As autumn officially begins, representatives from projects supported by the ExxonMobil Foundation will convene at the ExxonMobil Downstream Headquarters in Fairfax, VA for the Twelfth Annual Meeting of the Mathematics Specialist Program Teacher-Leaders. The conference, which begins in the late afternoon on September 21 and ends at noon on September 24, will allow participants to connect with colleagues across projects and to hear and interact with a host of stellar presenters who will be leading key sessions: Ruth Parker and Patty Lofgren; Deborah Ball and Hyman Bass; Tom Carpenter and Megan Franke; Doug Clements and Vicki Bachman; Lee Stiff and Skip Fennell. Please find information about many of these presenters and their topics in "Getting Acquainted," directly below. Also in this issue are details about the pre-sessions and breakout sessions that will be offered.
Many thanks to planning committee members Vicki Bachman, Virginia Bastable, Christopher Kribs-Zaleta and Sherry Rosenberg for their help in putting together what promises to be a wonderful conference. If you have any questions regarding the annual meeting, please contact Joe Gonzales at joe.e.gonzales@exxon.com or Jean Moon at mbb321@ultranet.com.
The ExxonMobil Foundation is pleased and honored to have with us for our annual meeting the presenters introduced in this column. Along with brief biographical sketches and descriptions of the invited presenters' current endeavors, the titles and topics of their sessions may be found here. Also see a listing of recent publications of some of them. Thanks to all who were able to forward information for this column. Ed.
Ruth Parker and
Patty LofgrenOn Friday morning, Ruth and Patty will be launching the meeting with an interactive session entitled "Patterns, Functions and Algebraic Thinking." If you've attended past conferences, you've already had the pleasure of meeting these two engaging leaders in mathematics education reform. If you're new to the annual meeting, you're in for a real treat. And so are ExxonMobil employees who work at the Fairfax, VA site. Ruth and Patty will be presenting a public engagement session for them on Thursday afternoon.
Ruth and Patty direct MEC, the Mathematics Education Collaborative, located in Ferndale, WA. Through MEC they engage parents and the public in sessions about how mathematics is taught and learned as well as facilitate collaboration among parents, teachers, administrators and community members in restructuring mathematics education. Their goal always is to have diverse stakeholders at the table from the beginning as they work towards securing quality mathematics for all children. (Please see Intersection, September 1999 and February 2000.)
Another focus of their work is administrator support. Ruth and Patty help administrators learn how they can support teachers who are changing their practice and interacting with parents and how they can facilitate change on their campuses.
In addition, they have designed and presented a series of nine-day mathematics content courses for teachers. The courses are meant to give teachers the experiences that deepen their own understanding of mathematics so that they can more effectively teach powerful mathematics to students. Next month's Intersection will feature an article by Marty Belanger and Martha LaPointe, teacher-leaders in Maine, who enthusiastically report on taking this course just last month.
Both Patty and Ruth are former classroom teachers.
"Developing Useful and Usable Mathematical Knowledge in Teaching" will be presented by Deborah Ball and Hyman Bass on Saturday morning. This working session will examine and re-frame the problems faced in the mathematical preparation of teachers, and will examine the questions central to improving how we prepare teachers who not only know mathematics but can make effective use of mathematics to help all students learn.
Deborah Loewenberg Ball is currently
Arthur F. Thurnau Professor
of mathematics education and teacher education at the University
of Michigan. Those who attended the foundation's annual meeting
in 1992 will remember the meaningful, interaction sessions
Deborah led as the featured presenter that year.
Deborah's work as a researcher and teacher educator is rooted in practice, drawing directly and indirectly on her many years of experience as a classroom teacher. Ball's work focuses on studies of instruction and of the processes of learning to teach. She also investigates efforts to improve teaching through policy, reform initiatives, and teacher education. Two research projects are the site for her current work.
Ball is co-directing a large longitudinal study of whole-school reforms designed to improve instruction and learning in reading/language arts and mathematics in high-poverty elementary schools. The Study of Instructional Improvement seeks to develop a theory of instruction and of intervention that will develop knowledge of the processes and outcomes of instructional improvement.
