For the last time this century, the Exxon Education Foundation
hosted individuals from Foundation-supported projects across the
U.S. as well as others interested in the Foundation's work for
the eleventh annual meeting of the Exxon Education 
Foundation/NCTM Mathematics Specialist
Teacher-Leaders. Held in Exxon's Conference Center at corporate
headquarters in Irving, TX, the extended weekend of learning,
sharing and networking began with pre-sessions on Thursday
afternoon, September 16, and ended at noon on Sunday, September
19 with a session led by NCTM President Glenda Lappan.
Featured presenters were Nicholas Branca, Pat Wasley and Glenda Lappan. Joan Akers, Bob Callahan, Bonnie Tank, Bob Speiser and Chuck Walter presented and facilitated breakout sessions. Pre-sessions were led by Cathy Allen and Chuck Walter.
The agenda provided participants unique opportunities to hear and interact with presenters, visit with friends and colleagues, meet Exxon employees over lunch, enjoy Texas Bar-B-Q and fajitas, and dine like royalty at the traditional banquet. As usual, Exxon was the perfect host; meals, accommodations and arrangements were outstanding.
Summaries of the sessions follow, and you will find photographs from the meeting throughout this issue. A special "thanks" to Patricia Baggett for contributing some of the photos. Others were provided, as noted, by professional photographer Jim Reisch.
Deserving recognition for their work in helping plan the meeting are Nancy Cole, Evelyn Dixon and Beth Williams. Thanks go also to Bob Witte's secretary, Tamera Nelson, and to Phyllis Tackitt from support services, for so beautifully managing all the administrative details.
Presentations by GuestsExxon Education Foundation President Ed Ahnert welcomed meeting participants, saying that the conference is always "the highlight of the Foundation's grant-making year." Bob Witte and Pat Hess also expressed greetings, and then Carol Brooks from the Tucson USD was asked to introduce Nicholas Branca. Nick has recently been an advisor to Tucson's K-3 Exxon project.
Carol remarked, "Nick is a mathematician. Those of us who know him know that if we could hang around him long enough we could really go places."
Nicholas is a Professor of Mathematics at San Diego State University. Among other responsibilities and activities, he currently serves as the principal investigator of the K-12 Mathematics Renaissance and The Video Cases in Mathematics Project. From 1992-99, he was the Executive Director of the California Mathematics Project. (See July/August Intersection.)
The title for Nick's presentation was, "What mathematics do teachers need to know to teach children to know mathematics?"
He began by asking, "What does that mean—to know mathematics? The other question is, 'So what is mathematics?'" Making his point by jotting some numbers on a flip-pad and simultaneously stating the algorithm that governed what he did with them, Nick asked, "Was that a math lesson?"
Responses led to interesting conversation that was typical throughout Nick's entire presentation:
"What was it about?" asked one individual.
Another said, "It was just a representation with numbers. There was no understanding."
"It depends on the audience," someone remarked.
"No learning took place," said another.
"For me, it was a math lesson," commented one more.
"If mathematics has to do with patterns, then it might be," said someone else.
"It couldn't be used to make sense of anything," stated another.
Nick posed other intriguing questions for audience members: "What is a number? What would happen if the symbols for 2 and 3 were reversed—2 for 3 and 3 for 2—so that our sequence was 1, 3, 2, 4, etc.? Or what if 9 became 10, and 10, 9? How would we write 11? What would happen to place value?"
During Nick's presentation, participants also explored the concept of counting, talked about the Hindu-Arabic numeration system, discussed operations on numbers and properties of those operations, and engaged in thinking about how language and convention play such a part in teaching mathematics.
Nick's valuable session not only helped participants examine how they think about mathematics, but more importantly, how young children think about mathematics as they begin to develop number sense, learn to count, and do operations.
Saturday AMReturning to delight her audience again this year, Pat Wasley was insightful, engaging, and both serious and funny as she explored critical issues around the question, "How do teacher-leaders facilitate change?"
