Under new math standards, students will be asked to explain why procedures work before they’ve mastered the procedures, writes Barry Garelick in The Atlantic.
Under the Common Core Standards, students will not learn traditional methods of adding and subtracting double and triple digit numbers until fourth grade. (Currently, most schools teach these skills two years earlier.) The standard method for two and three digit multiplication is delayed until fifth grade; the standard method for long division until sixth. In the meantime, the students learn alternative strategies that are far less efficient, but that presumably help them “understand” the conceptual underpinnings.
Students are expected to:
Make sense of problem solving and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
These are “habits of mind that ought to develop naturally as a student learns to do actual math,” Garelick writes.
True habits of mind develop with time and maturity. An algebra student, for instance, can take a theoretical scenario such as “John is 2 times as old as Jill will be in 3 years” and express it in mathematical symbols. In lower grades, this kind of connection between numbers and ideas is very hard to make. The Common Core standards seem to presume that even very young students can, and should, learn to make sophisticated leaps in reasoning, like little children dressing in their parents’ clothes.
Teachers will need to adjust Common Core guidelines, Garelick writes. But will teachers have the freedom to do so?
Some people are misreading the standards, responds William McCallum, a University of Arizona math professor and leader of the math standards team, in a comment. “The standards do not settle the debate on how fluency and understanding should interact in the curriculum,” he writes. The phrases “critical thinking” and “collaborative learning” do not occur anywhere in the standards.