THE BLOG
04/22/2015 08:39 pm ET Updated Jun 22, 2015

# Great Teaching Is The Real Test

The second and third weeks of April mean only one thing to administrators, teachers, students, and parents throughout New York: It's testing season. Across the state, students in grades three through eight have been sitting for three days of testing in English Language Arts and another three days for math. Many anxious families have been opting their children out of these standardized tests. Others have complained about the system as a whole and denigrate schools and teachers who embrace it.

I am a seventh grade math teacher at Success Academy, and our students have performed extraordinarily well on their state exams over the past six years. We have been accused of conducting endless, pitiless test prep to achieve these results -- of emphasizing robotic execution rather than critical thinking. According to our opponents, the abnormally high scores achieved by thousands of our students in low-income neighborhoods have been achieved by exclusively "teaching to the test." But nothing could be further from the truth. In math, our students do extraordinarily well not because we teach them how to take a test, but because our teachers guide them to fall in love with problem-solving.

Let me explain the difference. Most math classes teach formulas. Students memorize them, learn how to plug in numbers and arrive at an answer. When test time comes, they drag out those formulas, look for a multiple-choice answer that approximates what they think the solution is, and fill in the bubble on the answer sheet. In test prep, the focus is on quantity -- give as much practice as possible on as many types of questions as possible.

We take a very different approach. Instead of teaching formulas, we teach students how to think about math -- or rather, we help them come up with their own ways of thinking about math.

For example, there are lots of problems involving negative numbers on the seventh grade state math test. The test-prep approach involves plugging numbers into a pneumonic that students are supposed to memorize. There's "keep, change, change," which indicates that when you're subtracting two negative numbers, the two minuses equal a plus. Or "hate to hate equals love," which means when multiplying two negative (hate) numbers, they equal a positive (love) number. These simplified rules may help a struggling student pass a test in the short term, but they have nothing to do with math and in no way benefit long-term understanding.

When we teach negative numbers, we do things like explore temperature. I give out thermometers, and the students see what happens when the temperature is less than 0. Take away an ice cube, and the temp rises. Or we give out black poker chips to represent negative numbers and red chips for positive numbers, and as the kids work with them, they come up with rules -- we call them conjectures -- to describe how the reds and blacks cancel each other out. The kids test their conjectures against real-world problems -- If you have four black and three red, what is the sum? - to see if they are consistent. That way, the kids explore and make their own conclusions. With the teacher guiding their exploration, students are empowered because they own the learning and more motivated to master the concept. Math no longer seems arbitrary; instead, students discover it is the set of rules that defines our universe.

Instead of emphasizing quantity, our classes prioritize quality. For most of the year, my students focus on a small number of problems. We cover maybe three long questions in a 50-minute period. The kids work in pairs, finding creative ways to problem-solve together. Students share their strategies, and the class analyzes each one, discussing what they like about it and what could work better

It is only around the beginning of February that we start prepping for the state exam. In fact, that is the first time my class even sees a multiple-choice test all year. We start phasing in these questions and begin discussing things like process of elimination, pacing, how to use a reference sheet and estimation.

Frankly, to my students, the questions on these practice state tests seem pretty low-level. Our usual exams consist of open-ended, multi-step problems. They have meaning, and context - the strategies used to solve them could be applied to actual real-world problems.

Math is not about taking tests; it is about exploring, reasoning, figuring things out. Every one of my students has been exploring math at a high level since kindergarten. Creating an atmosphere of engaging mathematical exploration for thousands of students has not been easy - it requires much more preparation of teachers. However, once achieved, it explains why most teachers at Success expect their students to do extraordinarily well on the exam this year.

And test prep has very little to do with it.