Formerly a teacher and administrator who has worked in the past on projects with both John Goodlad and Ted Sizer, Pat is currently Dean of the Graduate School of Education at Bank Street College in New York City.
Acknowledging that there are a variety of models for change, and that most are not working well, Pat began her presentation by suggesting a few reasons this is true. For one thing, teaching is an egalitarian profession. Another is that since change means evaluation, many find it threatening. Still another is that within school culture— although there is overt acceptance for change—change is still a covert activity. "Many teachers can't imagine change," Dr. Wasley said. "They have never seen it."
Speaking of what she learned in writing Stirring the Chalkdust, Pat remarked that in observing six teachers across the country for some years it was clear that for change to happen teachers had to be organized, bring in all stakeholders, build "colleague-ship," work within the school. As she did research for Kids and School Reform, she learned how critical it is that teachers be supported and given expertise as they "change their repertoire."
Pat led audience members through a
fascinating examination of pertinent major change theories of the
last fifteen years, including those of K. Loen; M. Fullan; G.
Hall and S. Hord; M. Bentzen; E.R. Saxl, M. Miles, and A.
Lieberman; C. Glickman; J. Goodlad. In particular, participants
expressed interest in Pat's presentation of Loen's
"force-field analysis" in helping individuals determine
priorities in their schools. Speaking at length about the
necessity of training people to engage in the holistic process
that brings school renewal, about the need "to undergird the
work of change with a set of ideas," and about the work of
engaging people in professionalism, Pat presented several models
that help make this happen. Before entertaining questions and
comments, she presented "Collected Wisdom About Making
Change," a compilation of what her research on change has
helped her learn. If you would like a copy of Pat's handout,
please contact me. Ed.
As she brought the session to a close, Pat referred again this year to "the tuning protocol," a useful strategy or tool to allow teachers to receive critical yet supportive feedback from peers. Visit www.essentialschools.org to learn more. Click on "Horace," and find Vol. 13, No. 2. Also at that site find The School Change Study by Dr.Wasley and her colleagues.
In parting, Pat said, "I am hopeful for your work, and I hope we see a change in math reform. Multiply your leadership capacity by one hundred, and go with gusto for the next round."
Sunday AMGlenda Lappan began a morning of informal conversation by bringing attendees up to speed on some of NCTM's endeavors and initiatives. In particular, she told audience members that the Principles and Standards for School Mathematics (PSSM) will be formally released at a press conference during the annual meeting in Chicago next April. "After all," she said, "it's for the membership; it's a document for us." Glenda added that there will be several "getting to know the document" sessions offered at the annual meeting.
Comparing the response to the release of the original Standards in 1989 with the response anticipated when PSSM is announced in April, Glenda quipped, "In 1989, no one was watching; no one cared. Now, the whole world cares."
In April, a print-copy and CD-ROM version of PSSM will be available to anyone for the price of NCTM membership. PSSM will also be accessible over the Internet. Glenda commented that the Addenda series for PSSM will come out more quickly than last time, and will probably be available for each grade band by 2001.
NCTM will soon have available "policy briefs" on calculators and on basic facts. Written in language that can be understood by parents, each will be illustrated by student work and list resources. Glenda also announced that this fall NCTM will launch "Figure This!" an initiative to help parents of middle-school students support their children in learning mathematics at school and join in "suppertime conversations" at home about mathematics.
Glenda's announcements about the work of NCTM began discussion on the new document as well as on a host of other issues. Near the end of the discussion—partly in jest, but mostly in earnest— various participants suggested "warning labels" that should appear on PSSM's front cover:
The discussion turned to professional development, and Glenda asserted that she hoped NCTM would find ways to "deepen the conversation among teachers." She has appointed a number of task forces to find more effective ways to make this happen as they develop, among other things, the contents for a "professional development toolkit."
Before Glenda had to leave, the group talked about assessment, and she mentioned that NCTM is drafting a policy brief on testing. Quoting a sage who said, "You don't fatten a hog by weighing it often," Glenda expressed disappointment with the "kind of assessment that never lets us know anything about kids."
