When I first began teaching math, I focused on what math skills needed to be taught. It was a changing time in California mathematics with the old guard and their traditional ways pitted against us young, progressively-minded newcomers who wanted to have students explore numeracy and solve the problem-of-the-week. At the end of each day, I slumped at my desk and asked myself, “Now that I have taught that concept, what comes next?” The what of mathematics consumed my thinking. We were moving from a pencil-and-paper age to a calculator-and-computer age, so it was a time of redefining the content of mathematics. Whereas my elementary teachers simply turned to the next page of the textbook, we were asking, “Is it necessary to learn to master long division with decimals?
How important is factoring in this digital age?”

Over the years the pendulum of mathematics swung back and forth between focusing on conceptual understanding or on computation. During these swings, I began to explore the how of teaching. What is the best way to communicate mathematical thinking and processes to the student? Do we begin with a problem? with manipulatives? with a procedure? The emphasis of the how over the what redirected my teaching. The what was still the destination, but the how was the vehicle that would get us there.

This idea was confirmed when I recently read Chris Shore’s blog on the “4½ Principles of Quality Math Instruction”. In the article, Shore noted that the top performing mathematics nations do not demonstrate a similarity in their instructional techniques. However, they do have common underlying principles. Although the what is taught in various ways from one high performing nation to the next, those nations share certain principles. These were the same principles that govern successful math teachers everywhere: Commitment to a few high standards, initial instruction in concepts prior to procedures, good questioning strategies and high accountability.

The focus on how I taught mathematics occupied much of my planning time. However, as the years wore on, I found that I was tiring of the profession. I was floundering through my fourteenth year in education when I learned the lesson that changed my teaching forever. Misbehaving students were making every day a nightmare. I was ready to quit when one morning I decided I had had enough. No longer was someone else going to determine what kind of a day I was going to have. From now on I was going to have a good day regardless of what the students tried to do. I started smiling at their snarling faces. I talked kindly even when they were surly. I commented on their new shoes, asked about their interests, and commended their
accomplishments. The transformation produced immediate results as I connected with my students for the first time.

That’s when I learned that who I taught mattered much more than what I taught. In the past, I had always tried to learn more about math. Now I tried to learn more about my math students. I discovered that students don’t learn math from mathematicians; they learn from people who care about them, and for the first time, they had my heart as well as my head.

There is a wonderful children’s book called The Velveteen Rabbit in which a brand new stuffed toy is given to a boy. Through the years, the boy loves the rabbit and holds it so closely that eventually all its fur is rubbed off. When he grows, the old rabbit is tossed out in the yard. That night the rabbit awakens for the first time to find that he has become real because he was loved. I thought I was a teacher when I first held my brand new teaching credential and state-adopted textbook. Over the years, my students pulled me so close to their hearts that all my hair has since been rubbed off! They grew up, moved on, graduated, and left me behind, but in the process they loved me and I loved them, and somewhere along the way, I became real. We can’t teach the what until we have answered the how. And we can’t teach at all until we know the who.