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Coaching to WinMany thanks to Amy Morse, project director of a newly-funded initiative, for her introductory article below. Thanks also to math coach Anne Goodrow for this wonderful photo. Welcome, all! Ed.
The Boston Public Schools are in the exciting, challenging—and sometimes overwhelming—early stages of massive reform in mathematics education. In the fall of 1999, Math Leadership Teams were formed in 41 of the 87 elementary schools across the city. These teams of teachers and administrators are taking the lead in participating in professional development seminars and implementation of the newly adopted curriculum, Investigations in Number, Data and Space. Although the commitments are extensive, and the investment is long in hours, we are definitely on our way to a new era in math teaching and learning.
One of the most important features of such a sweeping reform effort is the level of support offered the teachers. Two key components are a strong and challenging curriculum and substantive support from administrators. The developers of the math plan worked hard to ensure delivery of the proper materials to support the teachers’ implementation of the new curriculum. We depend on the curriculum to be comprehensive and engaging—a critical partner for each teacher in his or her practice. The math plan in Boston also calls upon principals to appreciate the need to create opportunities for teachers’ collegial work and to engage in their own professional development as instructional leaders.
A sturdy foundation of support in the effort is Boston’s new cadre of elementary school math coaches. These coaches play many roles. The coaches might collaborate with math leadership team teachers directly in their classrooms by co-teaching. They might offer model lessons as well as consultation and support. Most importantly, the coaches strive to facilitate substantive discussions about mathematics and children’s thinking in each of the city’s school communities. In addition to being responsible for the professional development in individual schools, each coach offers a series of Developing Mathematical Ideas (DMI) seminars (referenced in the January issue of Intersection). A number of coaches are also offering ReLearning to Teach Arithmetic seminars in schools. Both seminars are designed to help the teachers re-examine their own mathematics content knowledge and students’ mathematical thinking. They are an integral part of the professional development component of the math plan.
The coaches, all of whom are in a new role in the system, come together for their own professional development, too. In September, the coaches met for a three-week institute—engaging in mathematics, examining the Investigations and Developing Mathematical Ideas curricula, and creating a community of professional developers as learners. During the school year, the coaches continue to come together each Friday to investigate the role of coaching and to critically examine the work in which they are so deeply engaged.
We are finding, not surprisingly, that this role of a coach is, by its very nature, multi-faceted and complex. In Boston, one aspect of the work we are doing this year with ExxonMobil support is wrestling with the question, "Just what is this role of coach?" It seems that if the role is articulated and examined, even as it veers—sometimes careens—in wildly different territories, we might better develop maps and guidelines to rely upon in our day-to-day work.
In particular, writing journal entries and cases about the coach experience in all its different dimensions is one important way of articulating our questions about the role and the particulars that embody it. The ExxonMobil grant offers us an opportunity to develop this aspect of examination. Capturing essential elements of coaching in writing will provide us with opportunities to examine the role, take it apart, understand it, learn from it, and catalogue it in a way that will help us develop the most effective strategies for enacting the role.
Maura Murray, author of the article below, is an assistant professor of mathematics at Salem State College in Salem, MA and a ExxonMobil Foundation Project NExT fellow. She is leading the newly-funded project she describes below. Thanks for contributing this article, and welcome! Ed.
Salem State College, in partnership with the Salem, MA public schools, recently received a planning grant from the ExxonMobil Foundation. The grant will support an after-school seminar aimed at building a network of teacher-leaders from each of the seven elementary schools in Salem.
The city of Salem is located twenty miles north of Boston and is known for the infamous "witch trials" of 1692. The Salem public schools, currently in a period of change, comprise a small urban district that serves a very culturally and economically diverse student population. Over the last year, the Salem public schools reviewed and evaluated mathematics programs. After piloting various programs, Everyday Mathematics—developed through the University of Chicago School Mathematics project—was chosen as the new mathematics curriculum for all of the Salem elementary schools.
With the adoption of the program, professional development of teachers has been critical. The Salem school district has run in-service days for all of the teachers. With the support of the ExxonMobil Foundation, we now have the support to send two Salem teachers and myself to Mount Holyoke College to attend the Developing Mathematical Ideas (DMI) Leadership Institute. In the fall, we will have an after- school seminar using the DMI materials as our focus. The seminar will bring together teachers from each of the schools in Salem. We will also plan family math nights and discuss the mathematical needs in the district.
