricula] doesn’t necessarily mean it’s the best one,” she said she tells her preservice teachers. “We can be critical of it.”
Her ideas on how to introduce new concepts overlap with those of Dan Meyer, best known for his TED Talk, “Math Class Needs a Makeover.” (The two also graduated the same year from Stanford.)
- Common-Core Subtraction: Teaching Many Methods
- Schools Teach Common-Core Math to Two Generations
- Should ‘Regrouping’ Be Taught Earlier Under Common-Core Math Standards?
- Life Equation
A version of this news article first appeared in the Curriculum Matters blog.