Thanking Bob Witte and the Foundation for inviting her to our meeting, Glenda left the rapt audience with these encouraging words: "It's nice to know that you're worried about the kinds of things that I'm worried about." Indeed.
Group Sessions Two pre-sessions were offered on Thursday afternoon for those able to arrive early. Chuck Walter from Brigham Young University in Provo, UT, facilitated the session on pre-service education and Cathy Allen from Bellevue, WA moderated discussion about ideas from the Developing Mathematical Ideas (DMI) Institute.
In the session led by Chuck, participants discussed the complex issues arising from the question, "What mathematics should a pre-service teacher know?" The DMI session focused on how that model of professional development helps teachers work from and build upon children's understanding of mathematics and why the model is so powerful.
Following a Bar-B-Q buffet, Anne Herndon and Holli Aflatouni answered questions and solicited comments about our listserv that, thanks to Bob Speiser, makes its home at BYU. As EXXONTNT facilitators, Anne and Holli want to increase the number of subscribers, particularly classroom teachers. Reflecting on the session, Anne writes:
"One of the insights I gained [from the discussion] was the impact the stories of classroom teachers has on individuals on the listserv who are not working with children on a regular basis. An interesting group for me are the 'lurkers,' and many of the teachers on the list are lurkers. I think there is a great deal of value in listening to the conversations on the listserv, but the power that their stories have for others in the group is something I was not aware of until it was brought to the forefront in that conversation."
She continues, "Linda Coutts
brought up the idea of a safe place to share ideas and that has
stayed with me as has Sherry Rosenberg's thought that the
listserv has been an important resource for her in terms of
research-based information."
In her comments, Holli notes that someone suggested that current users personally invite teachers to subscribe and that another participant remarked that providing teachers with transcripts of recent conversations might move them to participate once they had been made aware of the depth and breadth of discussions. She also remarks that the suggestion was made that users who wished to initiate a discussion include the word "Discussion" in the subject line so that readers understand what's intended.
Here's how to subscribe to EXXONTNT. Send an e-mail message with these words in the BODY of the message: subscribe exxontnt. (You can put those words in the subject line of the e-mail for your own purposes, but you will not be subscribed unless they appear in the BODY of the message.) The account from which you send your message will be subscribed to the list. Please address the e-mail to majordomo@math.byu.edu. After subscribing, you'll receive more information.
Friday and Saturday PMAs in previous years, meeting attendees had the pleasure of dining with Exxon employees over lunch on Friday. This tradition is anticipated and valued by both guests and employees since it gives individuals a unique opportunity to learn more about one another in an informal setting. Following lunch, break-out sessions were offered on four different topics. The same sessions were also offered on Saturday so that all attendees had the opportunity to attend all four groups.
Joan Akers presented a session on the Learning Record Assessment System. This is a tool used to gauge student understanding of and progress in mathematics at five levels of performance. Originally developed for assessing student progress in reading and writing, the Learning Record Assessment System is based on a year-long collection of student work from multiple sources. It includes parent input as well as teacher observations. Joan shared a "Mathematics Understanding Scale" and a "Mathematics Disposition Scale," and participants tried out these tools to evaluate a student's work. To learn more, visit www.learningrecord.org.
In another session, Bob Callahan spoke
about his experience last year as "Teacher in
Residence" in the mathematics education department at Chico
State University, Chico, CA. Relating to the audience the
benefits that accrue from bringing together administrators and
teachers from the school district, individuals from both the
mathematics and education departments at the university, and
someone in the role of an elementary teacher in residence, Bob's
upbeat presentation had participants talking afterwards about how
their districts could duplicate that model. For details, see Intersection,
March/April 1999. 
