Welcome to today’s online chat with President Cathy Seeley. Here’s our first question, which is from
Fort Worth, Texas
There were two incredible experiences beyond my working toward my master’s degree that stand out as improving my own understanding of content material. Being an elementary teacher can be very intimidating when participating in national programs, but the NSF/NCTM sponsored Geometry Seminar in the early 90s in Golden, Colorado was a phenomenal collaboration between teachers and professors of all grade levels. The Leadership Program in Discrete Mathematics helped me to gain a confidence in my own understanding of the math content I am teaching more than just about any other course I can recall. I would love to see NCTM and NSF team up again to offer elementary teachers programs similar to these.
Thanks for this reminder. I think this type of leadership development and personal/professional growth is exactly what NCTM and NSF should be about. Let’s hope we can create opportunities at least this powerful in the future.
Albuquerque, New Mexico
I definitely agree that working to be the best teacher one can be is the only way to keep above the muck that is the result of No Child Left Behind and the general atmosphere towards education these days. The thing that has helped me the most is talking to other teachers about our teaching. A weekly study group or math teaching class, which I had the opportunity to lead through our teachers union, does so much good. We learn from each other, stay focused and enthusiastic about our jobs, and feel reinforced that what we’re doing is important yet difficult work.
What a great model for ongoing professional learning. It sounds like a combination of professional growth and group therapy! I think we have to look for opportunities to learn and grow and reinforce our best thinking, and not get caught in negativity when there are pressures to operate in specific ways. Thanks for sharing this model that any group of teachers could implement.
Yes, many of us formed a learning community that not only developed our mathematics teaching skills but provided us with an opportunity to develop, write, and train other mathematics teachers. Dr. Dorothy Strong created a pool of mathematics leaders who became administrators with terminal degrees. We continue to meet and share ideas even though some have retired or moved on to other geographical areas. Our lifelong commitment to mathematics education is evident in our daily lives.
Thanks, indeed, to Dorothy and other visionaries who push us to make more of ourselves and connect to each other. As we move toward reaching our potential, we greatly increase the likelihood that we can help students reach theirs. Collectively, we can accomplish great things! (Incidentally, Dorothy has not only created a learning community in Chicago, but she has also participated in shaping the landscape at NCTM and across the nation.)
I am currently a student teacher, so my experience is not extensive. But I recently read Ginsburg’s book on flexible interviewing, and I have to say it’s made a major impact on my students. Today, for instance, a second grade student was in tears trying to borrow, despite the manipulatives she had. Ginsburg popped into my mind, and as we dialogued, it became clear that she was using the manipulatives with absolutely no understanding of place value! In about 15 minutes’ time, she was on track and smiling. WOW!
This is a terrific example on a number of counts. First, it is so important for teachers to help students make the connection between the activities they do (especially with hands-on materials) and the mathematics they represent with the materials. This is a sophisticated process that takes knowledge and expertise. It is far more than telling students, “Here is the rule, now model it with these tiles.” Rather, it is about helping students see relationships and processes and eventually move toward formalizing them with numbers and symbols.
Even more important, though, was your personal interaction with this student. You talked and listened and you found where she was stuck. This allowed you to make an efficient teaching decision to give her the experience she needed right when she needed it. You may just be starting out, but you have learned a lesson about the importance of listening that will allow you to become an excellent and effective teacher who can make those critical ‘just-in-time’ decisions for students.
Last February I began a journey to gain Rank 1 status by completing a CEO (Continuing Education Option) program. We’ve had few opportunities provided in our district for math professional development. This is a need in our school and district. I haven’t had the enthusiasm for (primary) math that I have had for (primary) language arts. This program made me look at myself and find the professional development I needed. I have joined NCTM and have explored the Web site with all its membership features. I have used my journal Teaching Children Mathematics (along with archived articles), read several books, visited numerous sites, and started a group that has studied Learn Math: Geometry, an Annenberg online course. I look forward to other online courses from NCTM as well. Learning as a student again has opened my eyes to how relevant math is for me and my students. Working with colleagues to further our math curriculum expectancies has been a benefit to the students and faculty.
What a great story to motivate other elementary teachers! Your journey is a great example of becoming the Best Math Teacher You Can Be. We benefit both from the individual learning and from being part of a community learning together. As you become increasingly more knowledgeable and experienced, your needs will also evolve. NCTM will continue to look for ways to meet your needs all along this wonderful career adventure you have undertaken.
Why are the teaching principles in the standards so hard for teachers to use? Throughout history, we have heard from “student centered” philosophers, from Socrates to Montessori, to Dewey, to Bruner, to ..., yet we still don’t get it. For example, back in the dark ages (the 1960s when I began teaching) I believed that understanding the principles that underlie algebraic tasks was far more important than procedures for carrying out the tasks. As a typical lesson on, say, factoring I began by having students find the factor of 6 or 10, or some trivial integer. Then I asked if they could find the factors of something like 91 or 221, and offered no help. They “played” and eventually “guessed” the correct factors. My question was simply “How do you know?” The answer was obvious— multiply the factors. After that, for the next week or so we simply “played” at finding things that “multiplied” to get the answer. (They had just finished the chapter on multiplication of polynomials.) I had no rules for positive or negative symbols, trinomials, binomials, common monomial factors, etc. The only rule was “If you multiply and get the given expression, you ‘factored’ it. Way to go.” Now this is not a major reconstruction of the curriculum, it is simply letting kids figure it out. How well did it work? Honestly, my kids generally did better than the other algebra teachers who had to “show” all of the dozen or so cases, leading coefficient “1,” common monomial factor first, difference of squares, and on and on. Nonsense. Kids worked out most of those themselves. They even factored x^3 - 1, when I gave them a hint that = x - 1) is one of the factors.