Ball is also studying the practice of elementary mathematics teaching. The Mathematics Teaching and Learning to Teach Project focuses on the mathematics that teachers need to know in order to teach mathematics well. Ball's principal collaborator on this work is Hyman Bass. The research team studies classroom teaching and analyzes the mathematical entailments of the work, a sort of job analysis. This project also explores how records of practice (e.g., videotapes of classrooms, student work) can be used to support communication about teaching and learning among a wide range of stakeholders.
A professor of Education and Mathematics in the University of Michigan's School of Education, Hyman Bass is the chair of the Mathematical Sciences Education Board (MSEB) and the president-elect of the American Mathematical Society. His chief fields of interest are algebraic K-theory, number theory, group theory (geometric methods), algebraic geometry and mathematics education.
Hyman Bass is a member of the national Academy of Sciences and has been both a Solan and Guggenheim Fellow. He was awarded the American Mathematical Society Cole Prize in Algebra, and has served on numerous important professional committees. His contributions to mathematics and mathematics education are significant and abundant and his publications are numerous.
Please see the section above for information about The Mathematics Teaching and Learning to Teach Project in which Hyman is engaged with Deborah Ball.
After lunch on Saturday, Tom Carpenter and Megan Franke will present "An Overview of the Elementary Grades Algebra Project" about the work they are doing with local elementary teachers in understanding how young children begin to think of algebraic concepts.
A professor of Curriculum and
Instruction (Mathematics Education) at the University of
Wisconsin–Madison, Tom Carpenter is also Director of the
National Center for Improving Student Learning and Achievement in
Mathematics and Science, funded by the Office of Educational
Research and Improvement of the Department of Education.
Tom's research integrates the study of the development of children's mathematical thinking, instruction that supports that development, and professional development that fosters instruction that leads to learning with understanding. Rather than studying learning and instruction as it currently exists in schools, Tom has been working collaboratively with teachers to conduct design experiments to investigate what is possible. All of this work has been framed in the context of teaching and learning particular mathematics content. Tom's current research focuses on the development of algebraic thinking in the elementary school, in particular the development of generalization, justification, and proof.
Tom is former editor of the Journal for Research in Mathematics Education and is currently serving on the National Research Council's study panel, The Mathematics Learning Study.
Megan Loef Franke is an Associate
Professor in the Graduate School of Education and Information
Studies at the University of California, Los Angeles, where she
studies the development of teacher and student learning in the
context of mathematics. Through her work on the Cognitively
Guided Instruction Project she has developed a conception of
teacher learning focused on self-sustained, generative change.
Currently Megan works with forty elementary school teachers within a single school to investigate professional development that supports teachers' generative change. She is Co-Director of Center X: Intersection of Research and Practice at UCLA, and a partner in the Professional Development Collaborative of the National Center for Improving Student Learning and Achievement in Mathematics and Science.
Following the presentation by Tom and Megan, Doug Clements and Vicki Bachman will present issues and lead discussion on "Mathematics Standards for Preschool and Kindergarten Education." Vicki Bachman will be in the role of responder.
In this very issue, readers will find several pages reporting on a recent conference on this topic that was organized by Doug. You'll also see a photo of him there.
Doug Clements is Professor of Mathematics and Computer Education at the State University of New York at Buffalo. Previously a kindergarten teacher for five years and a preschool teacher for one year, he has conducted research and published widely in the areas of the learning and teaching of geometry, computer applications in mathematics education, the early development of mathematical ideas, and the effects of social interactions on learning. With colleagues, he developed a K-5 mathematics curriculum, Investigations in Number, Data, and Space. In that context, he and his colleague Julie Sarama have developed several constructivist-oriented software packages, including a version of Logo and Logo-based software activities to complement the curriculum.
In a current NSF project, "Building Blocks–Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development," he and Julie Sarama will develop mathematics software and activities. Doug was on the writing team for the revision of the Standards, NCTM's Standards 2000 project.
Vicki directs an ExxonMobil-sponsored project in the Iowa City schools. Readers will remember a recent Intersection article (February 2000) Vicki wrote with Cathy Allen– project director in Bellevue, WA–about their rewarding networking experiences and collaborative endeavors that allowed them to share and swap ideas about issues of mutual concern.
