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Many thanks to Holli Hall, a math specialist in Arlington, TX and one of the "caretakers" of the exxonmobiltnt listserv, for sharing her experiences in this article. Ed.
Last year
I was offered an opportunity to become a Math Instructional
Specialist at a new elementary school that was scheduled to open
in August of 2001. Yvonne DuPont, who was my assistant principal
at that time, had received the position of principal at the new
campus, Veda Knox Elementary School. Not only was the position
one that I had dreamed of, Yvonne was exactly the kind of
principal that educators hope for. She is progressive, positive
and believes that all children can learn and deserve every
opportunity that we can give them. I quickly accepted the
position and began my new job this year.
My primary responsibilities are serving as a resource for teachers, monitoring TAAS tutoring for grades 3-6, and helping teachers grow into math professionals who believe in letting children construct their own mathematical thinking. Through my many years of being involved with ExxonMobil, the Ft. Worth Museum of Science and History, and Dr. Christopher Kribs-Zaleta, I believe the best model for professional development is to let the teachers take on the role of learners in an environment alongside their students. I began my year this year surrounded by hundreds of boxes of math manipulatives waiting to be unpacked, and teachers—some new and some veteran—all anxious and excited about beginning a new school year.
My first step after spending hours unpacking boxes was to allow teachers to come and look at all the resources available to them. Many felt overwhelmed at the amount of manipulatives at their disposal and some weren’t quite sure what do with all of them. Fortunately, the district had also provided us with many books that were filled with activities such as the Marilyn Burns Replacement Units and Math and Literature Books. Teachers repeatedly commented on how lucky they were to be in a school with so many goodies to choose from! Our student population is predominantly minority and economically disadvantaged so it was very exciting to have so many wonderful things to help our children learn.
By having teachers come to my room and go through and pick and choose what they wanted, it allowed me time to talk to them and get feedback about what they wanted help with this year. I was thrilled to find so many teachers who were so open minded and virtual sponges for all my ideas and philosophies. I was so used to fighting uphill battles with teachers who did not agree with my teaching methods, I couldn’t believe I was surrounded by such positive energy and teachers who were looking forward to hearing my suggestions.
My next step
was to make a schedule so that I could bring all of our classes,
pre-K-6, into my "Math Lab" to do a variety of
activities. Since—with 400 students—our school is
relatively small by Arlington’s standards, I am able to get
every child through the Math Lab once a month. As I schedule
classes to come and visit the Math Lab, I meet with their
teachers to find out what they are studying in math or what kinds
of things they would like me to do with their students. Some
teachers are very specific about the objective they would like me
to cover while some give me broad topics or even specify a
particular manipulative they would like me to show them how to
use. I feel that by getting feedback from teachers, I can best
serve their needs and the needs of the students. I try to do
activities with the students that have follow-up’s that I
can give teachers to carry over into their classrooms.
In October, through the help of our Family Liaison, I was able to get sixty pumpkins donated to use in the Math Lab. I knew that many of our students had never had the experience of cutting open and working with pumpkins so I thought this provided an excellent opportunity for predicting and measuring. We predicted and measured weight, circumference, and the amount of seeds in the pumpkins. I will never forget the looks on the children’s faces as they reached into the guts of the pumpkin to pull out the seeds. I allowed the teachers to take the seeds back to class and was thrilled to see all the different extensions they made from the Math Lab activity. A first grade class "planted" their seeds in ziploc bags and hung them in the window to sprout. Then they drew pictures and wrote about it. Another class cooked their pumpkinseeds and ate them. Several teachers saved the seeds for us to plant in the spring in our courtyard. Our principal is allowing us to dig out an old sandbox and create our very own pumpkin patch. The school’s Family Liaison has given me information about grants I can apply for to get all the soil and fertilizer. I am hoping that her Dad’s Club will help us with the planting in the spring.
Anne Herndon at the Fort Worth
Museum of Science and History has been a tremendous help to me as
well this year. I have used many of the museum’s kits in the
Math Lab and many teachers in my building have utilized them. One
kit that is one of my favorites 
is the Tops Learning Environment. It
has a variety of different tops in it and materials such as
plastic plates and wooden dowels for children to construct their
own tops. I used this kit with pre-K, kindergarten and first
grade. With pre-K, our primary goal was for the kids to spin the
tops. While many had never even seen a top and had a difficult
time at first, with practice they developed into pretty good
spinners. Kindergarten was better at spinning and enjoyed looking
at all the tops and watching them spin. With first grade, I
allowed them to have some time to spin the tops and then let them
work with a partner to construct their own tops. We then launched
the tops with hand mixers. The students made amazing observations
about the tops they built, and analyzed different aspects of the
tops such as the size of the plate and the length of the dowel
they used. Laral Coe, a kindergarten teacher (and former student
of Christopher Kribs-Zaleta), took the tops kit back to her
classroom so she could set up a center to have her students build
tops. I went into her room during one of their top building
sessions and watched and listened to her students hard at work.