I know I am preaching to the choir, but why is this so difficult for teachers to do? I believe that NCTM is right on target with what should be done in mathematics classes across the country, but what we don’t have a handle on is how we can get teachers (the 90 percent who don’t adhere to the principles) to buy into it.
I will be retiring in about 9 months, but frankly in my 40+ years in mathematics education, it is still not much different today than it was in 1962.
Thanks for this reminder that sometimes “back to the basics” can mean going back to what we have always known about effective teaching. Indeed, asking students to think, justify, explain, and reason has always lay at the heart of the best mathematics teaching. I join you in asking why this seems to be both championed and argued about as we advocate the kind of teaching that helps students learn for their future. “How do you know?” is simply one of the best questions math teachers have asked for years.
And thanks for your incredible commitment of 40 years! I’m confident that we can continue to increase our effectiveness, individually and as a profession.
Wonder and imagination are magnificent motivators. I have often asked new teachers where the wonder is in their next lesson. Often they haven’t thought about this deliberately and it changes their perspective. Of course, I also have to remind myself at times to articulate this to myself as well. Most teachers know that when we engage a student’s sense of wonder it is magic. I’d be interested in a forum that shares how teachers awaken such wonder in mathematics.
These are such important elements that can get lost in an environment where the emphasis is on teaching a list of objectives or getting ready for the test. I think it’s tremendously important to encourage teachers to focus on wonder, imagination, and creativity in their teaching and in students’ learning. I believe there are ways to foster these traits while still helping students meet accountability standards. We can surely explore ways for teachers and others to exchange ideas about this and other topics. Thanks for this reminder!
Following are three questions that were submitted in advance that Cathy will answer together:
Lake Elsinore, California
I relocated from the San Diego area this year, but have continued in a wonderful Math Specialist Certificate program sponsored by San Diego State University and the Qualcomm Corporation. A combination of 6 units of math pedagogy courses and 6 units of hands-on math designed for teachers of upper elementary and middle school students, this program focuses on helping students construct their own meaning in mathematics. Activities and concepts by respected math experts such as Burns, Fosnot, Van de Walle, Cathcart, and NCTM make this program rich in practical math application and technique for teachers. Opportunities to reflect and collaborate with other math colleagues are also key. I highly recommend this program to anyone in the San Diego area or surrounding cities. This year, a primary grades program was also launched. Both of these programs are overseen by the Professional Development Collaborative.
The most enriching experience I have had and continue to have is my relationship with the Developing Mathematical Ideas program through Mt. Holyoke. The quality of the program as well as the opportunities to explore my understanding of mathematics with other professionals from all over the United States makes for a most profound and rich learning environment.
I just want to say if anyone has an opportunity to take DMI (Developing Mathematical Ideas), take it. You’ll improve your own math content, get a window into student thinking around important mathematical ideas, and improve your abilities to facilitate mathematical ideas and concepts in your own classroom.
You’re in good hands with both of these programs (San Diego State University and DMI). These are great examples of the kind of program that can help teachers grow in their own knowledge and also become more effective as teachers. Thanks for sharing.
I think a big part of creating wonder is to have a genuine interest and fascination with the world around you. When you are personally amazed or impressed with something yourself, it’s not a big jump to share that amazement with your students!
I agree with you. One of our challenges is to find ways to keep that genuine interest and fascination with the world alive for us as educators. Looking for opportunities like the study group in Albuquerque or other types of collegial exchanges can help with that if we focus on real growth.
The best professional development for me has been working with my colleagues as we implement a standards-based curriculum and learn more about how students make sense of mathematics. As a “coach” for mathematics teachers, I have been lucky enough to work with teachers who are always striving to do better, and who have found that if we all work together, we can get so much more accomplished. The results, when students explain their thinking and engage in real mathematical discourse, are truly exciting.
This is a common theme—we grow by our own learning and by being part of a learning community. Often, working around a strong curriculum program can be a wonderful vehicle for learning mathematics and for expanding our repertoire of learning approaches. It sounds like you have a positive environment where teachers are supported in a variety of ways, including quality curriculum and the support of a facilitating coach. Thanks for sharing this model.
The two best math workshops I’ve experienced are: Ms. Ball’s Musical Ballpoints. She provides an active, engaging, hands-on, minds-on way to teach math following multiple pathways to learning. She integrates music, songs, charts, and cheers to teach from multiplication table to statistics—mean, mode, medium; how to use body parts to remember measurement table.