In May, Vicki was a participant in the Conference on Standards for Preschool and Kindergarten Mathematics Education organized by Doug. Please look for her comments about it in this issue.
In the closing session on Sunday morning, "Conversation with the President," the new NCTM President Lee Stiff will be joined by Skip Fennell and Doug Clements (introduced above) to spark discussion about the recently released Principles and Standards for School Mathematics (PSSM). Meeting attendees will also have an opportunity to hear Lee speak when he delivers a keynote address at the traditional banquet on Saturday evening.
As all of you know, Lee Stiff is NCTM's
new president. After serving as president-elect for the past
year, he took the gavel as president at NCTM's Annual Meeting in
Chicago this past April.
A professor of mathematics education at North Carolina State University, Lee has also been a middle-grades mathematics teacher. He has served as a member of the Board of Directors for NCTM and for the North Carolina Council for Teachers of Mathematics as well. In his address in Chicago, he made clear his sincere appreciation for teachers. He remarked: "My father had a third-grade education. When I came home from school, he couldn't help me with my math. My mother barely stayed in high school. When I came home from school, she was at work. I'm saying to you, if there's a reason I'm standing in front of you today, it is because of teachers like yourselves. And the reason I'm standing in front of you today is because there are people who had expectations of me and who said, 'No, I don't care how much you complain, you're going to do this.'"
You may listen to a webcast of Lee's address at the Annual Meeting's close at www.nctm.org/meetings /2000/Chicago, and view "We Must Lead the Way," at www.nctm.org/news/articles/2000.
We are grateful and honored that Lee will be joining us.
Francis (Skip) Fennell is a professor of education at Western
Maryland College. He has served as department chair, coordinator
of undergraduate programs in teacher education, and acting dean
of graduate studies (twice) during his twenty-plus
years. Fennell has had experience as an elementary and
middle-grade classroom teacher, principal and supervisor of
instruction.
He has published articles in numerous professional journals as
well as written textbooks and materials for students and teachers
of mathematics.
Skip is a past member of the Board of Directors of the NCTM and the current president-elect of the Association of Mathematics Teacher Educators (AMTE). He is a writer of the recently released Principles and Standards for School Mathematics. In 1997, he was honored by Western Maryland College by being selected Professor of the Year (See Intersection, November / December 1997). In addition, he was the CASE Carnegie Foundation Professor of the Year, for the state of Maryland in 1997. In April of 2000, he received from NCSM the Glenn Gilbert Award for service as a leader in mathematics education.
From 1997-1999, Fennell served as Program Officer in the area of instructional materials development and teacher enhancement for K-8 mathematics within the Division of Elementary, Secondary, and Informal Education at the NSF.
As mentioned in the last issue, two concurrent pre-sessions will be offered once again for those who can arrange their schedules to attend. The discussion groups are slated for 2:30–5 PM on Thursday afternoon. "Children's Thinking about Geometry, Measurement and Data," will be led by Virgin1a Bastable, Deborah Schifter and Jill Bodner-Lester with facilitation by Christopher Kribs-Zaleta. Skip Fennell will lead "Critical Issues in Number and Operations," and Sherry Rosenberg will facilitate.
Break-out sessions on a variety of topics will be offered on Friday afternoon. Sherry Beard, of Marilyn Burns and Associates, will present her work with school administrators on mathematics reform; Carol Brooks, project director within the Title One Mathematics and Science Programs in Tucson, AZ, will discuss the mini-grant program used in ExxonMobil-supported schools; Susan O'Boyle, project director in Houston, TX, will describe the use of study groups in that project; and Casilda Pardo, a teacher-leader in Albuquerque, NM, and an appointed member of the National Research Council's Committee on Math Learning, will talk about their soon-to-be-released study.
In this section of the newsletter you will find comments from the key organizers of a recent conference followed by reflections about the sessions from several attendees from their different perspectives. Many thanks. Ed.
Doug is a professor of Mathematics and Computer Education at the State University of New York (SUNY), Buffalo. Ann-Marie, also at SUNY, Buffalo, is a doctoral candidate in early childhood education.
