Bob Witte, Irving, Texas
Many thanks to all of you who contributed such thoughtful and eloquent reflections about your experiences at the conference. Ed.
The NCTM Annual Meeting in San Francisco was my 24th consecutive conference. I feel very fortunate to be a part of a very wonderful family of mathematics educators, and to be a part of the EXXON family in particular. I attended very excellent presentations, and I would like to reflect on what was most meaningful to me:
As a member of the Association of State Supervisors of Mathematics, I attended the ASSM sharing session where each state leader told of the state's progress. What I heard was encouraging in what many consider difficult times (math wars, mathematically correct, back to basics). The participants were eloquent about their battles with superintendents, administrators, parents, legislators. They were concerned about test results driving decisions, including textbooks. However, we also heard about their tenacious efforts to improve mathematics education in their states and their successes (they take time and we have to be patient). There were many initiatives described that support what we believe: meaningful mathematics for all children, taught by caring and knowledgeable teachers. A promise of good things to come. (For example, the Portland adoption is one of those good things!)
Among my ASSM colleagues, I also sensed strength and conviction: we will "fight" for what we believe. In some of the NCTM and NCSM sessions, the same message came across. Let's be on the offense, not on the defense.
The most important piece of the conference for me was being together with my math family from all over the country. It reaffirms my sense of community, of belonging, of knowing that we are many, and that we stand and work for the best education for our children.
There was one more thing I learned that I will share because it was so neat. My own talk was on K-6 Measurement. When I arrived in SF, I realized that I should include something local in my talk. I did some research, checked with the SF Public Library, and found the total length of the cable used in the Golden Gate Bridge. It was approximately 80,000 miles long. Remembering that the diameter of the earth is about 8000 miles, and since the circumference is about 3 times the diameter or 24,000 miles, I found that the cables used on the bridge would have gone around the earth over 3 times. A nice connection in geometry. I also learned a lot more about the geometry in SF, including the steepness of the roads which are expressed in fractions. For example, some streets have slope 1 to 2 (1 unit up to 2 across)—they are killers! Others are 1/3. The national requirements for handicapped ramps is 1/12. That gives you a great application in comparing fractions.
Bob Witte, Irving, TexasThose of us who get to attend NCTM with the K-3 math specialist teachers have the privilege of being part of that large group—maybe 300 at a meeting such as this annual affair. We run into each other all the time, and that means we are not likely to get "lost" among the 18,000 or so other participants. I hope everyone who attends can be a part of some "family" like ours.
I am especially interested in the progress of reforms that improve instruction, and, thus, concerned about opposition to the NCTM Standards. It is possible, at the meeting, that I see what I want to see, but I do think the Standards are making progress and that some of the critics are quieting down (or losing interest). What I see is that NCTM leaders and teachers are devoting more thought to addressing parents and the public—and I believe, getting better at explaining all of this in ways that are easier to understand and more brief, so people will more likely listen.
In particular, I believe session 477, "Reform Mathematics vs. the 'Basics': Understanding the Conflict and Dealing with It," presented by NCTM director John Van de Walle from Virginia Commonwealth University, may be the clearest and most persuasive explanation I have seen. (Find it at: www.nctm.org/meetings/1999/Annual/Handouts/477.html. ) For example—about constructivism: "Construction requires tools. The tools children use to construct knowledge are the ideas they already have....They must call up those ideas that are relevant and use them to give meaning to the new or emerging or changing ideas that they are developing."
About why it is O.K. for students to explain to each other, but teachers should refrain: "...students will question their peers when an explanation does not make sense to them. However, from the teacher, the explanation is usually taken on faith—it comes from the Teacher!"
I had one of the most exciting NCTM conferences ever. I got to be on the program committee and we worked over 600 days on the conference!
