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The Touchstone

Gojak_Linda-100x140By NCTM President Linda M. Gojak
NCTM Summing Up, December 4, 2012

There is a tale from the Middle Ages about a magic pebble, called the touchstone, that when rubbed against any metal, would turn the metal into gold. It was said that this pebble could be found on the shores of the Black Sea. It looked like any other pebble on the beach. The only difference between the touchstone and the other pebbles was that it was warm to the touch, and all the others felt cold.

A young man who had heard many stories about the touchstone decided to sell everything he had and to travel to the shores of the Black Sea in search of the valuable stone. There were, of course, millions of pebbles on the beach. So each day he walked on the beach, picking up pebbles. He would pick up a pebble. and if it felt cold, he would hurl the pebble into the sea. Then he would pick up the next pebble. He did this hour after hour, day after day, and year after year. Pick up a pebble. It is cold. Throw it into the sea. Pick up the next pebble. He never gave up. He kept trying until one day—a rather ordinary day—he picked up a pebble, and it was warm. Then, out of habit, he threw it into the sea.

What does this story have to do with teaching mathematics? In this time of pacing guides, implementation of new rigorous standards, high-stakes assessments, and teacher evaluation protocols, it is easy to become overwhelmed by routines over which we have no control and to lose focus on the touchstones—the students whom we teach.

As professionals, we participate in “teaching habits” to help ensure that our students will be successful. We prepare lessons. We attend meetings. We read articles. We might participate in a study group or another professional growth activity. All of these activities are important to being prepared to teach mathematics. However, if we lose sight of the significance of our daily instructional practices and the impact that they have on the accomplishments of each student, these habits serve little purpose.

Like the young man in the story, we can become so wrapped up in our day-to-day routines that we forget what our focus must be. We cannot become complacent about helping our students develop a deep understanding of the mathematics that they are learning. It is easy to fall into the habit of teaching—to go through the motions of teaching without thought. If doing the same thing day in and day out becomes our habit, it will also become the habit of our students, who will simply go through the motions of doing math. The general routines of teaching have the potential of taking over. Rather than helping us, they begin to dictate to us and hinder our important work of reaching students.

Whether we are new teachers or veterans, we need to keep our attention on our teaching touchstones. Our work each day, in each class and for each student, must stay focused on instructional moves that help students develop a deep understanding of mathematics. Covering the material or preparing for the test is not enough. Allow yourself time to think about what question to ask a student in a classroom discussion. Consider and respond to a student’s comment or explanation before continuing. Focus the lesson on helping students to make sense rather than to demonstrate facility with a procedure. Reflect on how to assess students’understanding beyond the written test, and consider how the understanding that you gain can shape your next lesson.

The critical teaching habits are those that affect each student’s learning. They require us to be cognizant of every teaching decision that we make. And, as much as we take time to plan, our interactions with our students happen in the present. They do not allow teaching to become a routine of throwing pebbles into the sea. They are what create touchstones from each student whose life and future we impact.

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