We are very excited about this opportunity and would like to thank the ExxonMobil Foundation for its support. A special thanks goes out to Jean Moon for all her help in beginning this process of bringing together mathematics teacher-leaders in Salem.
Maura Murray, author of the article below, is an assistant professor of mathematics at Salem State College in Salem, MA and a ExxonMobil Foundation Project NExT fellow. She is leading the newly-funded project she describes below. Thanks for contributing this article, and welcome! Ed.
Salem State College, in partnership with the Salem, MA public schools, recently received a planning grant from the ExxonMobil Foundation. The grant will support an after-school seminar aimed at building a network of teacher-leaders from each of the seven elementary schools in Salem.
The city of Salem is located twenty miles north of Boston and is known for the infamous "witch trials" of 1692. The Salem public schools, currently in a period of change, comprise a small urban district that serves a very culturally and economically diverse student population. Over the last year, the Salem public schools reviewed and evaluated mathematics programs. After piloting various programs, Everyday Mathematics—developed through the University of Chicago School Mathematics project—was chosen as the new mathematics curriculum for all of the Salem elementary schools.
With the adoption of the program, professional development of teachers has been critical. The Salem school district has run in-service days for all of the teachers. With the support of the ExxonMobil Foundation, we now have the support to send two Salem teachers and myself to Mount Holyoke College to attend the Developing Mathematical Ideas (DMI) Leadership Institute. In the fall, we will have an after- school seminar using the DMI materials as our focus. The seminar will bring together teachers from each of the schools in Salem. We will also plan family math nights and discuss the mathematical needs in the district.
We are very excited about this opportunity and would like to thank the ExxonMobil Foundation for its support. A special thanks goes out to Jean Moon for all her help in beginning this process of bringing together mathematics teacher-leaders in Salem.
This article about an initiative in north Texas was written by Christopher Kribs-Zaleta, who has a joint appointment in math and teacher education at the University of Texas at Arlington. He is also a ExxonMobil Foundation Project NExT fellow. His colleague, Holli Aflatouni, teaches second-grade at Bebensee Elementary School in Arlington, and is one of the listserv facilitators. Thanks! Ed.
I have been working since last fall with a group of fifteen elementary math specialists from Grand Prairie and Arlington, TX, in a professional development setting. We meet once a month in facilities provided by Grand Prairie ISD to discuss issues related to children’s construction of number and operations. Our seminars run all day long. In the morning, we work on mathematics problems which relate to a given math topic. In the afternoon, we use video and text case studies to guide discussions of how children learn that same topic.
In December, for instance, we discussed place value. In the morning, we explored how to use the Mayan number system (vertical base twenty place value) and how to represent numbers in various bases. In the afternoon, we watched and read about children struggling to make the leap to working with tens, and later about others trying to extend their knowledge to the hundreds’ place. The teachers come from a variety of backgrounds and all grades K-5, so their experiences as well as their questions do much to inform our discussions.
I have been especially lucky that Holli Aflatouni is part of the group. Holli and I have extended our partnership in the last year to include bringing my preservice elementary teachers at the University of Texas at Arlington (UTA) to work with children at her school—sometimes as a field trip for the entire class and sometimes individually for early field work. Both the UTA students and the students of Bebensee Elementary have benefited greatly from that interaction. Holli and I are glad to provide the preservice teachers with opportunities to see first-hand how children construct their understanding of mathematics at a time when they (the preservice teachers) still have the chance to come back to class and ask questions about what they’ve learned. The rich bank of experiences Holli has been kind enough to share on the listserv has also proven an important element in our seminar discussions, which generate a lot of "what-ifs."
The project continues through the end of the school year, with every expectation to continue both of these aspects of it in new ways in the year ahead.
If you will be attending NCTM’s Annual Meeting in Orlando this April, you are cordially invited to the traditional come-and-go reception hosted each year by the ExxonMobil Foundation. Scheduled for Thursday evening, April 5, from 6 – 8 PM, the gathering will be held in the Signature II Room at the Rosen Centre Hotel. This occasion provides a unique opportunity for project participants, special guests and friends of the Foundation to engage in conversation over hors d’oeuvres and drinks. Please plan to join us!