Previously, we wrote about our Conference on Standards for Preschool and Kindergarten Mathematics Education (Intersection, January 2000). Funded by the ExxonMobil Foundation and the National Science Foundation (NSF), this conference, held May 15–17 in Arlington, VA, was designed to bring consistency to the many standards and guidelines across the U.S. and thus help create developmentally appropriate curricula. The gathering brought together varied groups of people, including the following:
Several panelists presented research reviews detailing what is known about the mathematical learning of preschool and kindergarten children. Developmental and cognitive psychologists and mathematics educators addressing these issues included Arthur Baroody, Doug Clements, Karen Fuson, Herbert Ginsburg, Rochel Gelman, Constance Kamii, Alice Klein, Catherine Sophian, Prentice Starkey, Paul Trafton.
Adding their perspective on the foundations of mathematics, mathematicians included Susan Addington, Debra Borkovitz, Roger Howe, Ken Millet, and Maggie Myers.
New projects developing mathematics curricula, including software, for preschool and kindergarten have been recently funded by the NSF. The principal investigators described their projects, including Beth Casey, Carole Greenes, Julie Sarama. The emphasis in these presentations was on the mathematical goals and objectives of the projects. Other research-based curriculum and teaching projects were described by Sharon Griffin, Alice Klein, and Prentice Starkey. They showed that certain children are at risk for starting school mathematics behind their peers and that–provided good experiences in preschool–they can learn significant ideas and skills in mathematics.
A mixed group of experts discussed implementation issues. They included Bob Balfanz, Nita Copley, Jeane Joyner, and Mary Lindquist.
Several early childhood experts offered invaluable insights on the needs of young children and their teachers. These participants included Sue Bredekamp, Carol Copple, Greta Fein, and Lilian Katz.
We do not have room to name everyone. A list of all 107 participants, including biographical sketches for all the presenters and panelists, can be found at the conference web site, www.gse. buffalo.edu/org/conference.
What did the presenters, panelists, and participants talk about? Topics included standards for preschool and kindergarten math education; initial number and quantitative concepts; number and operation; geometry and measurement; the role of algebra, data analysis statistics, and probability; mathematics curricula for young children; problem solving, reasoning, communication, connections, and representations; implementation and communication. Following each set of expert panel presentations, participants convened in break-out sessions to discuss the issues that emerged in the whole-group sessions. These groups addressed specific issues such as (a) the synthesis of research on early mathematical thinking and conceptualization of the foundations of mathematics as a discipline; (b) learning and teaching and various areas of mathematics in early childhood; (c) the scope, form, and ideal specificity of standards or guidelines for preschool mathematics; and (d) practice and policy relevant to preschool mathematics education.
It is within these small working groups that state participants had an opportunity to share their work and their state's positions in an informal, interactive and dialogic context. Similarly, teacher-leaders from ExxonMobil projects shared their professional experience.
As we discuss later, a final report will contain a full reporting of what was said. Here are a few highlights.
A Triumphant Success Feedback from the participants highlighted that the conference proved to be an exceptionally rewarding experience, both professionally and personally to participants. Here is a sample of quotes.
We would like to take this opportunity to extend our appreciation to all participants who contributed high-spirited dialogue.
One of the many contributions the ExxonMobil Foundation made was sponsoring the attendance of several kindergarten teacher-leaders, building on the Foundation's long-standing support of early childhood mathematics. The ExxonMobil Foundation will also be hosting a small follow-up meeting of 15 conference participants. This group will produce a final report that shall consolidate recommendations from the conference. The report will also include papers written by presenters and age-specific recommendations for mathematics for young children.
The first draft of the working group's report and recommendations will be disseminated to a representative sample of the main conference's participants for their reactions. Their advice will guide the working group in developing a final report that will be published and disseminated to all participants, as well as to other pertinent federal and state agencies. It will be available at the conference web site.
The Conference on Standards for Preschool and Kindergarten Mathematics Education provided a unique opportunity for federal and state educational agencies to ensure that young children will receive the most enriching mathematics education possible–one that is mathematically and developmentally appropriate and sound. We believe that the work that transpired at the conference will be critical to achieving common, efficacious standards and goals. This conference brought together diverse societies, which concentrated on one critical focus. Further, evaluations from conference participants showed that the conference was successful in developing a rich communicative context. That is, ideas were openly shared and the presentation of research and other current work in the field appeared to enhance the knowledge of the participants.
