The common-core math standards require that students learn the standard algorithm for multi-digit adding and subtracting—you know, the process in which you line the numbers up vertically to add or subtract and regroup as needed—by the end of 4th grade.
But waiting until then to teach the algorithm is a big waste of time for some students, writes Tom Loveless, a senior fellow at the Brookings Institution.
Students begin learning to add and subtract in 1st grade under the common standards. So teachers will conceivably spend several years having them do so with alternative methods, such as drawings, which can be tedious and make students hate math, says Loveless. “For many 4th graders, time spent working on addition and subtraction will be wasted time. They already have a firm understanding of addition and subtraction.,” he writes. And that “will shorten the amount of time available to teach other topics.”
As I’ve written before, one of the main differences between the Common Core State Standards for mathematics and previous state standards is the focus on conceptual understanding. Students still learn procedural skills—algorithms and formulas—but they often learn them a bit later than before. The idea is that students should have a solid grasp of underlying concepts before they learn the faster “shortcuts.”
Previously in Massachusetts, students were introduced to the algorithm for multi-digit addition and subtraction in 2nd grade. In California, students learned the algorithms for addition, subtraction, multiplication, and division in 4th grade.
Other experts have also argued that students should practice algorithms earlier rather than rehashing their conceptual understanding for so long. Barbara Oakley, an engineering professor at Oakland University in Rochester, Mich., wrote last year: “Having students stop to continually check and prove their understanding can actually impede their understanding, in the same way that continually focusing on every aspect of a golf swing can impede the development of the swing.”
Interestingly, one of the lead writers of the common-core math standards, Jason Zimba, defends the way the standards are organized not by saying that 4th grade is the best time to learn the algorithm, but by saying that teachers have the leeway to teach it sooner.
In a January blog post, as Loveless points out, Zimba wrote that the 4th grade standard is a “culminating” standard, and that teachers can begin introducing the algorithm as early as 1st grade. He even draws out a table for how to do that and still be consistent with the common standards, which he emphasizes are not as prescriptive as people think.
Loveless relates all of this to the history of the “math wars,” which I won’t go into here. But ultimately, this boils down to a discussion of whether the standards themselves or local implementation are at fault when things go wrong in classrooms. When a 3rd grader who fully comprehends subtraction spends many hours and evenings drawing hashmarks to illustrate multi-digit problems—which the writers would inevitably say they never intended—who should take the blame? And is the solution to change the standards or to alter teacher training and materials?
CORRECTION: A previous version of this post stated the wrong grade in which the prior California standards required students learn the algorithms for addition, subtraction, multiplication, and division. Students learned them in 4th grade.
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A version of this news article first appeared in the Curriculum Matters blog.