The article below, along with the accompanying photos, features the work of Brian and Donna Kaumo, fifth-grade teachers in Albuquerque, NM. The article originally appeared in the Fall 2000 issue of The Lamp, a quarterly magazine for shareholders that is published by the Exxon Mobil Corporation. Teresa Cage is the author; Greg Sorber, Black Star, is the photographer. You may also read this on-line.
Let’s start by exercising your brain," Donna Little-Kaumo announces to a class of fifth-graders at Whittier Elementary School in Albuquerque, New Mexico.
She flashes onto a screen an image of a shape created with cubes. After only four seconds, she removes the image and asks the students to re-create the shape using brightly colored cubes.
As the students go about their work in teams, Donna moves from table to table to ask them to describe what they saw on the screen.
"I saw a little dog," says
one youngster.
"I saw a fat L," offers someone from the adjoining table.
"I saw a T with a cube on top if you turn your head sideways," proclaims another.
"Man, oh man, let me look in that head," responds Donna, playfully. "Pay attention to what you are doing to remember," she adds. "Your brain is an incredible place. Do you see that you start cuing in to things you already know so that you can learn something new?"
Next, the students, some of them with learning disabilities, make boxes to hold the cubes. They study a box pattern and write down their predictions about how many cubes will fit inside. They copy the pattern onto graph paper, then cut out and tape together boxes to prove their predictions.
"Where
will you start drawing the pattern?" Donna asks one
learning-disabled student.
"In the middle," he answers.
"Good thinking!"
Knowing where to start and having the confidence to draw the pattern are big steps for students with learning disabilities, many of whom have trouble with reasoning and organization skills.
Through their work in Albuquerque public schools, Donna and her husband, Brian Kaumo, have helped pioneer a new approach to teaching math that works for both general and special education students. And they’ve done so with funds from the ExxonMobil Foundation through its K-5 Mathematics Specialist Program.
"That program, launched in 1988, is designed to change the way math is taught in the elementary grades," says Dr. Jean Moon, ExxonMobil Foundation advisor. "It focuses on strengthening teachers’ knowledge of math and their understanding of how children learn math."
Through some 300 grants to 100 projects in 29 states, teachers are discovering that kids learn best with problem-solving approaches that go beyond the traditional method of only putting pencil to paper.
"New research has taught us that children learn best for the long term if they can be part of actually constructing their understanding of key ideas and concepts," says Moon.
What that translates into in an Albuquerque fifth-grade classroom is a math lesson with two or three problems rather than 30. Kids work in teams using graph paper, scissors, tape, plastic cubes, string—materials they can get their hands on to solve the problem.
"Instead of memorizing the formula for determining volume," says Donna, "students create boxes and fill them with colorful cubes to understand spatial relationships. It can be noisy and messy, but also lots of fun and effective."
They learned just how effective this year when many of the general education students of teachers in the ExxonMobil project scored higher in math than the national mean scale. What’s more, special education students in a number of classes had higher test scores than some of their peers outside the program. They also continue to move closer to the national mean as they progress through the grades.
Brian and Donna’s work within the Albuquerque project has shed new light on the teaching of learning-disabled children.
"In educating these special-ed kids, the focus is too often on the deficit," says Brian. "We try to teach to their strengths."
"Brian and I have a passion for making sure learning-disabled kids are held to the same standard as others in the classroom," adds Donna. "When we were in the classroom, they appreciated our trust in them and rose to the occasion.
"The thing that has mystified me is that these kids provide a common-sense approach to problem solving that seems to escape some of our general education students. Several have been able to move into general education mathematics classes in the sixth grade. For the students and parents, this achievement offers a first glimmer of hope."
At the heart of this improvement for both general and special education students is the continued development of better teachers.
The
ExxonMobil Foundation Mathematics Specialist grant in Albuquerque
funds 250 teachers in 18 schools. These funds are used to build
teacher expertise in mathematics, research how children think
about and learn mathematics, and assess children’s
mathematical thinking.
Teacher study groups meet after school for three hours each week to study mathematics, examine student work, share ideas, vent frustrations and learn from each other.