The follow-up meeting will blend these ideas and produce reports, in several forms, to disseminate what has been learned. This final report, with recommendations, will constitute a set of guidelines that will enable standards writing groups to create consistent and complementary standards, which are based on understanding of current research, practice, and policy in early childhood mathematics education.
We invite you to visit www.gse.buffalo.edu/org/con ference. There you will find the papers written by conference experts regarding the main conference issues. Further information regarding the final report shall also be posted at this site in the future. For more on the PSSM, see www.nctm.org/standards.
Our sincerest appreciation is extended to the ExxonMobil Foundation and to the National Science Foundation for their support in creating such a valuable forum for a diverse set of professionals to collaborate on critical issues for the mathematics education of young children. We wish to acknowledge the contributions of all participants. Such prolific dialogue would not have been possible without the knowledgeable input of all individuals, as well as the mutual respect for individual ideas.
Vicki directs the ExxonMobil project in the Iowa City schools.
The Conference on Standards for Preschool and Kindergarten Mathematics Education, which was organized by Doug Clements and supported by the ExxonMobil Foundation and NSF, was truly a one-of-a-kind event.The stated purpose of the conference was to provide an opportunity for communication and collaboration between a number of important contingencies who are in a position to impact mathematics education for young children.
During fast moving panel discussions, a wide variety of guests provided thumbnail sketches of ideas, perspectives, reflections, endeavors, and research findings which focused on an array of mathematical topics relating to young children. It was a fascinating couple of days. The impact of this meeting will be felt as these various groups work to bring the newly completed Standards 2000 to life in early childhood settings during the coming years. Practical collaborations among participants began to focus on how to reach optimal numbers of people who impact the lives and development of young children. It was a very thought provoking and unique conference!
Alice is currently working as an early childhood education supervisor in the Houston Independent School District, TX.
"Balanced" is the word that comes to mind when summarizing the Conference on Standards for Preschool and Kindergarten Mathematics Education held outside Washington, D.C. this past May. Experts in the field of mathematics presented ideas on content, while early childhood experts made sure that developmentally appropriate implementation was considered. Writers of state curricula were also present to share their perspectives, as well as professors of mathematics teachers and early childhood classroom instructors. All had a stake in this important task of guiding mathematics standards at the preschool level.
As an early childhood supervisor of prekindergarten & kindergarten teachers in 24 schools in the Southwest District of the Houston Independent School District, I am greatly concerned with both content and implementation, and value the importance of math standards for improving instruction in these foundational years.
"A mile wide and an inch deep" was the often repeated description of the math curriculum in our country. This appropriately describes the math instruction in the early childhood classrooms as well, especially PreK and Kindergarten. Typically teachers and administrators have underestimated the intellectual abilities of young children, but that is changing.
Early childhood teachers and administrators are discovering the "secret of childhood" that Dr. Maria Montessori so clearly describes in her book by the same title. Current brain research is also supporting this secret: that young children have absorbent minds, capable of understanding vast knowledge and deep concepts; that children burst into knowledge and go through sensitive periods for learning.
Teachers need content guidance in the form of a curriculum, both at a particular grade level and in alignment with the preK-12 grade continuum. In the Houston ISD, Project CLEAR* has been written for grades K-12 in Reading, Writing and Mathematics, but prekindergarten was not included! In addition, prekindergarten is becoming a full-day program in several schools, illustrating the importance of math standards to lay down a foundation rich in content and appropriately delivered. The love of learning, inherent in the early years, needs to grow along with a child's understanding of mathematics.
This message was given loud and clear at the conference by early childhood experts such as Sue Bredekamp, one of the definers of developmentally-appropriate practice and by Kathy Richardson, who developed videotapes on assessing young children's mathematics knowledge. The work of both women has been extremely valuable to improving early childhood instruction around the nation. Kathy reminded us about the importance of teachers asking questions, not just giving answers, and of honoring the work of each child based upon what each one is thinking.
What is developmentally appropriate for three-, four- and five-year-olds is to have learning centers where hands-on activities, cooperative learning and time to explore and discover can be given. Young children learn through movement and should not be seated in desks, all in rows, all on page 4 of a workbook!
