Cast your minds back to English III in high school, and you'll remember reading Carl Sandburg's poem, "Chicago," a paean to that city. No doubt the lines you'll recall are "Hog butcher for the World, Tool Maker, Stacker of Wheat...City of the Big Shoulders." Look it up and you'll enjoy reading once again other lines that pay tribute to the energy, vibrancy, and vitality of Chicago. Wrote Sandburg: "Come and show me another city with lifted head singing so proud to be alive and coarse and strong and cunning."
All that and more is what you'll find in NCTM's host city for the Annual Meeting, April 12-15. If you'll be there, the ExxonMobil Foundation invites you to the traditional reception that allows project participants, guests and friends of the foundation to gather for conversation, hors d'oeuvres and drinks. Slated for Thursday evening, April 13, from 6-8 PM, this event will be held at the Hyatt Regency Hotel in "Grand B" located on the Ballroom Level of the East Tower. We hope that you'll try to be present for a brief program beginning at 7 PM. There is no need to RSVP, just plan to join us!
For the past three years, some of you who have been fortunate enough to attend NCTM's Annual Meeting have shared your experiences there—and your reflections about those experiences—in a supplement to the May Intersection, "A Collection of Reflections."
If you'll be at the conference this April, please consider writing a few lines about it for that supplement. Nothing lengthy is requested; the average length of past reflections has been 125 words. You may write about any aspect of the conference: a session that moved you, an exhibit that inspired you, a presenter who changed your thinking. Please send your thoughts to yours truly no later than Monday, April 24.
The ExxonMobil Foundation is pleased to announce a new opportunity for funding within the Elementary Mathematics Program.The initiative is focused on encouraging and supporting active collaboration between sites. Letters of the announcement are being sent to current project directors.
Networking Grants is an initiative that provides funding to support activities proposed by project sites wishing to collaborate with one another on topics of mutual interest. Presently, there are several across-project, networking initiatives. As featured in the last issue of Intersection, Bellevue, Washington and Iowa City, Iowa are working together on assessment and aspects of the Developing Mathematics Ideas (DMI) professional development curriculum. Since last spring, a study group at Liberty School in Murray, Utah and Professor Chuck Walter of Brigham Young University have been working with the Albuquerque, New Mexico project on a variety of topics—assessment, research lessons for teachers, and pre-service education.
The foundation's hope is that project directors, teachers, and mathematics specialists will have an opportunity to strengthen project activities by collaborating with another ExxonMobil site. Since common interests are often identified during conversations that take place over coffee or on a bus ride during the annual meeting the foundation hosts each September, Networking Grants has been created as a way to to bring these hopes for collaboration to fruition.
Networking grants for up to $4000.00 per collaborative endeavor will be awarded on an annual basis. These grants are in addition to the ExxonMobil funding made to an individual project site. Grant funds are to be used for travel between sites, lodging and meals, and teacher release-day costs, as well as for meeting costs that might result from collaboration activities.
To apply for a grant, those interested will need to prepare in concert with the project director or mathematics specialist from another site a short proposal that answers:
Once the proposal has been developed, it should be sent for review to Jean Moon. Jean will be in touch if further detail is required.
Proposals are currently being accepted, and are welcome at any time. Please direct questions to Joe Gonzales at (962) 444-1122; e-mail, joe.e.gonzales@exxon. com, or to Jean Moon at (978) 448-0626; e-mail, mbb321@ ultranet.com
Many thanks to Eula Ewing Moore, professor of mathematics education in the College of Education at Brigham Young University, for contributing this report about the project in which she is engaged. Ed.
More than two years ago, the faculty and building principal at Cascade Elementary School in Orem, UT, recognized a pattern in mathematics achievement —their students were capable problem-solvers but had less facility in computation, especially the recall of basic facts. Because the traditional curriculum in place was not providing the support teachers and students needed, the faculty made a bold choice. They made MathLand their school-wide adoption, beginning with the primary grades. They also committed themselves to teaching computation conceptually.
In 1998, the Cascade principal invited
Eula Monroe of nearby Brigham Young University (BYU) in Provo to
join with the faculty as they worked on improving the teaching
and learning of mathematics. About the same time, Chuck Walter
and Bob Speiser—also of BYU—were studying mathematics
teaching and learning at Liberty Elementary School in Murray, UT.
The work at Liberty received funding from the Exxon Education
Foundation. During 1999-2000, this funding expanded to include a
working relationship with a study group at Cascade Elementary
School.
The Cascade study group has met regularly, and helping students learn their basic facts has been one of their primary goals. A fundamental principle has guided the group: students should have opportunities to learn these facts in ways that help them remember, not rote memorize them. Active participants in this group are teachers Amy Reid (K-1), Lori Aldredge (1st grade), and Lynnette Dowdle (3rd grade), as well as mathematics curriculum specialist and classroom teacher Nancy Hale (6th grade), building principal Georgia Davis, and Eula Monroe. To help them work toward their goals for 1999-2000, they are studying ways to implement the problem solving approach of MathLand to full advantage. Last October they attended the NCTM Western Regional Conference in Boise, ID; they continue to read extensively from the literature in mathematics education—trying new ideas and discussing them with one another; and they have met with the Liberty study group on three occasions. Because the Liberty teachers and the principal have worked together for about two years, they provide a helpful model for a study group; Cascade's longer experience with MathLand is of help to Liberty, which began implementation of this program in Fall 1999.
