Translation? Here's the information on the September 21 to September 24 Annual Meeting of the K-3 Mathematics Program Teacher-Leaders hosted by the ExxonMobil Foundation and NCTM. Thanks to the work of the conference planning committee—Vicki Bachman, Virginia Bastable, Christopher Kribs-Zaleta and Sherry Rosenberg—the meeting promises to provide a wealth of opportunities for sharing, networking and learning.
This year's conference will be held at the ExxonMobil Downstream Headquarters in Fairfax, VA. Following tradition, the meeting will begin with two concurrent pre-sessions between 2:30 - 5 PM on Thursday afternoon, September 21. In one pre-session, Skip Fennel will lead discussion about "Critical Issues in Number and Operation" and Sherry Rosenberg will facilitate. Virginia Bastable, Deborah Schifter and Jill Bodner-Lester will offer the other pre-session, "Children's Thinking about Geometry, Measurement and Data," with Christopher Kribs-Zaleta as facilitator. The participation of all of these individuals is greatly appreciated.
In addition, the Foundation is pleased that the following presenters will join us: Ruth Parker and Patty Lofgren will lead the first session on Friday morning; Hyman Bass and Deborah Ball will present on Saturday morning; Tom Carpenter and Megan Franke will lead conversation on Saturday afternoon; and Doug Clements and Vicki Bachman will present Saturday's closing session. It is an honor that NCTM President Lee Stiff will address us at our formal dinner on Saturday evening, and engage us in an informal "conversation with the president" on Sunday morning as well. Joining Lee will be Doug Clements and Skip Fennell. Details about our presenters, their publications and their topics for the conference will appear in the July/August Intersection.
As usual, there will be opportunities for attendees to participate in breakout sessions led by a stellar cast. This year the Foundation is happy to have Sherry Beard, Susan O'Boyle, Casilda Pardo and Carol Brooks to lead us in conversation on a variety of topics. In particular, the sessions will allow opportunities for sharing what has come out of some of the mathematics specialist projects along with other ideas and activities that may be of help to projects. Please find details in the next issue.
If you've received an invitation to the meeting, but have not yet responded, please do so at your earliest convenience. Questions? Please contact Joe Gonzales at joe.e.gonzales@ exxon.com or Jean Moon at mbb321@ultranet.com.
Only the Name Has ChangedTo reflect last winter's merger between Exxon and Mobil, and the subsequent change in the Foundation's name, the listserv is now EXXONMOBILTNT. If you want to subscribe, here's how:
Send an e-mail message with the words subscribe EXXONMOBILTNT in the body of the message, not just on the subject line. The account from which you send your message will be subscribed to the list. Please address the e-mail to majordomo@math.byu.ed. After subscribing, you'll receive more information. Summer affords you a wonderful opportunity to find out what the conversations on the listserv are all about. Please join!
Anne Herndon and Holli Aflatouni—the folks who nurture the listserv and spark cyberspace discussions—will be facilitating a session about the listserv after dinner on the opening day of the fall meeting (Thursday, September 21). Please plan to bring your comments, questions and suggestions to that meeting.
Many thanks to Pat Baggett, department of math sciences, New Mexico State University in Las Cruces, NM for contributing this report about the success of an institute held there this spring. Ed.
On March 18-21, as a part of the New Mexico Collaborative for Excellence in Teacher Preparation, we held our Third Annual Mathematics Education Institute for university instructors involved in mathematics content and methods courses for prospective and practicing K-8 teachers. The Institute was held at New Mexico State University (NMSU) in Las Cruces. About 25 participants visited two sections of our K-8 teacher preparation courses, Math 112/501 (Fundamentals of Elementary Mathematics II) and Math 301/501 (Elementary Mathematics with Technology), involving a collaboration between K-8 teachers in the Las Cruces Public Schools and elementary education undergraduate students working in a mentor/apprentice arrangement. (Prospective and practicing teachers meet in a joint university class and try some of the units they do in the university classes with children in real classrooms.)
Institute attendees, some from as far away as New Jersey and Montana, participated in two days of workshops during which materials used in the courses were presented and distributed. They also visited classrooms of teachers taking the courses at times when materials from the courses were being taught in schools.
