Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Mathematics: What's the Big Idea?


– Cathy L. Seeley/Austin, Texas

Real teachers in real schools face real challenges implementing the numerous standards and recommendations for mathematics teachers today. Many teachers reading the National Council of Teachers of Mathematics' (NCTM's) Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) get excited about the possibilities for new kinds of instruction just as they are also bogged down by the overwhelming expectations about how they should provide that instruction. Within the complex description these two volumes provide about what teachers should do and how they should act, ten basic metaphors seem to emerge about new teacher roles. Some of these roles may feel fairly comfortable to some of you, and other roles may remind you just how hard it is to live up to you own ideals as a teacher.

  • The teacher as architect: Architects create the environment in which we live and work-both the buildings and the feelings they evoke. Similarly, the teacher as architect creates the learning environment for students. From the arrangement of furniture that facilitates discussion, thought and exploration, to the feeling students experience when they walk into the classroom, the teacher establishes an atmosphere where mathematics and learning are important. Most of all, the teacher creates a place where students feel safe to take risks and share ideas, while learning to value the opinions of each other.

  • The teacher as composer: As a composer creates a musical score for performance by musicians, the teacher creates the tasks in which students will engage. Within the rich environment created by the teacher as architect, the teacher as composer designs or selects something for students to do that will engage their intellect, stretch their thinking, increase their mathematical understanding, and expand their toolkit of how to solve problems in their real world.

  • The teacher as movie director: Once a teacher creates the learning environment and develops the tasks on which students will spend their time, the teacher as movie director steps in to determine how the actors will relate to each other, their tasks, and their environment. The idea of discourse includes questions like: How will students interact with each other as they go through an activity? What will the teacher do or say with students? What questions from the teacher can push a student's thinking just a little farther? What kinds of communication can really help a student develop mathematical understanding? These elements of discourse provide a foundation for student's reflection and communication that can lead to the power of making generalizations and reasoning mathematically.

  • The teacher as stockbroker: Much as a stockbroker constantly analyzes the stock market, the teacher as stockbroker constantly analyzes the teaching and learning that occur within the classroom. What worked today and what didn't work? What will I do differently next time? What is worth the precious investment of my students' time tomorrow?

  • The teacher as ship captain: When captains of large ships have set a course, they cannot afford to sit back and wait until they either arrive at their destination or crash on the rocks. Ship captains must constantly be alert to shifts in weather, ship traffic, and coastlines, and they must be prepared for unexpected disasters. The teacher as ship captain deals with even more unpredictable factors than nature and commerce and must constantly be evaluating how and what students are learning. We cannot afford to wait until a student crashes on the rocks before noticing a pupil has veered off course. Rather, the teacher must work closely enough with students so that s/he is providing ongoing course correction whenever misunderstandings begin. The teacher as ship captain may not always correct the student directly or immediately, but rather, the teacher makes a decision about what kind of experience can help the student to get back on course in a meaningful and timely way.

  • The teacher as mayor: NCTM's standards describe the mathematics classroom as a mathematical community, where students and the teacher are actively involved in creating their learning experience. This learning community needs the strength of a knowledgeable and compassionate leader who considers the needs and talents of the student-citizens, while providing a vision of where the community is headed and support for getting there. Giving students responsibility for their own learning means giving up some control and creating a new kind of classroom leadership that truly guides, encourages, and enlightens along the way.

  • The teacher as the red jacket: A traveler making a long trip is likely to pass through an airport hub like Atlanta, Dallas, Chicago, or Denver. In these hubs, hundreds of planes land and take off and thousands of travelers make connections between flights every day. The teacher can serve the role of the person wearing a red jacket who greets the weary, confused and distracted traveler to assist in making connections. The teacher as the red jacket helps students experience the rich connections between the threads of mathematics like algebra, probability, measurement and geometry. The teacher as the red jacket helps student see the connections between mathematics and science, social studies, physical education and the arts. And most of all, the teacher as the red jacket helps students make the vital connection between mathematics and the world outside of school.

  • The teacher as student: Nowhere is a commitment to lifelong learning more important than in teaching. Even if every teacher today were completely knowledgeable about teaching standards-based mathematics, using current technology, and understanding new fields of mathematics, within six months or a year or two years, there would be a new need for professional development. Today's teacher cannot afford to remain static for more than a short time when the world is in a state of dynamic flux and we daily witness changes in technology, mathematics, schools, students, and society. In this setting, the teacher as student makes a lifelong commitment to professional development.

  • The teachers as recruiter: Mathematics teachers have traditionally done a good job of encouraging students to pursue mathematics-related fields. Encouraging students to become mathematics teachers, however, has often been something we are reluctant to do, especially for our favorite students (or those we are related to). We sometimes communicate that teaching isn't as worthy a profession as other more lucrative options. If teaching isn't now a career worthy of our future adults, it is our responsibility as professional educators to transform it into something that is. The responsibility of the teacher as recruiter is to communicate not only to students but to the broader community how important and rewarding our profession can be. The ideal of teacher as recruiter is reflected in an experience shared with me by Kathleen, a teacher who recently received a Presidential Award. As she stepped down from the platform after her statewide award ceremony, she felt a tap on her shoulder and turned to see her former high school mathematics teacher. Kathleen shared with her former teacher that she was the inspiration for Kathleen choosing a career in teaching. As they were hugging, Kathleen felt a tap on her other shoulder. She turned to see a former student who told Kathleen that Kathleen was her inspiration for becoming a teacher. We can all truly hope that the torch will continue to be passed from generation to generation so that some of our finest minds can continue to prepare new generations of students who can think and learn mathematically.

  • The teacher as prospector: This is the bottom line of teaching. Picture the scene: You're in a cave. It's dark, damp, musty, and cold, and you are surrounded by solid rock, with nothing but a dim bulb on your helmet and a pick-ax in your hand. But in the face of this bleakness, you keep chipping away and chipping away and chipping away, because you know that somewhere deep inside that solid rock are some incredible uncut gems and some well disguised nuggets of high-grade ores. That's why you became a teacher. That's what keeps you teaching when new expectations seem unattainable.

Permission granted by the author to reprint with credit for non-profit educational purposes. Cathy Seeley, Austin, TX, copyright © 1994.

Mathematics: What's the Big Idea?


© Annenberg Foundation 2017. All rights reserved. Legal Policy