How do I know that I'm right? Our ongoing quest to improve our teaching practice.
The rewards of effective discourse are many. Not long ago, I was observing students work out a problem together. When they finally "got" it, one of the students exclaimed, "We are so smart." Isn't that what we are striving for? Not "the teacher is so smart," not "they are so smart," but "we are." In that statement, I heard both confidence and community. Healthy discourse promotes these things. -- Cynthia Lanius, BRAP Project teacher
This quote exemplifies the reflection on teaching experienced by seven mathematics teachers from around the country who have been participating in Bridging Research And Practice (BRAP). We collaborated jointly and with researchers from the Math Forum to address the questions that so many educators ask themselves daily.
While mathematics is often thought of as the discipline of "the right answer," we are uncomfortable with this designation when it interferes with more far-reaching goals. We prefer to reflect and ask "How do I know I'm right?" as we assess our efforts to help students express their mathematical thinking, learn from mistakes, experiment
effectively, and pursue their mathematical interests. How does the important effort to "get the right answer" fit with these goals? How can we transform a student who asks "Is this right?" into one who reflects "Does this make sense?" and "Am I communicating my understanding effectively?"
Similarly teachers are always asking themselves whether or not they are "reaching" all their students. Teachers ask themselves, "Are my students engaged? Do my students understand the mathematical ideas? Are my students able to explain and justify what they know? Can they go beyond the answer? How can I help them develop confidence
to persevere? " In other words, teachers are always asking themselves, "Is what I'm doing in my classroom encouraging and supporting my students' learning mathematics?" or (echoing the student's question) "How do I know that I'm right?"
We are reminded that "Effective teaching requires continually seeking improvement." (PSSM, p.19)
In order to improve, we often need to step back from the classroom activity to look at our practice. This can be very challenging in the middle of a hectic teaching day. Professional development (inservice) sessions that attempt to provide this time to reflect, sometimes feel disconnected from our own concerns about what is going on in our classroom at the time. How do we make the link?
Through our involvement in BRAP the seven of us created a bridge between research into teaching and learning generated by the university and our own practice in the classroom. This joint research venture between The Math Forum, TERC, and Michigan State University supported our professional growth as we gained new insights and excitement about our chosen career. During the past two years we have shared rich mathematics problems and chose one of them to teach in our classes. We videotaped those classes and watched them together. We talked about our teaching, and read research articles and books, reflecting on their implications for our practice. We have worked together face-to-face and participated in conversations through email and virtual meetings. Pursuing questions that arose from our discussions, we have conducted research through our practice.
"Opportunities to reflect on and refine instructional practice…are crucial in the vision of school mathematics outlined in Principles and Standards. To improve their mathematics instruction, teachers must be able to analyze what they and their students are doing and consider how those actions are affecting
students' learning." (PSSM, p. 19)
This opportunity is open to all teachers through participation in BRAP's videopaper, Encouraging Mathematical Thinking: Discourse Around a Rich Problem. Project teachers who taught a similar problem in classrooms of various grade levels, filmed their students and reflected on their learnings in a web-based article that is an ongoing paper. Colleagues who are interested in using collaboration, communication, and reflection as tools for professional growth are invited to join in our conversation. There is a link to an online discussion from every page of the videopaper. In addition, we encourage professional development staffs and pre-service educators to encourage their participants to become involved in our collaboration.
We invite you to join us and teachers from other classrooms to deepen our understanding of mathematics, teaching, and learning. Our work together is a powerful model for professional development.
What we know is that the improvement of teaching is never finished, and we may never know we are "right," but collaboration, communication, and reflection on teaching help to make us effective teachers in the classroom.
-- Susan Boone, BRAP Project teacher
Judith Koenig, Boulder Valley School District, Colorado and
Susan Stein, Wilmington Friends School, Delaware