When we read the Common Core State Standards, or when we used to read other state standards, in math, we often see the word ‘fluency.’ For example, one first-grade Common Core standard in math says students should be able to “add and subtract within 20, demonstrating fluency for addition and subtraction within 10.” This refers to being able to do arithmetic quickly.
In the younger grades, I have known more than a few students who were frustrated by fluency. A big part of that is how teachers chose to teach them to regurgitate basic math facts with a high speed.
Typically, what happens is teachers give students a worksheet, say, with 50 addition problems on it, and the class races to finish it in a certain period of time. If a student can’t finish on time, he or she is considered “failing.” Students who pass it go on to the next level in whatever game is being played, and students who achieve a certain level by a certain date get a good grade.
In one school, Center Elementary in the Plum Borough School District in Pennsylvania, students in kindergarten through sixth grade receive military-like dog tags after achieving a certain degree of fluency in math, the Pittsburgh Tribune-Review reports. On one side of the tag is a mustang—the school’s mascot—and on the other, an example of the math benchmark they’ve mastered.
“Our goal with this new math fluency incentive is to ensure we have a dedicated focus on mastering basic math facts while at the same time making this learning motivating and fun for students,” principal Jeff Hadley was quoted as saying.
And motivation is the key. Especially in the younger grades, extrinsic rewards can be a powerful motivating force for students, as long as teachers strive to convert those extrinsic rewards, like the dog tags at Center Elementary or the candy and movies at an Illinois school, as we reported a few weeks ago.
However, compelling research about timed math tests, the object of fluency found at many elementary grades in the Common Core, has shown that they can often increase anxiety toward mathematics and could hurt children’s development.
In this month’s issue of Teaching Children Mathematics (20(8):469ff), the National Council of Teachers of Mathematics suggests that timed math tests for basic math facts are “one of the initiatives mandated by many school districts that [the author places] high in the category of uninformed policy.” Those are pretty strong words, written by Jo Boaler, professor of mathematics education at Stanford, and published by the national council.
So, while the use of extrinsic rewards can lead to success in getting students to do something they wouldn’t naturally want to do, such as spitting back answers on a timed math worksheet, we must evaluate whether the use of that timed math worksheet is good or effective in the first place. Writes Ms Boaler:
Starting in first grade in my local school district, students receive a 50-question test to complete in three minutes. The district requires the tests to be given once per term, but some teachers give them weekly. One teacher explained that she does so because the first time she gave the test, many of her students cried; she now wants to get her students “used to them.”
I have had the same experience in the elementary schools I’ve sat in on. No good ever came from these math tests that amount to too much “answering” time and not enough “learning” time. What can be done instead to teach the standard? Fluency, of course, is no less important than it ever was, but timed tests aren’t a good way to teach it, because they make math an unpleasant learning experience for too many kids and turn many of them away from math.
Instead, Ms Boaler recommends establishing environments for learning in the classroom that encourage students “to appreciate the beauty and diversity of math, learning new ideas without pressure or anxiety.” That does not mean taking a test that requires correct answers to 50 questions in three minutes. And it doesn’t include labeling students who don’t work as fast as other as failures.
Fluency is something that comes naturally if kids want mathematics. The desire can still be encouraged through the use of extrinsic rewards, but the dog tags should be given for something other than completing a timed test in a certain time period.