Project teachers also helped write new performance-based assessment standards for the district and are increasingly involved in curriculum decisions.
In addition, some attend an annual ExxonMobil Foundation conference that provides professional development, networking and discussion with ExxonMobil employees about the importance of mathematics in their work.
Donna now directs the Mathematics Specialist project in Albuquerque. This year she hopes to increase parent involvement, explore ways to work with teachers in middle schools and intensify efforts toward special education.
"As teachers, we are beginning to understand math and the way people learn in ways that will help students succeed in the new world," says Donna. "Teacher development is not about a one-time workshop, but involves a long-term investment. The ExxonMobil Foundation understands this."
News has been received that Bob Witte has been invited by the Mathematical Association of American to present the annual Leitzel Memorial Lecture at the 2001 Summer Mathematics Meetings. The meetings will be held in early August at the University of Wisconsin in Madison.
Bob plans to speak about mathematics education from the perspective of his experiences as ExxonMobil Foundation’s K-5 Program Officer. Readers will recall that Bob retired at the end of January 2000.
All the best, Bob! Ed.
Many thanks to Jay Hoffman, Superintendent, Nuview Union School District, Nuevo, CA, for contributing the first review below. The second was submitted by Terri Goyins, a teacher in The Woodlands, TX. Thanks to each of you! Ed.
Reviewed by Jay N. Hoffman
Despite our own love of teaching math, most of us will concede that we know others who detest it! For us, the fulfillment of seeing kids grow mathematically is a tremendous motivator to provide the best possible teaching/learning environment. For our non-math oriented colleagues, the notion of joy and creativity in teaching math is, at best, somewhat foreign.
Confronted with the daunting task of teaching a seemingly insurmountable amount of content within a year’s time, many teachers resort to the common practice of simply moving page-by-page through the book. This practice results, unfortunately, in the treatment of all concepts and content in a uniform, but disconnected manner.
Marilyn Burns and Robyn Silbey, authors of So You Have to Teach Math? Sound Advice for K-6 Teachers (Math Solutions, 2000) have provided an alternative to the page-by-page, day-by-day strategy in their first chapter, Preparing for a Successful Year. The book is designed in a question/answer format, with 101 questions and answers provided in 13 chapters and 120 pages. The very first question, "What’s the best way to get a handle on all the math I need to teach during the year?" is answered by reminding the teacher to have an overall sense of what students should know by the end of the year. In addition, Burns and Silbey cite the importance of teacher awareness of state, local and national standards, coupled with locally selected instructional materials.
The authors’ intent is that the book will be used as a reference and discussion guide, rather than as a cover-to-cover reading assignment. Chapters two through thirteen include the titles Planning Effective Math Instruction; Leading Class Discussions; Number Sense and the Basics; Using Manipulative Materials; Dealing with Calculators; Incorporating Writing into Math Class; Linking Math and Literature; The First Week of School; Connecting with Parents; Handling Homework; Preparing for Administrator Observations; and Making Plans for Substitutes. Teachers facing challenges in any of the above areas may just turn to that chapter and read the questions and answers most relevant to their own situation.
This is a practical book. I intend to buy copies for all of my K-6 staff, including our principals. I’m hoping that the book will provide the basis for deeper understanding and enhanced communication among staff members as they plan for student instruction and staff professional growth.
As superintendent of a small school district, I know that the high-stakes state testing program has created a great deal of anxiety about academic instruction. So You Have to Teach Math? Sound Advice for K-6 Teachers is a valuable tool in building the professional competence and dialogue necessary to continue improving.
Reviewed by Terri Goyins
What are your real feelings about homework for students? We all look at homework quite differently. Three groups of people have a big stake in homework—teachers, parents and students. Unfortunately, they all have different perspectives on the subject.
These viewpoints are discussed in the book titled Math Homework That Counts, Grades 4-6 by Annette Raphel. It is published by Math Solutions Publications (August 2000), a division of Marilyn Burns Education Associates.
The introduction discusses a research-project finding that roughly half the teachers consulted believe the major reason for homework is to reinforce what is being learned in school. The teachers stated the school day wasn’t long enough for practice and that homework developed a sense of responsibility in children.