When I started thinking about San Francisco two years ago, I wanted to contribute something very special. I looked back on my experiences as a part of FAME (Fellows for the Advancement of Math Education), a program made possible by an absolutely glorious NSF grant we received due to initial and then continuing support from the Exxon Education Foundation. A big part of the grant was our taking math content classes. As I thought about all the wonderful classes we had, one stood out very clearly in my mind. That class was the Math History class we took 5 hours a day for two weeks one summer following three classes of trigonometry, algebra, and geometry all mixed together. We worried whether or not we'd be prepared for a math history course, and many of us didn't know what a math history course might be about!
Florence Fasanelli, then of the Mathematical Association of America, was brought in from Washington D.C. to be our instructor. She brought us hundreds of hand-outs, books, and pictures. In addition, she had a gift for telling wonderful stories and getting us absolutely enthralled with math history.
Each day Florence would give us copies of nets taken from mathematicians' original works. Nets are the patterns that you use to cut out and make models of three-dimensional shapes. I don't know where the word "net" came from, but it is the word that mathematicians use(d) to describe those things. In our class, Florence always insisted on using copies of the actual nets created by the mathematician if she could find them in textbooks, history books, wherever. They were often quite small and could be difficult to work with, but it did make you feel connected somehow with the real mathematician.
In the session in SF we worked on nets made by Grace Chisholm Young. In 1905 she wrote a book on beginning geometry, The First Book of Geometry, that she used in teaching her own children. We used nets from that book at the session. Using copies of actual nets is one of Florence's very special touches that made math history come alive for me. Because they were always so tiny, we would laboriously cut out and tape the shapes. Florence would always insist that we leave the shapes on the tables. She'd insist that we leave our papers and pictures and notebooks on the tables, too. Our room and tables got to be awfully messy looking! We wondered why Florence would want us to make such a mess.
Then one morning Florence put a copy of an old picture (from the fifteenth or sixteenth century) on the overhead. It showed mathematicians around some very messy tables with papers and books and three-dimensional shapes. They were showing each other stuff in books and arguing and discussing. When I saw the picture and looked around our room, I realized the picture was us! We looked just like those mathematicians! And that was the very first time I ever thought of myself as a mathematician. It was a special moment I'll never forget.
I decided that the experience I had was one that other elementary teachers should have and I know it's one that very few ever do have. What better place to provide such an experience than an NCTM Annual Meeting? I contacted Florence to ask her if she'd consider doing a session on math history especially for elementary teachers. We decided a mini-course would be a good venue since you need a little time to really get into the math.
Florence planned and presented a lovely afternoon for us. One of my favorite parts was at the beginning where we learned how to interpret the formula for figuring the volume of a truncated pyramid from the original Egyptian hieroglyphics. Then we built pyramids and fit them into a cube and finally used the formula and some good mathematical thinking to figure out the area. So much fun! We made see-through Platonic solids with pipe cleaners in the fashion of Leonardo Da Vinci. We learned wonderful stories about famous mathematicians and we did great math. We truly became students of mathematics. What a pleasure!
Florence Fasanelli opened a wonderful world to me. Having the privilege of asking her to speak in San Francisco was one of the highlights of my serving on the Program Committee.
Anne Herndon, Fort Worth, TXThe very first session I attended—Learning to Listen to Children's Mathematical Thinking: Implications for Mathematics Instruction, presented by Cathy Grant and Ellen Davidson—dealt with courses where the focus is on becoming more sensitive to constructivist views of mathematics.
These courses were developed for administrators, rather than teachers, which I thought was an interesting twist. During this session, the distinction between developing practice and changing practice was discussed. I never really distinguished between the two ideas, but since that session have thought a great deal about the difference in helping beginning teachers or preservice educators develop their practice, and helping inservice teachers change practice. In my mind, both have very different challenges. I wonder if these groups need to be approached differently, or if the approach when working with these groups can be the same, and they'll take different experiences away?
I have no answers at this point, which reminds me of a quote we have hanging for floor staff in our museum, "An answer to the question is the bullet that kills the conversation," or, in this case, the thought process.
Because of Cindy's enthusiasm when she encouraged us over EXXONTNT to attend Florence Fasanelli's session, I did. Like Cindy, I was also enthralled by the experience of interpreting the Egyptian hieroglyphics to determine the volume of a truncated pyramid. The manipulation of the 3-D objects to further my understanding of how the formula was derived gave me a conceptual understanding of the formula that I had previously accepted just because I'd been told it works.