The kindergartners were also good at analyzing different elements
of their tops and would adjust their design to create a better
spin. It was an educational adventure for all of us!
With the upper grades, I have tried to use games that allow for them to problem solve and build strategies. One of the games I used was "Roll for $1," which I found in a Marilyn Burns resource. The game involves rolling a die and then the player can take as many dimes or pennies as appear on the die. The object of the game is to get as close to a dollar as you can without going over. Each player must take seven turns, which is where the strategy comes into play. As I watched students play the game, I was amazed at how many different strategies they came up with. I had students share different strategies and then gave them more time to play so that they could try out some of the strategies that they heard. At the end, I had students write about what they thought of the game and to describe the strategy they used or thought worked the best. While some of the students told me that they had written in math class before, most had never had the opportunity to write about a math activity. Examples of student work are included as part of this article.
The rest of the school year holds many exciting challenges. Dr. Kribs-Zaleta and I plan on collaborating as much as we can. This week he and I will be meeting to start working on writing applications for grants from MET. (See "Still Time" below. Ed.) I hope to receive funds to make kits for my teachers to use as a resource that are similar to the kits I have been checking out from Anne Herndon. The response to her kits has been so favorable, and teachers keep giving me suggestions on different math topics they would love to teach with the kits. I would also like to write a grant to create a website with different topics and questions that would allow students from across the country to interact with students in my building. If I receive the funds for this project, I am hoping my colleagues from the listserv will let their students participate and respond to my students. I will also be open to any suggestions for topics on the website such as grade level math challenges, bulletin boards, etc.
I am looking forward to Mary Jane Smith paying us a visit on November 27. She is coming to do a calculator activity with a fourth-grade class and then will conduct a two-hour workshop for teachers after school. I feel that I owe my enthusiasm and success to all the support I have received over the years from my ExxonMobil family. I would not have been able to grow into the math educator I am today without all of your help and pep talks when I felt like I was swimming upstream! We are truly fortunate for the connection that we all have through ExxonMobil.
Lance Menster, Coordinator for School Programs, Houston Annenberg Challenge and Susan O’Boyle, K-5 Mathematics Initiative Program Manager, Houston ISD, Southwest, sent in this article. Thanks! Ed.
One year ago
in Houston, we were asking ourselves: What is the work of an
elementary mathematics specialist? What kinds of interactions
between math specialists, classroom teachers, administrators, and
parents are important and possible? What kinds of knowledge,
expertise and support do math specialists need in order to create
whole school change in mathematics?
These questions, in large part, resulted from a project that has grown from eight to thirteen elementary schools, from a team of five to fourteen elementary mathematics specialists, and to increased professional development opportunities for classroom teachers in the Houston ISD, Southwest District. This increase in project scale—while exciting—brings new complexities.
In year two, we continue to work with these questions but new ones as well: How do we serve over 140 classroom teachers participating in 48 hours of Developing Mathematical Ideas (DMI) seminars over the course of this school year? How do we provide active participation in their child’s mathematics education to Spanish-speaking parents? How do we provide multiple learning opportunities for a team of committed math specialists as co-teaching facilitators of professional development, coaches, and learners of math content and leadership? How do we develop advocacy among administrators, parents, and the greater Houston community toward our goals of improving the teaching and learning of mathematics?
While the project’s goal—to bring together mathematics specialists, principals, teachers, parents, and the community to engage in learning to improve student achievement in mathematics—continues at the heart of our work, the steps in reaching it are becoming increasingly challenging. Year-two math specialists have assumed and are serving different roles in mentoring relationships with new math specialists. They support structures around co-teaching relationships, the expansion of professional development for teachers, (including DMI’s "Building a System of Tens" and "Making Meaning for Operations") consistent grade-level planning meetings and the formulation of Campus-Based Math Leadership Teams.