A session led by Bob Speiser and Chuck Walter introduced attendees to a project they carried out with Kellie Freestone's kindergarten children at Liberty Elementary School in Murray, UT. Learning that Kellie's students enjoyed Tana Hoban's books of photographs featuring shapes, colors, textures, animals, etc.. (visit www.amazon.com for titles), Bob and Chuck purchased "disposable" cameras so that Kellie's students could snap and title photos of their own. As they shared slides of the children's photos, Bob and Chuck led a discussion about what the children chose to photograph, if or how they had composed their pictures, and what the photos might indicate about the children's understanding of mathematics.
Bonnie Tank spoke in her session about her experiences helping educators recognize what it is that makes a school ready for change, what it is teachers want for children in mathematics, and what elements have to be in place to make those things happen. Together with a colleague, Bonnie visits schools, talks with teachers, and identifies through a rating system three things to work on in improving mathematics instruction at their campus. Then the teachers take it over. As part of her presentation, Bonnie gave an overview of "Empowerment Evaluation," a program assessment model used for on-going evaluation and renewal in the San Francisco USD Exxon Mathematics Project. (See D. Fetterman et al, Empowerment Evaluation, Sage Publications, CA, 1996).
Each year attendees dine sumptuously at a banquet hosted by the Foundation in Exxon's own Granite Cafe. This year's menu starred herb-seared beef tenderloin and grilled Atlantic salmon. Kudos to Tony Smith, Director of Exxon's Conference Center and Director of Catering, and to Executive Chef Lorie Finkelman-Short for helping to create such a memorable evening and such an exquisite repast.
Foundation President Ed Ahnert welcomed guests to this "celebratory dinner" marking the eleventh anniversary of the K-3 Mathematics Specialist Program. He spoke about this year's achievements and the expectations for next year. Then he introduced NCTM President Glenda Lappan.
In her opening remarks, Glenda thanked
the Foundation for the opportunity to "...drop in on a group
like this, to be with people who are trying to make a difference
and who keep an eye on what's important—the children."
Elaborating further, she remarked, "Educational reform is
all about doing what good teachers have always done, connect with
kids."
Recalling the excitement and hard work that came with writing the original Standards "gathered on a mountaintop in Utah with some of the people in this room," Glenda reviewed the original goals and the effect they've had:
Glenda spoke from the heart about how mathematics educators should hold onto their intentions and persevere in spite of opposition. "Our fundamental commitments to a high-quality mathematics education is right. It's on target. We don't have all the answers, but we're continually seeking to do better."
Citing evidence that students are studying more challenging mathematics, that students are taking more mathematics in high school, that more states are developing comprehensive curricular frameworks for mathematics, and that standards for teacher preparation are much higher, Glenda said, "The direction we're moving in is a powerful one, and we are making progress." It was an inspiring and encouraging message.
As many of you know, at the end of this year Pat Hess will be
retiring as the Foundation's Project Facilitator, a position
she's held since 1989. In honor of the occasion, Ed Ahnert
surprised Pat with the gift of Tiger in the
Children's Garden: The Exxon Education Foundation K-3 Mathematics
Specialist Program, 1988-98. A compilation of stories about
various projects and people at Foundation-supported 
sites, the booklet was written by Susan Ohanian and
dedicated to Pat. She was delighted to receive it! A limited
number of booklets are available. Contact Bob Witte to request
one. Ed.
The inscription reads in part: "The Foundation gratefully acknowledges the many contributions of Pat Hess, who was Program Facilitator for the K-3 Mathematics Specialist Program from its beginning through 1999."
Another tribute to Pat was presented by Jean Ehnebuske, Jean Moon and Bob Witte. Gathered for Pat in two volumes were letters, cards, drawings, poems, works of art and other expressions of gratitude and friendship sent by friends and colleagues in Foundation-supported projects old and new, near and far, small and large. Here's Pat's note of thanks:
"I want to thank all the Exxon/NCTM K-3 members for the wonderful gift of memories you've given me. I continue to pick up a volume and reread an entry every day. It's like having an internal video of each project. I can see your school, I can see you teaching, and I can see your students. Thank you so much for such a living remembrance of my work with you." Pat
Many thanks to Chuck Walter and Bob Speiser for contributing the article below about their collaborative project with teachers in Albuquerque, NM. Ed.