Paul Trafton, from the University of Northern Iowa, said, "What children know can't be separated from how they learn," and emphasized the importance of allowing time to let children share their thinking. He talked about the mathematical power of children's thinking and how we must provide tasks that challenge. I had attended a workshop given in Houston by Paul just one month prior to the Math Standards Conference. His delightful presentation gave marvelous examples of how young children can be challenged to think deeply about mathematics. He gave specific activities that we could take back to the classrooms and implement.
Connie Kamii, from the University of Alabama, gave input from her studies of the work of Jean Piaget and how children learn. Other experts shared their research into how young children learn patterns, geometry and measurement and how they construct knowledge based upon the context of their lives.
It was fascinating to hear from so many experts on areas of importance to the writing of national mathematics standards. I was grateful for the balance that was present at the conference and for the opportunity to participate. Hats off to Doug Clements!
*To find out more about Project CLEAR, log on to www.houstonisd.org.
Jennifer teaches five- and six-year-olds in the Albuquerque Public Schools.
The recent conference on Standards for Preschool and Kindergarten was a heady experience for a teacher plucked out of the midst of five- and six-year-olds and plunked down amid writers, researchers, professors and administrators. One minute you're talking about sharing the blocks equitably with truculent students and the next you're helping to set standards that will guide the practice of thousands of your fellow teachers. I must confess that the first evening left me more than slightly daunted by this prospect. What could a teacher contribute to this lofty discussion led by the lights of our field and people that I'd been reading and trying to follow for years? I decided to follow Mark Twain's advice. You know, the quote about rather remain silent and have them think you a fool than to open your mouth and remove all doubt. So, I opened my ears and listened intently. The following is what I think I heard, but because I'm sure that it isn't as complete as it should be, check out the conference web site.
The conference was set up with panel discussions on a topic that were followed by break-out groups to further consider the ideas presented within the panel discussions.
Our first session asked the question: "What are the advantages and disadvantages of having standards in mathematics for young children?" Sue Bredekamp of the NAEYC (National Association for the Education of Young Children) spoke eloquently of the need to have consistent expectations for children and their caregivers. This provides the advantage of being able to communicate with teachers, administrators, parents, and children what should be taught and what should be achieved during a period of time, while allowing for developmental differences among children. If you have doubts about the developmental appropriateness of curricular goals, I urge you to read Sue's paper on the conference web site. My favorite quote of the conference came from Cheryl Tibbals, Council of Chief State School Officers, during this panel. She said, "Errors are portals of discovery." So feel free to open some portals today. Who know what you could discover?
Following the panel discussion, we broke into working groups to explore this question further. The discussion was fast and furious, but we were in agreement that standards need to be written. Many in the group expressed the idea that standards were going to be imposed by state agencies, school districts and legislatures, so the people who are best equipped to make these decisions should take the initiative and begin this process. Many individuals shared what is happening within their state and presented materials that may be valuable to others in creating state benchmarks and standards. During informal discussions at lunch, dinner and breaks, I gathered that most of the working groups had arrived at this same conclusion.
I found the panel discussion on Initial Number and Quantitative Concepts to be fascinating. In kindergarten, we spend most of our learning time working toward number sense and competence in this area, so I was most intrigued by the research presented. Catherine Sophian has some perspectives on learning and teaching that have implications for not just kinder and preschool teachers but for children in the upper grades learning about fractions. Her views, available on the conference web site, can give all of us ideas about developing curriculum that helps guide learning.
Our working group tackled this topic by discussing not just what is taught but how it is taught in a typical classroom. Some of the researchers expressed a fear that children are not given sufficient curriculum but are merely playing most of the day with teacher intervention only when behavior problems arise. The teachers in the group expressed doubts about worksheet curriculum that does not address children's need to explore with their senses and added that what may appear to be just play to an observer in the classroom is learning on a different level Sometimes I felt that we were talking about the same things but using a different language and so missed the commonalties that we all see in children's learning. Perhaps we need translations provided in our own jargon to understand each person's points! We never came to any solutions about what should be taught in this area, but the discussion was wonderful and lively. It provided me with thought toward my own practice and how I can explain it to others so that they will understand what I'm doing at a particular time.