I immediately started thinking how I could bring it back to let my teachers experience the activity. Dr. Fasanelli's session also sparked my interest in the history of mathematics and mathematicians. Don't tell my daughter; she will tell me I need to get a life! I must be honest in saying that I have picked up books on mathematicians before and put them down. However, now I am curious.
Thanks to Cindy, I went to the session. It opened a new interest for me in the field of mathematics. The more I learn, the more I realize how much more there is to learn.
One session I attended, "'Got Math?' Identifying and Communicating the Mathematics Embedded in Integrated Activities," was very helpful in deciding if some activities provided meaningful math experiences. The speaker, Vena M. Long from the University of Missouri-Kansas City, provided us with questions to answer as we looked at three different activities: "Is there any significant math to explore?" "Will there be any learning taking place?" "Does this honor the equity issue (accessible to all students in some form)?" and, "Are there any inferences about math power that might be made given a student's response?"
The audience responded to the questions and made informed choices for rich math experiences. It became evident that the value of activities is often dependent on the locale of the students. And often students' individual interests led to a deeper investigation. In my opinion, having the questions to guide the choice of curriculum helps us focus our thinking.
There was a presentation at the Research Presession that was absolutely riveting to all who attended. Entitled "Beyond the Ivory Tower: The Politicization of Mathematics Education Research," the session featured, among other speakers, Bill Jacob talking about issues around "'Research Based' Mathematics Education Policy: The Case of California, 1995-1998, Preliminary Version," Bill Jacob, University of California, Santa Barbara and Joan Akers, Consultant, San Diego. Bill discussed his and Joan's paper, examining how one line of state law, stating that educational reform efforts must meet the further criteria of being research based, has been used by the California State Board of Education to direct policy in mathematics education based upon a narrow ideological view of mathematics learning, teaching, and research.
The paper provides background describing the state structures for setting policy, previous Mathematics Frameworks, the development of other documents and the adoption of instructional materials since 1995. The second section of the paper describes how the 'research basis' for the new Framework was developed and 'authenticated' by the State Board of Education. This includes summaries of a presentation by E. D. Hirsch, writings by David C. Geary (who became a major author of the Framework), a report funded by the Board reviewing mathematics education research, and reactions to the report by several groups. The third section discusses the influence on the Framework of the research basis and of mathematicians who contributed to the final draft. The paper ends with the authors' concluding remarks and an appendix which analyzes some of the research articles included in the Board-funded research report. This paper is a story with important implications for education researchers, policy makers, and classroom teachers. I have a copy of the report and would be glad to send it to anyone.
The NCTM Conference in SF was extremely valuable. However, to avoid the choices being overwhelming, I found it very helpful to go with just a few goals in mind. I wanted to get a sense of how the NCTM Standards were looking in classrooms across the nation. I also wanted to find more research to validate the powerful change in instruction and philosophy we are touting. The third idea I pursued was the success of teacher training. I found scores of courses that fit my menu and I was challenged, stimulated and encouraged to learn that we are on the right track. It will take a lot of work and commitment but I trust we will do it with respect and patience.
There is definitely an analogy to be made between sending a teacher to a conference such as NCTM's Annual Meeting and releasing a child into a candy store. The bad news is that with 1,212 sessions to select from, you're forced to make some tough choices. The good news is that you can hardly go wrong.
One of the Research Presessions I found especially engaging was "Parents as Mathematics Learners: Shifting the Focus of Engagement," presented by Amy Morse of the Education Development Center, and Liz Sweeney, a teacher in the Boston Public Schools.
Amy and Liz have offered for parents in both urban and suburban settings weekly seminars of between four and eight weeks in duration in an endeavor to engage parents in mathematical learning, have them appreciate the complexity of learning mathematics, help them understand how to support their children's mathematical learning, give them an opportunity to communicate about mathematics, and help immerse them in the language, content, and environment of reform classrooms. The researchers have used cases, videos, and student work in helping parents become more knowledgeable about what their children are learning.