Karin Matray, Director of Professional Development for the Las Cruces Public Schools, gave attendees an overview of the School District and its 33 schools, and also led a tour of the Teachers' Center, where many professional development events are held.
Some attendees presented papers at a mini-conference, providing opportunities for sharing innovative mathematics education programs occurring at their home institutions.
We had a number of group lunches and dinners, where we introduced out-of-staters to the New Mexico state question, "Red or green?"
Each semester since fall 1995, the Department of Mathematical Sciences at NMSU has offered courses taken together by Las Cruces Public School teachers and university undergraduates in the elementary education program. The courses combine Math 111/112— required for preservice teachers—with a graduate course— Math 501—for K-8 inservice teachers. The courses present rigorous, challenging math content that is divided into modules containing material that can be used directly in classrooms. Inservice teachers and preservice teachers are paired together. Teachers use the material in their own classrooms, and preservice teachers go into the classrooms of their mentors to observe and even teach under supervision.
In spring 1998, a third partnership course began—Math 313/513— Algebra and geometry for K-8 teachers (sponsored by ExxonMobil). And in fall 1999/spring 2000 we offered a fourth course—Elementary mathematics with technology—sponsored by the New Mexico Commission on Higher Education.
In fall 2000 we will offer a fifth course—Mathematics and science with technology— sponsored by NASA.
Lessons in the partnership classes are built around projects that are meaningful to children and sometimes combine several topics from mathematics and science. Computation is done mentally or with a calculator or computer. Students usually work in groups, and communication is a part of many lessons.
We are developing these courses in collaboration with both the Las Cruces Public Schools and the NMSU College of Education, which now offers a mathematics teaching field for elementary education majors as well as a Master of Arts in Teaching with a specialty in mathematics for practicing K-8 teachers.
Materials for the courses come mostly from Breaking Away from the Math Book: Creative Projects for Grades K-6 (Baggett & Ehrenfeucht, 1995); Breaking Away from the Math Book II: More Creative Projects for Grades K-8 (1998); a third book that is in press; our web site, math.nmsu.edu/ breakingaway/, and other materials being developed and tested.
We plan a fourth Institute in spring 2001 and hope that readers of Intersection will attend!
Did you know that you can view all issues of Intersection from January 1999 to the present on-line at www. intersectionlive.org? Please visit, and let you colleagues and friends know, too.
Many thanks to new contributor Jennifer Kibler from Parkdale Elementary School in East Aurora, NY for contributing the first review below. The book was donated by Susan Ohanian, an author of several education titles. Ed.
Susan O'Connell's Introduction to Problem Solving: Strategies for the Elementary Math Classroom (Portsmouth, NH: Heinemann, 2000) is an excellent problem solving guide and resource for both new and seasoned teachers. Throughout the book, O'Connell presents eight different problem solving strategies, as well as assessment techniques and real-world problem solving ideas.
O'Connell begins by emphasizing the role of problem solving in mathematics. She states: "Problem solving is the reason we teach mathematics." Indeed, there are many skills that are to be taught and practiced daily in all classrooms. O'Connell doesn't suggest that teachers replace these lessons solely with problem solving opportunities but she does point out that, "Problem solving becomes both the starting point and the ending point to well-balanced mathematics lessons." In presenting lessons in this manner, students are introduced to a problem, are able to see the need to acquire a new skill, and are eager to apply the skill to solve the problem at the conclusion of the lesson. Beyond tips for organizing effective lessons, O'Connell provides teaching strategies for developing students' skills and attitudes leading to success in problem solving.
In Chapter 2, Guiding Students Through the Problem Solving Process, O'Connell provides a five-step problem solving checklist. This is a general checklist that students can follow each time they encounter a problem to solve. The first two steps guide the student to really understand the problem, become familiar with the information, and identify the question being asked. The last two steps require the student to check the answer and reflect on the process. Teachers will appreciate O'Connell's use of summary sentences after students have solved a problem. This strategy provides an additional "written check" of students' understanding of the problem.
Chapter 3 focuses on the assessment of problem solving. O'Connell emphasizes the role of ongoing assessment and provides teachers with great ideas for assessment using observation, holistic rubrics, and analytic rubrics (for assessing specific skills). She also suggests that students be given opportunities to reflect on their own problem solving.
