Dear Christina,

At the end of two semesters of the math for elementary teachers courses, you were assigned to read the Richard Skemp article “Relational Understanding and Instrumental Understanding,” and to apply the ideas of the article to your own learning in these courses.

You wrote elegantly about your understanding of fractions, of decimals, and of how the courses helped you to make sense of relationships between these ideas; relationships that had eluded you through many years of schooling.

And you finished your paper with a question for me:

Throughout [these courses] you have followed through with intentional teaching as well as not letting us get away with instrumental … understanding. You have challenged me to think beyond what I think I know and to confront the math concepts that I thought I would never comprehend. That said, I have already taken some education courses and many of the texts express the importance of teaching…that accommodates the different learning styles in the classroom…My experience within many levels of schools is that there is no accommodation for different learning styles and that most curricula are still set up for instrumental understanding and that leaves a lot of students slipping through the cracks when they are highly capable and bright children. **How can a teacher in today’s schools find the time to teach to all, especially with all the standardized testing, and curricula that don’t fit the … learner?**

These are important questions. No matter the grade level, no matter the subject, no matter the political environment, these are questions that thoughtful caring teachers (and most of us are!) struggle with.

The present testing environment in public schools and the recently developing politics around public school teaching change the pressures around these questions, but the questions have always been there.

Many people have written passionately on this topic. Rather than give a comprehensive answer, I’ll focus on what I find to be the most important piece of answering this question.

In a word: listen.

Of all the things you can do in the classroom that take up time in class, the time spent listening to your students will pay off the most.

Instead of assuming you know what your students will struggle with, listen to them to find out.

Instead of planning tomorrow’s lesson based on what comes next in the textbook, listen to your students’ ideas and use them to help you decide what makes sense to do next.

Instead of telling them how they should see the world, listen to how they do see it.

And if you listen, you’ll say less. But what you say will relate to your students’ ideas.

And if you listen, you’ll cover less. But your students will hear more.

Let me tell you about two people who have had a profound influence on my own teaching.

### Anne

Anne Bartel taught me to listen to students. Anyone who has been involved in mathematics teaching and learning at the state level in Minnesota or in the Minneapolis Public Schools has met Anne, and odds are good they consider her a mentor.

I met Anne in my second year of teaching (spring, 1996) and had the opportunity to work closely with her for a number of years. She is an incredible listener. She puts people at ease. She makes them feel that they are being heard and understood. Anne, at about 5 foot 2, can hold the attention of a large group of fussy teachers in large part because they know she’s listening.

For a couple of summers of professional development work, I marveled at her ability to work with adults. But I didn’t strive to emulate her model. I figured I would have to develop other skills in my own work. I figured I could never do what she does. I figured she could do it because *She’s Anne Bartel*. She had a natural gift that most don’t have, right?

Wrong.

Over time, I came to realize that she could do what she does because she learned to do it. She studied it. She practiced it. And she could teach it.

I realized that if studying makes you that good, I’d better get to work. I’ve been working on it ever since (for about 14 years now).

I hope it has shown in our two semesters together. I hope you and your classmates have felt listened to, have felt that your ideas have been valued and incorporated into the courses.

I know we studied fewer topics than another version of each course might have covered. But in reading your paper, and the papers of your classmates, I have some strong evidence that you have made connections among the big ideas of these courses; that you have retained what you mastered and that you continue to think about these ideas and to wonder long after we have moved on.

I would gladly pit you all against a group of students coming through a course that emphasized coverage in a lesson-planning smackdown (that is why we are studying this stuff, right? so that we can teach children someday?)

This isn’t pie-in-the-sky idealistic stuff. I can point to any number of practices in these courses, any number of topics we spend extra time on, any number of ways of approaching ideas that result from my listening to my students.

I have learned by listening what future elementary and special education teachers know and what they struggle with. I have learned what attitudes about mathematics and about themselves as learners of mathematics they bring to my classroom on the first day of class. And I continue to listen because there is always more to learn.

Which brings me to the second person I want to write to you about.

### Gary

Gary Knowles was the head of my teacher education program at the University of Michigan (he has since changed institutions at least once and I don’t know where he is now).

Gary made a huge impression on me because his practice was consistent with his professed beliefs about teaching and learning. As teachers, we often say to ourselves and others some form of the following, “I know my students don’t get it, but I don’t have time…” or “I know I should, but…”

These words would never pass from Gary’s lips. He knew that teachers need to think about their practice, to discuss with others, to problem-solve, to reflect. In effect, Gary knew that teachers improve their practice in large part through listening to themselves.

Everything else in our program followed from that core belief. We were trained to write reflectively, to question critically and to talk intelligently about our teaching.

Now, at the college level, our constraints are quite different. But the same principle applies to Gary and to me as it does to public school teachers. You need to identify your core values and you need to teach within the constraints of the system in which you choose to work.

As you know, I have tried to have an impact on your core values around teaching-not least by having you read Skemp. But for me, Skemp’s article is just a summary of a discussion we have had for a full academic year now. I have enjoyed it; I hope it has been meaningful for you.

I know you’re going to be a great teacher, Christina. Keep in touch.

Your colleague,

Christopher