Posamentier: Math teachers need flexibility to motivate students

As President Barack Obama contemplates his second term, he should consider how the agenda for our schools should change. Mathematics continues to be increasingly important, but perhaps for the wrong reason: It's one of the subjects used for the assessment of teachers, principals and schools.

Student achievement on standardized tests is a main criterion for assessing teacher effectiveness, and many teachers feel they must teach to the test. But motivating students requires a great deal of creativity from teachers, taking into account a variety of psychological, environmental and cultural factors.

When I was a new high school mathematics teacher in the mid-1960s in New York City, I taught a course in general mathematics intended for students who were oftentimes truant and largely aimless.

The first topic was arithmetic with fractions, which the students immediately resisted. On the second day, I told students to leave their textbooks home and instead bring in a pair of dice and a deck of playing cards. To my surprise, the class was in full attendance the following day, appropriately equipped.

In those days, the big game on the streets was craps, a game based on probability -- your chances of rolling a winning number, such as 1 out of 6, which can be represented as a fraction. I asked one of the boys sitting in the back to explain the game, and he reluctantly marched to the front of the room with his dice and explained the rules in heavy street language.

As the class became more comfortable with these simple probabilities, we applied them not only to craps but to other dice and card games, which all required adding and multiplying fractions. Since there were no calculators available then, I did these calculations for the class. Over several days, the class had perfect attendance -- up from its expected 50 percent. A different relationship with math had begun.

One day, some students complained they felt handicapped with my performing the calculations to arrive at the answer. I knew then that I'd won; they now really wanted to learn the topic they had shoved aside. The class mastered these procedures and the others that followed, since they were finally genuinely motivated to learn mathematics.

Nowadays there is often talk of making mathematics relevant to students. As I experienced back in the Bronx, it must relate to the interests of the students, not necessarily those of the teacher. An outstanding current math teacher who manages a mathematics support website, success-in-math.com, Steven Brunnlehrman, has experienced a similar phenomenon.

He writes on his blog about his own " 'trial by fire' at a very large, inner-city high school." One of his earliest successes wouldn't be possible in an environment where teachers must adhere rigidly to a set curriculum. A student was testing him by bouncing a basketball during class. "I took the ball, bounced it a few times, and then guided the students through the calculations to find the volume of air within the ball," he writes. "For that moment the students were mesmerized by a real-life application of math, even though the computations themselves were for two grade-levels above them."

The major change affecting many states, including New York, is the adoption of the Common Core standards that U.S. Secretary of Education Arne Duncan describes as "an important step toward the improvement of quality education nationwide." The Common Core State Standards Initiative cautions, however, that the "standards do not tell teachers how to teach . . . so that teachers can build the best lessons and environments for their classrooms." I hope today's math teachers and the principals evaluating them will take that to heart.

The Common Core State Standards Initiative may well recognize that the most difficult part of any math lesson is how to implant within students a desire to learn the material.

Let's revisit how we teach mathematics. Enrich the curriculum and find the best ways to motivate our students to enjoy this critical subject. They will learn math better -- and, ironically, ultimately perform better on tests -- than they will if we merely "teach to the test."

Alfred Posamentier is the dean of Mercy College's School of Education and the author, most recently, of "The Secrets of Triangles."