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."
Understanding Concepts
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 3rd 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."
Teacher Leeway
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?