In Chapters 4 - 12, O'Connell presents each of the following strategies: Choose an Operation; Find a Pattern; Make a Table; Make an Organized List; Draw a Picture or Diagram; Guess, Check, and Revise; Use Logical Reasoning; and Work Backward. These chapters allow teachers to take an in-depth look at each problem solving strategy. For each strategy, O'Connell provides ideas for student practice, student work highlighting the use of the strategy, and several classroom-tested tips. Readers will find that these tips and practice activities can be used at a variety of grade levels. O'Connell does a fine job of encouraging readers to have their students reflect on their use of the strategy and explain their thinking. She even provides questions that will encourage students to talk about their work. This type of classroom conversation benefits all of the students in the class. It also gives the teacher some insight into what the students are able to do and how they are processing the information being presented.
Chapter 12, Real-World Problem Solving, begins with this quotation: "The excitement of learning and applying mathematics is generated when problems develop within the context of a situation familiar to students."— Judith S. Zawojewski.
O'Connell explains that when students are presented with real-world tasks, they begin to see that problem solving exists far beyond the classroom. She gives ideas for using real data from menus, travel brochures, the newspaper, and numerous other resources. For each resource, she suggests a variety of uses. These activities even include many options for open-ended problem solving.
In the final chapter of the book, O'Connell challenges teachers to accept the challenge of ensuring that problem solving is "the central focus of the mathematics curriculum." Appendixes A through I provide many resources to help any teacher apply the strategies and teaching tips presented in the book and to meet the challenge presented in the final chapter. O'Connell has provided problem solving checklists, key concepts posters, an observation checklist, assessment tools, pinch cards (for student response), strategy icons, practice problems (for each strategy), real-world problem solving resources, and a parent letter listing tips for helping children get "unstuck."
What more could one ask for in a problem solving guide and resource? After reading O'Connell's book, one doesn't need to go elsewhere to find charts and checklists to apply the strategies that are presented here. Everything has been included in this teacher-friendly book. I would recommend this book for individual teachers, as well as for teacher discussion groups and schools looking to build consistency from one grade level to the next.
Jean Moon contributed the review below. Many thanks, Jean! Ed.
"It is teaching, not teachers, that must be changed," and it is on this premise that Jim Stigler and Jim Hiebert develop the ideas contained within their book, The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom (The Free Press, 1999). Content for these ideas came from the video study of eighth-grade students contained within the Third International Mathematics and Science Study (TIMSS). The video study compared the teaching of eighth-grade mathematics in Germany, Japan, and the United States. Hiebert and Stigler worked together on this video study. What became apparent to them in the process of viewing and analyzing these tapes were noticeable "gaps" in general methods of teaching mathematics across the three cultures.
The authors quickly assert that their book is more than another litany of praise for the merits of Japanese education. Rather, they make the case that this is a book about the deficiencies of American teaching methods and the prospects for improving those methods. They state, "In our view, teaching is the next frontier in the continuing struggle to improve schools. Standards set the course, and assessments provide the benchmarks, but it is teaching that must be improved to push us along the path to success." To this end, the authors draw on a quote from Jerome Bruner (The Culture of Education, 1996):
"It is somewhat surprising and discouraging how little attention has been paid to the intimate nature of teaching and school learning in the debates on education that have raged over the past decade. These debates have been so focused on performance and standards that they have mostly overlooked the means by which teachers and pupils alike go about their business in real-life classrooms—how teachers teach and how pupils learn."
So what do Stigler and Hiebert report as the lessons learned from the TIMSS Video Study that sets the stage for their book? In addition to the "teaching, not teachers" focus, they note two others:
What are the main cultural differences among these three countries when it comes to teaching mathematics? The authors write:
"Our impression is that teachers in Germany are in charge of the mathematics and that the mathematics is quite advanced, at least procedurally. In many lessons, teachers lead students through a development of procedures for solving general classes of problems. There is concern for technique, where technique includes both the rationale that underlies the procedure and the precision with which the procedure is executed.
"In Japan, teachers appear to take a less active role, allowing their students to invent their own procedures for solving problems. And these problems are quite demanding, both procedurally and conceptually. Teachers, however, carefully design and orchestrate lessons so students are likely to use procedures that have been developed recently in class.
