Developing Young Mathematicians

As an educator, my math classroom is significantly different from the one in which I was raised. I think many of our students’ parents feel the same way. In fact, during conferences, I’ve had several parents proclaim, “That’s not how I learned math.” To reassure them, I’ve explained my perspective as an educator and a parent. Many times, the explanation starts at the beginning-what they know to be true about their own math experiences.

Rewind twenty-five years to the math classrooms of my youth and most likely theirs; Situated neatly in rows, desks faced the front of the room. A math textbook lay open. On the left side of the page, there were step by step procedures for solving problems, and on the right page 25 or 30 practice problems with one or two word problems at the bottom. The teacher’s lesson began by working out the practice problem step by step while the students watched and memorized the procedures. Our task during class was to mimic perfectly the procedure and to work out the other practice problems independently. At the end of the period, we would pass our papers to the front of the room for the teacher to assess our progress.

I was a good math student, always able to follow the teacher’s directions and mimic the procedures. And, it didn’t take me long to realize that I didn’t even need to read the word problems at the bottom of the page, I just needed to pull the numbers out of the paragraph and use the same procedure for solving.

Does this scene sound familiar? It’s the way most of today’s teachers and our students' parents were taught math. Fortunately, it’s not the way our children are learning. Instead, based on research like TIMSS (Trends in International Math and Science Studies), and teachers’ professional development through organizations like the National Council of Teachers of Mathematics, educators are learning to better prepare students to think mathematically.

Thirteen years ago, as a beginning teacher, I learned about this shift in math teaching and learning at a national conference. Phil Daro, a Senior Fellow of Mathematics, helped me understand the need for change as he explained the three-pronged math approach . A conversation that I’ve replicated with parents and colleagues throughout the years. He began by drawing a triangle on the board and printing the word SKILLS at the top. Then, continued by creating the mental image of the typical classroom of my youth. Teaching and learning, decades ago, was focused on skills as the top and sometimes only priority. All too often concepts and problem solving were omitted, creating a deficiency that students struggled to overcome as they moved on to more advanced mathematics.

To illustrate how to prevent a gap in mathematical knowledge, and create a well rounded math student, Daro drew another triangle rotated 180⁰ so concepts and problem solving were now on top. Daro explained that math is three-pronged and, “Teachers must teach for conceptual understanding, build problem-solving skills, and strengthen basic skills.” Urging educators to tip the triangle upside down and select curriculum tools with an emphasis on concepts and problem solving, and then embed skills was the way to improve math instruction he assured. The connection I made to his simple explanation was immediate; Classrooms of my youth were skill driven classrooms; I didn’t learn to understand or connect concepts, generalize my learning, or problem solve. I learned to imitate my teacher. In that moment, I vowed, as a math educator, to teach my students to think mathematically, and as a parent I committed to helping other parents understand the need for this shift.

To accomplish my goal in the classroom, I piloted a conceptually based math curriculum tool, implemented internationally benchmarked math standards along with my state standards, and embraced the three-pronged approach using a sixty minute Math Workshop format and a fifteen minute Interactive Math Skills Block. Confidently, I set forth to create a culture of student collaboration and dialogue. Growing competent and fluent young mathematicians, who understood concepts, could strategically and flexibly approach problems, were procedurally fluent, and could articulate and justify their answers captured my full attention. And, trust me when I say, teaching myself to learn in this fashion was exhausting; There were days when I was only minutes ahead of my students’ learning. However, in the end, I captured the most amazing rewards. I, with the assistance of a few colleagues, helped paved the way for my peers by creating a shift in our practice.

Now, over a decade later, this passion still consumes much of my time and provides me with just as much satisfaction. Currently, as a staff developer, I chair our Math Council to lead with our vision and mission in constant view and assist to grow math leadership capacity in others. At the same time, I embrace my role to get new math teachers started on the right path from the very beginning. I continue to share my story with anyone who will listen. After all, I have the unique pleasure of teaching children and teachers to think mathematically.