Opportunities for principals have expanded beyond Lenses on Learning professional development from last year to include opportunities to engage with classroom teachers in DMI seminars in order to learn math content and ways in which children understand mathematics. (See "Focused in Houston," Intersection, September 2001.) Also, principals are participating in structured professional development alongside their math specialists. They are supporting teachers who are shifting from silent classrooms, student desks in rows, and textbook-driven instruction to students working collaboratively in small groups on meaningful open-ended, free response, multiple representation problem-solving activities that take time, space, and movement in order to develop deeper understandings of important mathematics. During monthly meetings with principals and math specialists, shared experiences include an exploration of the Investigations curriculum with Virginia Bastable, our project’s external consultant, an analysis of what is possible in mathematics reform, and a reflection and celebration on the progress we are making.
"Parents as Partners," another new component, focuses on building knowledge and involvement with family and community members in elementary mathematics. With guidance from Dr. Ruth Parker of the Mathematics Education Collaborative (MEC) in Ferndale, WA, several learning opportunities are being extended to help math specialists gain expertise in working with parents and to help parents in working alongside their child’s teacher in examining important mathematics. Additionally, parents are engaging in campus-based math parent nights as an extension of Ruth Parker’s work in Houston. DMI seminars are currently being offered for parent participation. In partnership with the Children’s Museum of Houston, children and their families are taking a bus trip from their child’s school to explore mathematics outside of the classroom. With support from ExxonMobil, the Children’s Museum of Houston is currently strengthening mathematics in the museum through a new exhibit, "Math Path and Magnificent Math Moments." (See "EM M3," Intersection, September 2001.)
Year two of the project began with a very public celebration on October 9, 2001. A special morning ceremony was held at Red Elementary, one of the original project schools, to announce the expansion and year one results of the project. Key educators and contributors took part in this special ceremony including Dr. Kaye Stripling, Houston ISD superintendent; Edward Ahnert, ExxonMobil Foundation president; Linda Clarke, Houston Annenberg executive director; Mary Jane Gomez and Maureen Huff, project principals; Robert Longoria, Red Elementary parent; Linda Ohia, Red math specialist and her co-teacher Michelle Easton. During this event, a highlight included Linda Ohia and her co-teacher facilitating instruction to fourth-grade students while guests and project partners closely observed and listened as students interacted with a variety of materials exploring mathematical ideas around division and leftovers. The children worked in pairs examining how to share 21 cookies with 4 people, 21 balloons with 4 people, and 21 dollars with 4 people. They also investigated what 21 divided by 4 looks like on a calculator. The student’s math ideas, thinking, and ways of representing division and leftovers in multiple contexts left a lasting impression on an audience seeing first-hand evidence of important and worthwhile mathematics.
How do we characterize a year’s worth of growth? We’ve grown from 8 to 13 project schools and from 5 to 14 math specialists. We have 140 teachers participating in DMI seminars; year-two math specialists mentoring year-one math specialists; 11 Math Leadership Teams; consistent bi-weekly grade level planning meetings among teachers in all project schools; 39 math parent night sessions; 13 family math nights; 13 school-based field trips to The Children’s Museum of Houston; 6 community awareness sessions; and a committed team of math specialists, teachers, administrators, parents, and project partners working as a community of learners to support our children’s mathematical future.
Last January, Sherry Rosenburg (CA), Charlotte Stadler ( NY), and Vandi Hodges (VA), initiated a column bearing this title by sharing reflections about their professional development experiences in Developing Mathematical Ideas (DMI) seminars.
Below, and in the January 2002 issue, you will find stories of readers who were participants in last summer’s DMI seminars. Because the response was so great, space constraints did not allow all reflections received to be published this month. Please look for the rest of them next month. Thank you all! Ed.
"We are thinking very deeply about ideas that seemed deceptively simple."
This is part of an e-mail that I wrote this past summer to Skip Fennell during my stay at DMIL Institute at Mount Holyoke College. Since returning from my trip "up north," many people have asked me to tell what I learned from attending DMI. I always have a difficult time articulating my experience. After fumbling, my response usually is, "You have to go because it is something you must experience yourself!"
The DMIL Institute is a constructivist learning model that challenges you to know yourself better as a learner and, perhaps more importantly, as a teacher. The experience requires you to closely examine your own mathematical understandings and helps you learn to do the same with students. As I prepared to work with my second-graders this year, I thought about some of the seemingly simple mathematical ideas we would work on together such as place value, addition, and subtraction. Reflecting back on what I learned from DMI, my goals became what I want them to understand about these related ideas, rather than merely "to be able to do." I redefined my role as a teacher from one who models how to solve problems to one who models: questioning my own understanding of an idea; constructing my understanding using context and models; knowing that my mathematical ideas are a work in progress; valuing the ideas of others; being flexible in how I solve problems; and challenging myself not to accept a surface understanding of what I learn.