The parents consulted by the researchers felt homework was to help their children be independent. Parents see learning how to do homework as an important prerequisite for success in later schooling and life. Somehow parents tie homework to successful students.
Students felt homework was to help them better understand what they had learned in class. They felt they would learn more, write better and do math better through homework.
Since teachers, parents and students voice different reasons for doing it, it is no wonder that homework is controversial. So how can we, as educators, fulfill all these missions through homework? Then——the other question I always ask myself as a fourth-grade teacher—how can we evaluate the worth and success of homework?
This book is an excellent resource for educators to have available. It discusses research about homework, gives suggestions for teachers to use with parents and offers some excellent ideas for good homework for children.
I live in an area where parents equate a great deal of homework with successful classrooms. I have had to evaluate my own feelings about homework. I have always felt that when children leave school, they should have time to play and enjoy family time. So, my solution has been to only have homework on Tuesday and Thursday nights. I try to involve the family in the homework by collecting data, requesting various family members to share their thinking, or asking them to play a math game together.
I used one of the activities from the book before Christmas. It involved the traditional song "The Twelve Days of Christmas." The students needed to figure out the total number of presents needed to be purchased in order to send all the things mentioned in the song. (Remember the gifts are cumulative in the song.) Then the students had to figure out how many of each kind of gift had to be purchased. It was a fascinating problem and the students (with their families) enjoyed the challenge. The students presented their findings to the class and compared their results. As luck would have it, a local radio station gave the same question to their listening audience. The winner received four tickets to attend a concert in Houston. One of my students was the lucky winner. This was a nice connection to the real world with their mathematics learning.
The appendix of the book contains this list:
As you can tell, this book is a must-have resource for educators who struggle with the homework issue. I highly recommend it to all newsletter readers.
See www.mathsolutions.com for ordering information for both of the titles above. Ed.
Thanks to Norma Sakamoto at WestEd for the item below. Ed.
| Q | What do teachers say about case discussions? |
| A | "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." |
| A | "We are always talking about empowering teachers. I think this is a great way to do it." |
| Q | What does this seminar offer? |
| A | 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. Read what teachers say about our project in the January and September 2000 issues of www.intersectionlive.org. |
| Q | What will I learn? |
| A | You will learn to examine the math, student thinking, instruction and language in a case; how cases are facilitated; how to practice the techniques if you volunteer; and how to introduce cases to others. |
| Q | What are the details? |
| A | Option 1, May 18 – 19, Learn about cases and facilitation. Cost, $350. Option 2, May 18 – 20, Learn about cases and facilitation and 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 more information, please contact Norma Sakamoto by phone at (510) 302-4206 or by e-mail at nsakamo@WestEd.org.
To register, please send your name, address, phone number, fax number and check (made payable to WestEd) by April 16 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; or by e-mail at cbarnet@WestEd.org.
Marilyn Burns Education Associates recently launched their on-line issue of the Math Solutions Newsletter. Issues of this free,quarterly publication may be found at www.mathsolutions.com/newsletter.
Highlights include stories about current practice in mathematics classes; news about inservice training; reviews of recent Math Solutions titles; letters and interviews; and a calendar of events.
This first issue includes an article by Beth Williams that originally appeared in Intersection, along with book reviews by Greg McMann and Tim Martin published recently in these pages. Check it out!
Why not volunteer to review a new title by Catherine Twomey-Fosnot and Maarten Dolk? Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction will soon be available from Heinemann. Please contact yours truly if you’re interested in making this title your own by volunteering to review it.
Also, two individuals have already offered to review Teacher Leadership in Mathematics and Science: Casebook and Facilitator’s Guide by Jean Moon and her colleagues (see January 2001 Intersection). Who would like to make that three? If so, please let me hear from you.
While you may have read that on way too many "conversation hearts" recently, that simple expression tells why this newsletter exists—it is, indeed, for you. Hopefully it connects you with like-minded mathematics educators and keeps you informed about events, research, opportunities and resources.
If you haven’t submitted an article recently, why not send something for the March issue? The deadline is Monday, March 12. Please send contributions to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; phone, (512) 869-1580; fax, (512) 869-8477; e-mail, jean@intersectionlive.org. Many thanks to all who contributed to this issue. You are greatly appreciated!
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