This past spring and summer, the study group at Liberty Elementary School in Murray, Utah concluded its first year in the Exxon network by joining with teachers in the well-established Exxon project at Albuquerque, New Mexico to undertake a collaboration to help both groups strengthen classroom practice, mathematical understanding and approaches to assessment.
As a first step in establishing this connection, at the
invitation of Cheryl Brown-Kovacic, Albuquerque Public Schools,
six teachers from the Liberty study group traveled to 
Albuquerque in mid-April. They spent two days there
visiting classrooms, talking with like-minded teachers, and
joining with groups of Albuquerque teachers working to establish
benchmarks for assessments used throughout the Albuquerque
project. Then, Teri Brown, a fourth-grade teacher at the Inez
Elementary School in Albuquerque, came to the Liberty School for
five days in early June to join a workshop led by the Liberty
study group and Professors Bob Speiser and Chuck Walter of
Brigham Young University.
For the coming year, the collaboration plans to continue these exchanges. This fall a group of teachers from Albuquerque will visit the Liberty School and Brigham Young University where professors Speiser and Walter have developed an innovative mathematics course for elementary education students. This pre-service course is a mathematics content course, which emphasizes pre-service teachers building their own mathematics intertwined with careful looks at children's mathematics.
The Liberty study group will visit Albuquerque, in two shifts, to learn more about assessment and more about building a network of schools, since Liberty would like to play a more leading role in its district. This study group has already made its presence felt by being one of the strongest voices convincing the district to adopt the MathLand program.
In addition, teachers at both sites, with Albuquerque taking the lead here in implementation, are keenly interested in learning from "research lessons," as practiced by teacher study groups in Japan. In particular, what does a research lesson contribute to better understanding children's ways of thinking and teachers' ways of working with that thinking?
At the annual meeting, yours truly offered free books to those who would review them. Thanks to Marti Belanger from Caribou, ME, and to Martha LaPointe, from Presque Isle, ME, for taking up the offer! I have another Math Solutions title for review: Getting Your Math Message Out to Parents, A K-6 Resource. I'll mail it out for keeps to anyone who'll review it. Ed.
This book by Linda Schulman Dacey and Rebeka Eston (Sausalito, CA: Math Solutions, 1999) is easy to read and full of usable ideas for teachers. Rebeka (Becky) Eston is a kindergarten teacher in Massachusetts. She co-authored "Pattern Trains and Hopscotch Paths," one of the units in Investigations in Number, Data and Space. Linda Schulman Dacey is a professor of mathematics and education at Lesley College (Cambridge, MA). Together they give us a view into Becky's kindergarten classroom where children are fully engaged in their mathematical learning.
The book begins with a complete overview of Becky's vision for "growing mathematical ideas in kindergarten." Becky describes how she fosters her students' sense of acceptance, security, and safety in exploring new ideas. The book goes on to explain room arrangement, classroom routines, and the children's responsibilities.
The next section of the book discuses curriculum development and the growth of the children's understanding. It details facets of good mathematical tasks including developmental appropriateness, authentic contexts, and multiple perspectives. Also explained in detail are weaving literature and mathematics into thematic units. The authors include how children represent their mathematical ideas and how their representations develop over the school year.
An important aspect of Becky's classroom is the value placed on children's thinking. Good listening skills are modeled and discussed so every child feels able to share ideas and possible solutions to the problem at hand. It's clear that this is a warm, supportive climate for young children.
This book has samples of children's work and assessment models. The ideas shared are practical and easily replicated. The title may suggest a kindergarten level, but most of the ideas are applicable to other levels. Primary teachers, in particular, will find this book to be a compilation of usable ideas that make sense in working with children.