In looking back over the events of the summer, DMI stood out for me as a very positive experience. It was, however, one of change once again.
Change is at times very awkward. It can be joyous, chaotic, and sometimes painful to let go of what one had previously formed as mathematical ideas. The DMI Institute allowed me to experience those events of change with colleagues who were also experiencing many of the same feelings.
I look forward to returning this upcoming summer to further my studies. I will always be grateful to Virginia Bastable and the other great facilitators who awakened my desire for change in my own practices.
Maura Murray, Salem State College, MA, and Sharon Jaworski and Kristin Wang, Witchcraft Heights Elementary School, MA, chose to write their reflection collaboratively. Ed.
In July of 2001, we attended the "Developing Mathematical Ideas Leadership Institute" as a team at Mount Holyoke College. At the institute we were given an opportunity to approach number and operations not only as educators, but also as learners. We embarked together with different expectations and experiences on what was to be an intense learning experience —one that none of us will soon forget.
The participants of DMI— educators and administrators from all over the continental United States—created a strong learning community along with the guidance and support of the DMI staff. The workshop challenged the way that all of us think about teaching. We all came to realize that number and operation could be approached in the classroom in as many ways as there are students. Rather than determining what students have yet to learn or fail to understand about mathematical ideas, we were asked to look at student work and determine what concepts and understandings had to be in place to explain their thinking. This was a far more challenging endeavor and was incredibly rewarding. We were also asked to look at some of the traditional algorithms that we had been teaching, along with some of the "tips" that we had been providing in order to "aid" students in obtaining a correct response to a problem. While the tips and algorithms did yield in many cases correct responses by our students, we discovered that many of them removed the meaning from the mathematics.
While our new understandings are exciting, we came to realize that they represent a huge responsibility. We all had to change the way that we were approaching the teaching of mathematics. We also felt that this learning experience must continue and this would require a great deal of support. We have established a DMI study group within the Salem Public School District with a group of ten great teachers. The group provides an opportunity for us to continue to develop as well as support one another in our new mathematical outlook, while simultaneously sharing the DMI experience with others.
We would like to thank ExxonMobil Foundation for the opportunity to attend the DMI workshop as a team. We would also like to thank the DMI trainers for the experience and all their guidance and support.
As a teacher who has always looked for ways to keep my classroom interesting and challenging to my students, I was intrigued with the DMI I sessions that I had attended during the school year in Houston. Finally, I was beginning to feel that I could now tackle mathematics with my students. As a primary teacher, I always thought the mathematics for my students was easy and very basics—something that I understood and felt I could teach. But as I read and participated in DMI I, I soon realized that I had loads to learn and understand about how children view their understanding of mathematics. And I thought that I was a great kid watcher and listener already. So when I was offered the opportunity to become a facilitator and attend DMI II at Mount Holyoke College, I eagerly accepted the chance to further my own learning while practicing the facilitation of DMI I.
During the summer, the sessions are much more intense because you are totally immersed in mathematics all day and night. This focused time with little distraction allows participants the time to reflect and ponder upon what has been discussed and read. While at Mount Holyoke I realized more than ever the need to continue learning mathematics as the learner and the teacher/facilitator. The time spent this summer has been invaluable for the work that I’m doing this school year. Having facilitators who are experienced in the classroom and who have been working with those who are in the process of changing and improving their understanding both as teachers and as learners helped to model and facilitate my own learning. But more than anything, this experience has changed my views of mathematics not just for the present but forever.
As I reflect on the two weeks spent at DMI, myriad mathematical questions, insights, and experiences continue to sort themselves out in my mind. Rich conversations about mathematics flood my memory. I’m energized to work with my fourth-grade class and with teacher colleagues in learning more about mathematics. Having taught first-grade for over 16 years, I’m a novice at fourth-grade mathematics, yet the familiar challenge of increasing student understanding remains the same.
Through the skilled questioning and guidance of its leaders, DMI provided the opportunity for a diverse group of teacher learners to question, assimilate and grow mathematically. We worked intensively for two weeks, becoming immersed in the program’s two main goals: 1) helping teachers become more competent and confident as mathematical learners; and 2) learning to promote and value mathematical thinking in our students. We discovered a common vision for promoting mathematical understanding. It was powerful!
Tackling problems presented at DMI presented a chance for me to expand my understanding of number and operations and to make connected sense of a "Big Picture" of mathematics. I was a student. I began composing, decomposing and recombining my ideas about, and my understanding of, mathematics. I looked toward to the task of organizing, prioritizing, and synthesizing what had been presented. The "Big Picture" of mathematics was becoming clearer. Connections and relationships began to be paramount in my learning and in my teaching.