Additional panel presentations focused on Number and Operations; Geometry and Measurement; Algebra; Data Analysis; Statistics; and Problem Solving; and also included presentations of prospective mathematics curricula for young children. Our discussions were amazingly respectful and thoughtful. They were recorded, and the transcriptions will be made available.
Our days were long and full, followed by dinner and speakers. If you ever have a chance to hear Janice Jackson of Boston College, I highly recommend it. She was magnificent in her defense of teachers and inspiring with her use of poetry and song.
The major points of the conference for me were:
So, what did I, my school and my community gain by sending me across the country for several days? I have a profound respect for the educators and dedicated professionals who go to work every day sometimes in the face of public disrespect and pressure to perform and wrestle with the big issues facing this country. I found new courage to tackle the coming school year with all its challenges and rewards–armed with research for doubting parents, ideas for teaching concepts, and guidelines to help me plan my route. I hope to spread this to the other members of my study group and to my school and the larger community.
Special thanks to Dr. Clements, Ann-Marie DiBiase, Julie Sarama, Jean Moon and the ExxonMobil Foundation, and the NSF for all their efforts to make this conference possible.
Many thanks to Terri Goyins, currently teaching in The Woodlands, TX, for reviewing this title. Ed.
This book by Phyllis Whitin and David J. Whitin was written to demonstrate the common beliefs about learning that cut across curricular fields. Historically, curricular groups have little communication with each other, but this book is the first joint publication by the National Council of Teachers of Mathematics and the National Council of Teachers of English. I look forward to more collaborative efforts such as this one for elementary teachers.
The activities in this book took place in a fourth-grade classroom with Phyllis Whitin as the teacher and David Whitin conducting research in the classroom. This book offers numerous activities but is not meant to be a prescriptive activity book. It describes how to build a mathematical community where each child's voice is heard and honored. The Whitins describe how writing and talking can be used to uplift individual voices and to enrich mathematical ideas. The principles of learning described here could fit with any mathematical ideas. This book invites you to act upon these principles of learning in ways that seem appropriate for you and your own classroom community.
Each activity described began with an introduction to the whole group. Next, the children explored the materials or the problem. The children's desks were grouped in clusters of four to six. Each group had time for small-group sharing which helps develop every child's voice and opinion. At the end of the lesson, the whole class gathered for a discussion. Many times the groups were stopped and the class would review new strategies that students discovered as they worked. Then students returned to their groups to draw upon those ideas. This strategy seemed to help support the more reluctant writers, but it often led the more capable students to connect ideas as well.
Often while writing one comment, the children would develop a new idea. I feel this is a critical step in mathematical writing. When a student is asked to commit thoughts to paper, important concepts may surface. The students in this classroom were aware that their journal entries contributed to their mathematics grade. In fact, children could only earn a grade of "A" if they solved problems accurately and explained them clearly in writing. The first chapter has examples of children writing about their mathematical experiences.
The book shows that writing and talking are ways that learners can make their mathematical thinking visible. Both writing and talking are tools for collaboration, discovery and reflection, and the authors show many examples that illustrate this.
Math is Language Too presents examples of how to use children's literature to involve children in sense-making and problem-solving. Children's literature is used to explore mathematical patterns and to both investigate and appreciate the meaning of mathematical vocabulary. Other chapters deal with mathematical algorithms and making personal connections to geometric ideas.
This book focuses on reading, writing, talking, drawing and doing mathematics and using these skills to express those sense-making efforts. Another thrust of this book is to emphasize the important classroom conditions that honor mathematical voices of all learners.
I highly recommend this title for your professional library.
This title is available from either NCTM or NCTE. It's $14.95 for members, $19.95 for non-members. Ed.
As I write this section, it's a record-breaking 107 degrees here in Georgetown, Texas. Definitely midsummer. Any day now I expect that the neighborhood children will try frying eggs on the sidewalk.
My dream is that I will find in my actual or virtual mailbox an article from you. Please accept this invitation to send in a few hundred words.
Many thanks to all who contributed to this issue. The next deadline is Monday, August 21. Please send items to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; phone, (512) 869-1580; fax, (512) 869-8477; e-mail, jean@intersectionlive.org. Thanks!
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