"In the United States, content is not totally absent, but the level is less advanced and requires much less mathematical reasoning than in the other two countries. Teachers present definitions of terms and demonstrate procedures for solving specific problems. Students, in turn, are asked to memorize the definitions and practice the procedures.
Stigler and Hiebert use three geometry lessons, one from each country, as confirming evidence to their descriptive generalizations. They offer a fairly detailed picture of teaching in each country by overlaying a common set of indicators onto each lesson:
No surprises here. In the context of these lessons, U.S. students encountered mathematics that was conceptually less advanced and fragmented. The authors conclude that because U.S. students do encounter less-challenging mathematics, presented in a less-coherent way, they must work harder to make sense of it than their peers in Germany and Japan. In terms of how the content is presented, a somewhat different picture emerges. Students in Germany and the United States, more often than in Japan, learn mathematics by following what their teacher does, either through questions posed by the teacher or by following the teacher's directions and then practicing a procedure.
In Japan, a somewhat different picture emerges where there appears to be more of a balance between teacher-directed and student-directed lessons. Students can be asked to work creatively to solve problems, and at other times, the teacher is in control of the progression of those solution strategies.
While Stigler and Hiebert discovered similarities in how lessons were organized in one culture, they also found significant differences in how lessons were organized across the three cultures. For example, in Japan and Germany, while classes were often organized around a problem of the day—just as in the United States—Japanese and German teachers rarely moved into demonstrating how to solve the problem. In the United States, it appears routine for the teacher to introduce students to a new or related mathematical idea by demonstrating how to solve the problem in a stepwise progression. By contrast, German and Japanese students work in groups or independently to develop the solution procedures. Near the end of the class these solution procedures are discussed and opportunities to practice similar problems can occur in class or through homework. Moreover, Japanese lessons—in contrast to American and German lessons—are distinguished by the time taken by the teacher— sometimes at the beginning, and almost always at the end of the lesson—to summarize the key mathematical ideas.
This cultural sameness in the progression of mathematics lessons is labeled "culture scripting": People within a culture share a mental picture of what teaching is like and act accordingly. Stigler and Hiebert comment, "The scripts for teachers in each country appear to rest on a relatively small and tacit set of core beliefs about the nature of the subject, and how students learn, and about the role that a teacher should play in the classroom. For example, the majority of U.S. teachers interviewed in this study (61%) described skills they wanted their students to learn; the goal is to perform a procedure and, as a consequence, solve a particular kind or class of problem."
By contrast, Japanese teachers report being guided by a belief that the primary goal in mathematics is to have their students understand the relationships among mathematical ideas. Moreover, for these teachers it is important for students to not think about solving problems using a single method. What contributes to these cultural differences, especially between the United States and Japan where such differences are most pronounced? In response, Stigler and Hiebert suggest four factors as contributors to these differences—beliefs about how learning takes place, the role of the teacher, individual differences and sanctity of the lesson. Below is a comparative example focused on sanctity of the lesson.
United States: Activities within lessons contain few conceptual connections between them or lack explicit attention to available connections. Because learning procedures is believed to depend largely on practicing, interruptions to lessons are not necessarily seen as injurious to student learning. Stigler and Hiebert report finding that almost a third of the U.S. mathematics lessons observed contained some type of interrupting event.
Japan: Mathematical lessons are planned as completed experiences. Much like a story, they have a beginning, middle and an ending. There is significant emphasis given to the coherency of a lesson, attention given to transitional points and points of summary. Lessons are not interrupted by lunch counts or P.A. announcements.
Thus far this book may sound to you as typical—you have heard much of the same content in different ways and in different contexts. Don't give up yet! This book does a good job of exploring the idea of teaching as a hard to change cultural activity. First, cultural activities are complex with connecting tentacles that go many places. Second, cultural activities are embedded in the larger culture, both in and out of the world of schools, in ways not readily apparent—the sense of we can't change what we what don't know. The more widely-shared a belief is, the less likely it is to be questioned, or even noticed.