I now see mathematics like a jigsaw puzzle having many pieces. All need to be assembled to create a picture. Without a frame or picture on the box, progress in working the puzzle can be disconnected, random, and difficult. I have watched many a young child delve enthusiastically into such a puzzle with no plan or idea of what was to be built, then become frustrated and quit. Others, by using the picture and the connecting structure of the frame as a guide, met success more easily. The significance of the picture and frame, both in puzzle-making and in building mathematical thinkers, is clear.
Like my first-graders’ approach to puzzles, my teaching of mathematics lacked a vision for connections and relationships in light of the "Big Picture." I was working diligently to implement "best practices" using materials and ideas from Dale Seymour, Kathy Richardson, Marilyn Burns, Math Their Way, our new Math Trailblazers curriculum and more. I was promoting understanding, but DMI is helping me to re-think my method.
DMI confirmed that mathematics is about understanding: about understanding the makeup of our number system, about understanding number operations and how they work therein, and about understanding relationships and connections. It’s clear to me that much of what is sometimes assumed to be quite "easy," "simple," or "straight forward" is actually quite complex when depth of understanding and flexible/facile use of that understanding are the goals. Time spent in solving mathematical questions often involves working through confusion to a solution. In my instruction and assessment I’m now asking, "What is it that this child understands about mathematics?" "What is next for this child to learn?" and "What connections/relationships are developing?" I’m taking more time to listen to students’ thinking and I’m asking them to explain that thinking. I sense more metacognition and sharing of strategies. My students and I are seeking to understand rather than just do. In my class we say it’s OK to be confused or to not know yet. The focus is on all students becoming confidently engaged in mathematics and expanding their knowledge. And we are having fun!
What does this all mean for me as a teacher? With an increasingly diverse and challenging student population, and increased performance expectations for both students and teachers, one could lose heart. I believe all my students can become thoughtful mathematicians and I am more confident in guiding them because of my experience at DMI.
The Lamp, a publication issued quarterly for ExxonMobil shareholders, features Houston’s Math Specialist Program in the most recent issue. Entitled "Learning that Counts," the article describes how the foundation, in partnership with the Houston Annenberg Challenge and Houston public schools, is positively affecting how mathematics is taught and learned in Houston’s Southwest District through support of the K-5 Math Specialist Program.
You may read issues of The Lamp online.
Congratulations, Houston! Ed.
Regrettably, due to the events and aftermath of September 11, the Thirteenth Annual Meeting of the ExxonMobil Foundation/NCTM K-5 Mathematics Specialist Program —previously scheduled for mid-September and subsequently rescheduled for mid-January 2002—has had to be cancelled.
Thanks to the folks at Heinemann, you can do just that. Guiding Curriculum Decisions for Middle-Grades Mathematics, a new title from Heinemann Publishing by Lynn T. Goldsmith, Ilene Kantrov et al, wants a home for the holidays. If you’d like to read and review it, please contact editor Jean Ehnebuske and it will be mailed to you pronto!
Although applications for NCTM’s MET (Mathematics Education Trust) awards must be postmarked by December 5, you might still make that deadline if you hurry! Visit NCTM for details.
If that deadline looms too near, please be aware that Toyota accepts proposals for the $10,000 Toyota TIME grant until January 10, 2002. That leaves plenty of time to put something together over the winter holidays, right? To learn more, call 888-573-TIME or e-mail toyotatime@nctm.org.
A Project of the National Alliance of State Science and Mathematics Coalitions (NASSMC), the NASSMC Briefing Service (NBS) provides daily to e-mail subscribers summaries of major news stories that are related to mathematics and science education. The service is free.
To learn more and become a subscriber, visit NBS. At the web site, you can also learn about the extensive "Living Archive" of past NBS briefs. Access to six databases allows users to sample or find lost or missed stories.
ExxonMobil Foundation and the National Security Agency (NSA) support NBS.
I’ve been a subscriber since ’99. I recommend it highly! Ed.
We haven’t had a year like 2002 since 1991. And we won’t have another for one hundred and ten years more.
But riddle me this, have you thought about appearing in the very first issue of the new year? It’s easy. Just send in an article by Monday, January 14, and there you’ll be! Resolve you that?
Thanks to everyone who contributed to this year’s issues. Working with each of you has been an editor’s dream.
Items and articles may be sent to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; e-mail, jean@intersectionlive.org; phone, (512) 869-1580; fax, (512) 869-8477. Happy holidays and best wishes to all for 2002!
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