Once we were settled on the plane for our three-hour plus flight to the east coast, I decided I'd better read something that would help me Monday morning with my class of third-graders. I decided to read a book that Jean E. asked me to review. What I discovered is a little gem of a book spanning grades 3 - 6 that is full of useful ideas for engaging students in learning arithmetic through investigations. (Not related to TERC's Investigations series.)
It All Adds Up! by Australian teacher Penny Skinner is distributed in the U.S. by Math Solutions Publications (Sausalito, CA, 1998). In the forward by Marilyn Burns, language differences are explained for those accustomed to reading only American English.
There is one powerful sentence that says it all for me. It is on page 40 in the middle of the chapter on addition: "All the practice children need at working algorithms can be provided by investigations." Children engage in a variety of investigations that lead them to discover patterns, solve problems and discover strategies for arithmetic. Each child's development of mathematical understanding, knowledge and skills will be furthered while working on computation. Problems and investigations set the context for purposeful computation. This is a concept that should become more a part of many classrooms.
Not only will the investigations in this book help my students develop mathematical understanding, they will help me further develop my understanding of our number system as I study with the children. There are many areas where I will benefit from doing the investigations. As a student, I would find doing these investigations a delightful way of practicing computation. I would be engaged in making sense of what I was learning. Samples of students' work illustrate their responses to problems and help define expectations from the investigations.
Student-posed questions are part of these lessons. Open investigations where all students work at their own level are central. In the activities, students work together benefiting from each others' understanding and questions.
I recommend this book to teachers as it is full of useful suggestions to provide students with engaging ways to develop mathematical ideas, skill in computation, and understand problem-solving. Monday morning after my flight home, we began an investigation of odd and even numbers from the book that continued into the next week.
Spelling Inquiry: How One Elementary School Caught the Mnemonic Plague, by Kelly Chandler and the Mapleton Teacher-Research Group, is a new publication from Stenhouse Publishers (1999, $16.00). Martha LaPointe, an "Exxon family member," is a member of the Mapleton Teacher-Research Group that wrote the book.
In the book, the authors discuss how they came to develop a program that fosters inquiry-based learning about spelling in K-5 student-centered settings. The narrative gives tips on concrete teaching strategies for spelling, tells how teachers changed their practice, and addresses assessment issues. For more information, visit www.stenhouse.com or call 1-800-988-9812.
View "Standardized Schools," an editorial by Susan Ohanian on-line at www. thenation.com. Susan's most recent book, One Size Fits Few: The Folly of Educational Standards, was reviewed by Cindy Chapman in the June issue of Intersection.
The Ninth International Congress on Mathematical Education (ICME 9) is scheduled from July 30 - August 6 in Makuhari, Japan. Attending an ICME is an opportunity that comes along only once every four years, and to make it possible for U.S. mathematics educators to attend, NCTM has received NSF funding that may be used by mathematics teachers, mathematicians, and mathematics educators to supplement travel expenses to ICME-9 and for a Post ICTM-9 Seminar Tour.
A selection committee comprised of individuals representing various professional mathematics associations will review the applications and award the grants both for the ICME-9 Travel and for the Post-ICME-9 Seminar Tour. Elementary, middle, and high school teachers are strongly encouraged to apply.
The travel grant application and selection criteria are available from NCTM, Department E, 1906 Association Drive, Reston, VA 20191-1593; telephone (703) 620-9840, X 2112; from NCTM "Fax-on-Demand" at (800) 220-8483 (select option 2, enter document 525); or from at http://www.nctm.org/icme9. The application deadline is November 1. Notifications will be made by December 15.
Submit a piece to be published here! A few scant months from now, you'll be celebrating a well-earned winter break and perhaps catching up with your reading. Others will be, too. Please consider contributing an article about your project that your friends and colleagues can read in the November/December issue. Besides, don't you want your article to appear in the last Intersection of this century?
Thanks to those who contributed to this issue. The next deadline is Monday, November 15. Please submit contributions to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; phone, (512) 869-1580; fax, (512) 869-8477; e-mail, jehne@ibm.net.
[Previous Issue] [Home] [Next Issue]