Toward the end of the book, then, the authors get to the heart of it all as they make a comparison between how the concept of reform is situated to work in each country. Whereas U.S. educators have sought major changes over relatively short time periods, Japanese educators have instituted a system that leads to gradual, incremental improvements in teaching over time. In the process, Japan has handed over to teachers the responsibility for improving classroom practice. Kounaikenshuu is the word used to describe the continuous process of school-based professional development that Japanese teachers engage in once they begin their teaching careers. In contrast to freshly graduated U.S. teachers who are asked to teach "reform-minded" mathematics instantaneously, the consensus in Japan appears to be that teaching is an ongoing process of research, collaboration, and practice. Participation in school-based professional development groups is considered part of the teacher's job in Japan. One is not expected to arrive as a teacher knowing it all, or for that matter, knowing it all in the course of a decade or more of teaching.
And as many of you know through your own reading, the organizing framework in Japan for professional development is the study by groups of teachers of mathematics lessons. In lesson study, groups of teachers meet regularly over long periods of time, from several months to a year, to work on the design, implementation, testing, and improvement of one or several "research lessons." As Stigler and Hiebert report, the premise behind lesson study is simple: "If you want to improve teaching, if you want to change those deeply rooted cultural scripts that too often guide classroom practice, then, the most effective place to do so is in the context of a classroom lesson."
The authors go on to describe in detail the lesson study process in mathematics, frequently noting that one of the keys to the success of this method is the time given to it. Another ingredient to the success of lesson study is the opportunity it provides to work with colleagues to develop a shared language for describing and analyzing classroom teaching, and to teach each other about teaching.
This book ends by exploring the realities for incorporating a similar professional development practice among teachers in the United States. Is it possible? I am not one practiced at giving away endings, so if your interest in this book has been piqued, I will let you find your own way to answering this question. During the meantime, let me say that I certainly did find value in this book because it explores a question that has guided my own thinking and writing for over a decade. What are the core behaviors that make up the profession of teaching? As Stigler and Hiebert so perceptively state in their book, "Perhaps it is ironic that professional status for teachers will come only when the focus shifts away from teachers and onto teaching." The book would make a good addition to a study group contemplating taking on the lesson study model. It is my understanding that the ExxonMobil project in Bellevue, Washington, did just that. If you are interested in what went on in Bellevue around The Teaching Gap, you might contact project director Cathy Allen.
Thanks to Carne Barnett at WestEd for sending the information that follows. Ed.
- What do teachers say about case discussions?
- "What you get is everybody's input into what they see, what the situation means, and, most important, how to change the situation to help a child learn."
"We are constantly talking about empowering teachers. I think this is a great way to do it."- What does this seminar offer?
- The cases are about real classroom situations and include dialogue and student work. You will begin by discussing cases on fractions and decimals, and then learn how to use the same techniques and skills to examine a primary grade case. Please read about our project in the January issue at www.intersectionlive.org.
- What will participants learn?
- You will learn: to examine the math, student thinking, instruction and language in a case; how cases are facilitated; to practice the techniques if you volunteer; and how to introduce cases to others.
- What are the details?
- Option 1, August 2 - 3, Learn about cases and facilitation. Cost, $350. Option 2, August 2 - 4, Learn to introduce cases to a new group. Cost, $450. Classes will be held in the WestEd office in Oakland, CA, across the bay from San Francisco. To receive a brochure and/or more information, please contact Angela Sackett by phone at (510) 302-4253 or by e-mail at asacket@WestEd.org.
To register, please send your name, address, phone and fax numbers, and check (made payable to WestEd) by July 10 to Carne Barnett, WestEd, 300 Lakeside Drive, 18th floor, Oakland, CA 94612. Reach Carne by phone at (510) 302-4206; by fax at (510) 302-4354 (fax); or by e-mail at cbarnet@ WestEd.org.
Summer means resting, relaxing, reclining, rejuvenating, rejoicing, renewing, reviving, recharging. Can it also mean reflecting, rewinding, researching, recapping, and reporting? You bet! Reaching readers reaps rewards!
Replies respectfully requested. Please send contributions by Wednesday, July 12 to crazy-with-the-heat editor Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; phone, (512) 869-1580; fax, (512) 869-8477; e-mail, jean@intersectionlive. org.
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