Two of several questions the researchers investigated were: "What can we learn from listening to parents' own past school histories in regard to how they respond to current school reforms?" and "What happens when parents become 'learners' and have the opportunity to explore their own mathematical thinking?"
Amy and Liz read to us many of the dreadful experiences parents shared about the way they "learned" mathematics in elementary school. It was noteworthy that not one of the "histories" shared was positive. Emphasizing that when working with parents it is critical to remember that all parents have their own experiences with mathematics as well as their own insights, and that getting to understand those things takes time, the researchers also shared with us the parents' responses to an end-of-seminar evaluation, "What Have You Learned?" It was clear that the seminars had made a difference in the way parents viewed mathematics and children's learning.
You can read more about their work in "Learning to Listen: Lessons from a Mathematics Seminar for Parents" in the February 1998 issue of Teaching Children Mathematics. You may contact Amy at amorse@edc.org.
Charlotte Stadler, New Rochelle, NYOne session I attended was "The Character of Schools That Serve Poor Children Well," presented by Philip Uri Treisman from the University of Texas at Austin. In this fascinating session Treisman recounted his experience in identifying schools with high percentages of minority and low SES youngsters where the gap in performance between these students and middle class students is lessening or in a few cases even disappearing. He said that he has data which refutes previous claims that the quality of schools does not effect academic performance and that family income and ethnicity are the immutable determinants of academic success.
Evaluating academic performance in math primarily on the basis of NAEP data, he said that he and his staff have identified several schools and districts where the performance of disadvantaged youngsters is very close or even equal to that of middle class students. These schools, he said, are primarily in South Carolina and Texas, two states where the educational structure rewards schools that raise the performance of disadvantaged and minority students. He insisted that unless a state particularly demands that schools raise academic levels for this at-risk population, these students will remain at the bottom of the barrel.
In addition, he said that though he favors a more constructivist approach to math education, his research did not find that the type of math instruction or materials used were the primary factors in bringing about success for underserved populations. He said that in "successful schools" some classes were using reform mathematics and some were using Saxon. Similarly, in schools where students were doing poorly, some were using reform mathematics and some were using Saxon.
The primary factor leading to successful student performance, he said, was a school atmosphere where teachers worked in a collegial way and where teachers and administrators shared a determination that all students can learn and a commitment to making that happen. In "successful schools" teachers were given time daily to meet and plan together.
More information can be found at the Web Site http://www-tenet.cc.utexas.edu/ssi, "Study of Successful Schools."
I attended the session "The Role of Cases in Teacher Education" primarily to hear Virginia Bastable, Deborah Schifter and Susan Jo Russell talk about the Developing Mathematical Ideas (DMI) Institute. Other presenters for that session were Susan N. Friel, Carne Barnett, Alma Ramirez, Marjorie Henningsen, Margaret Smith, Mary Key Stein, and Katherine Merseth.
The workshop focused on the use of case studies in teacher education and I went to the elementary session. We looked at some case studies as we did at the Exxon conference when DMI was presented. The DMI material that is currently being published seems well put together and very usable for inservice training.
One of the most interesting new ideas I got from the session was presented (I think) by Deborah Schifter. She said that they had been successfully using DMI with preservice teachers at Mount Holyoke. Previously I had thought that using case studies like these would not be appropriate for teachers who had had little experience in the classroom. How would they have a clue about what question to ask next to help a child move to a higher level of thinking?
Deborah said that at Mount Holyoke several undergraduates had taken the course, not as ed majors, but just because they needed an elective. She said that the use of cases served to demonstrate to these young people that teaching is an intellectual pursuit, a thought many of them had not previously entertained. She told us that often after taking the course, these students decide to become teachers. Using this material was a way to attract bright young people into teaching.
I thought that this was a fascinating idea. So many bright college-age women think that teaching is something you do because the hours or vacation schedule is good or because you "love children," not because it will be a fascinating, intellectually challenging profession.