Deep Into Math workshop also provides a workshop and textbook. Pat Jones is a former college professor who now teaches math methods and techniques to elementary and high schoolteachers. She teaches also using multiple pathways to learning and learning styles that promote ways of problem solving other than merely or by rote just choosing an operation. She also promotes hands-on, minds-on learning and teacher collaboratively prepared materials. She opened my thinking of math and consequently that of my students to better perform in measurement, number relations, geometry, use of charts, and T table. Can you believe it? I had taught math for 15 years before learning the value of using a T table.
What now? I continuously need workshops on ways to increase students’ retention of concepts. Further workshops on brain research focusing on how we learn and retain information are always helpful.
Yes, I have been and am currently a part of a learning community working together to become the best math teacher I can be. That current community is the Orleans Initiative for National Board for Professional Teaching Standards.
These are more examples of learning experiences that allow us to broaden our perspectives on mathematics and on teaching and that connect us to other teachers. I’m pleased to see a community around the National Board for Professional Teaching Standards (NBPTS). This level of master-teacher certification is a strong move toward the public (and ourselves) viewing teaching as an important profession. Repeatedly, I have heard from teachers who have gone through this process that they have grown significantly simply throughout the process of preparing to submit their application.
My most valuable professional learning was with Don Maas, California, on “Maintaining Teacher Creativity,” which I have passed on to many teachers. And my students love the active participation.
This program is interesting, because it is a good example of a learning experience not just for mathematics teachers. While not targeting mathematics, it focuses on deep thinking, reasoning, critical thinking, and overall expanding our view of how learning happens. This focus fits very well with the direction of mathematics teaching and learning called for in NCTM’s Principles and Standards for School Mathematics. It sounds like this has been a good experience for both you and your students.
Oak Ridge, Tennessee
Teaching the Everyday Math program for grades K–4 over the past six years has provided me with professional growth in better understanding math, its instruction, and how children learn. It has opened my mind to the potential growth all learners have through differentiated instructional strategies, and I am most thankful for having had this experience and training on the job. No matter the textbook(s) I use in the future, I know I will be a much-improved educator due to those six years with EM (formerly Chicago Math, developed through the University of Chicago).
Several years ago, I was privileged to be on a math specialist team from my school system participating in a 3- year training provided by the state of Tennessee. If only more teachers could have experienced the K–12 work sessions, they would have walked away with a broadened sense of how important each grade level math teacher is to the successful growth of their students. Respect for every grade level math teacher became apparent through the required activities and events where elementary had to work side by side with secondary teachers. Elementary staff became aware of how very important their instruction is to building a strong mathematical foundation, and secondary teachers were amazed to learn how very much elementary teachers provide mathematically.
Working around quality learning materials can be a great focal point for learning together. I’m a huge fan of elementary and secondary teachers learning side by side. I think that we strengthen our articulation across the grades, and we also learn how a foundation is laid and where students are headed. Also, sharing a learning experience is a nice way to strengthen our view or ourselves as professionals within a broader learning community.
Our school was asked to pilot Singapore Math with little background knowledge and training. We planned as teams. We had staff meetings to share the mathematics at each grade level so we could all get a more vertical view. We modeled lessons for each other and discussed best practices. Every teacher and student learned new approaches and strategies for teaching and learning math. In time and with hard, focused work, teachers and students succeeded in implementing the Singapore Math pilot.
Often, implementing a new program provides a window of opportunity for teachers to work together around learning and teaching mathematics. The key is to seize the opportunity to ramp up how we teach, not just to put new materials in the classroom. There is no silver bullet in terms of a single set of materials that will solve our problems. But there is something close to a silver bullet that lies in teachers working together to improve how they structure learning for students. Thanks for sharing this experience.
Syracuse, New York
My most valuable professional learning has come from two sources: dialogue with peers and the NCTM Web site and its publications.
I would like to learn more about managing my classroom and my time in a way that allows my time at home to be mine. Also I would like to learn more from my colleagues by observing them in the classroom.
My district financially supports professional development.
I’m delighted (and not surprised!) that NCTM is one of your favorite sources for learning. And the recurring theme of working with colleagues appears as your other.
I strongly support visiting other teachers’ classrooms. When I was a district math coordinator many years ago, I worked for a visionary Assistant Superintendent who required all of us who worked with instruction to spend 5 days a year teaching for teachers in the district. It kept us fresh and reminded us just a bit of the daily lives of teachers. It also gave the teacher a day to visit other schools. Maybe you can pass this suggestion on up the line.
In terms of classroom and time management, this is a good topic to put on our radar screen for future professional learning through NCTM’s resources.
Thank you all for your participation in today’s chat. A complete transcript will be posted tomorrow on the NCTM Web site. Watch the home page of nctm.org for the date of February’s chat.
Thanks for sharing your experiences about learning and growing. As we move through 2005, we can predict the likelihood of more requirements and more pressures on teachers. Let’s keep focused on how we can keep learning and growing, both in terms of teaching and in terms of mathematics, so that our students can all learn high-quality mathematics that serves them well for the future. Good luck on being the best math teacher you can be in 2005!