The Cascade study group has not found a quick recipe to student success with basic facts; however, their students are developing meaning by:
These strategies have been shared with parents throughout the year and will be the focus of Parent Night on March 29. After a year of intensive work and study, the group is more committed than ever to their choice. They are providing students opportunities to remember, not rote memorize, as a key to success with basic facts.
Many thanks to Vandi Hodges, Mathematics Lead-Teacher Specialist in Hanover County, for contributing the article below. Ed.
The Hanover Public School System has received a grant from the ExxonMobil Foundation for the past 10 years. The district maintains a rural charm but has a growing suburban population being within a 20-minute commute of the state capital in Richmond.
We currently have approximately 16,000 students in 3 high schools, 3 middle schools and 12 elementary schools. We will open a new campus at each level—elementary, middle and high school—in the next three years. Assistance from the ExxonMobil Foundation has played a critical part in helping Hanover build and maintain a strong mathematics program within a changing and growing district.
Initially our grant proposals focused on developing the leadership skills of our designated building-level mathematics leaders and showing them how manipulatives could help engage students in the learning process and promote student understanding of concepts. Dr. John Van de Walle from Virginia Commonwealth University helped with this early training. The teachers and students both enjoyed using hands-on activities. Their enthusiasm grew. Using leadership skills and confidence gained through Exxon training sessions, the mathematics leaders conducted workshops within their schools, the district, and at state and regional meetings.
As the teachers learned more about the NCTM Standards and research in mathematics education, they wanted to develop a better understanding of how the hands-on activities they had been using fit into the larger picture of helping students to understand mathematics. They needed to strengthen their own knowledge of mathematics concepts if they were going to effectively analyze student understanding. Three years ago they submitted a grant proposal focused on the need to improve their own content knowledge, strengthen their pedagogy and improve their implementation of assessment strategies.
Tom Rowan, faculty member at the University of Maryland and at Johns Hopkins, and consultant for numerous national projects, and Anna Suarez, now with the National Science Foundation, began working with the teachers, sharing their research and expertise. Among other training activities, Dr. Rowan and Ms. Suarez have shared video clips from Project Impact. These are helping teachers realize the variety of strategies and methods that children can bring to learning environments. Through group discussions and analysis of their own students' work, Hanover teachers are learning to teach for understanding.
Between sessions with Dr. Rowan and Ms. Suarez, teachers are often given a "homework" assignment to try in their school at multiple grade levels and abilities. At first the teachers were amazed at the multitude of strategies that very young children used to solve a problem. They were also distressed but not surprised by the frustration of older children as they confused algorithms that they had tried to memorize but never really understood. This evidence has convinced the teachers that students must be given opportunities to express their ideas. From this information teachers can help children build on their prior knowledge, help them learn to record their strategies, and help them solve problems in a way that they can understand. Several of our teachers extended their understanding of this process at the Developing Mathematical Ideas Institute last year. After sharing their experience and enthusiasm with other teachers in the county, some are planning to attend this summer.
One of our teachers' most recent "homework" assignments was to read the article, "Children's Understanding of Equality: A Foundation for Algebra," from Teaching Children Mathematics, December 1999. Karen Falkner, a primary-grade teacher in Madison, Wisconsin wrote the article in conjunction with Linda Levi and Thomas Carpenter who are studying the algebraic thinking of young children. Ms. Falkner asked her first/second grade class to solve the problem 8 + 4 = _ + 5. Previous research had shown that sixth-grade students thought either 12 or 17 went in the box. Ms. Falkner's students gave similar answers suggesting that even young children had established misconceptions about the equals sign. Hanover teachers took a similar problem (7 + 5 = _ + 4) back to their schools and found half of the fifth-graders tested got it correct but others chose either 12 or 16. In one first-grade class, one student answered it correctly and explained that the equal sign meant the two sides had to be the same. However the majority of the children interpreted the equal sign as a signal to do something. Dr. Rowan will share the Hanover findings with Dr. Carpenter in support of his research. Participating in this type of exercise generates a lot of discussion among teachers at the school level as well as in the ExxonMobil teacher-leader meetings. Through these discussions, strategies are shared and teachers become more effective facilitators of children's learning.
Dr. Rowan is also helping us with our curriculum work. Hanover has chosen to put both the new Scott-Foresman series and the Investigations materials in the elementary schools, initially giving the teachers a range of resources. Dr. Rowan is working with our staff to help teachers transition from the more traditional series to the Investigations materials over time. He and Ms. Suarez are currently working on a National Science Foundation grant with a school district in Phoenix, Arizona where Investigations in Number, Data and Space was selected as the primary mathematics instructional resource. Their experiences in this district have been helpful in moving our program along. The K-3 ExxonMobil teachers are instrumental in this curriculum revision process along with designated fourth- and fifth-grade teachers. They are currently revising the curriculum guides to combine the long list of Virginia's State Standards of Learning for Mathematics (SOL) into a more integrated and connected list of objectives. Correlations to the Investigations materials are being reviewed and new assessment items are being written.
The Virginia State Standards of Learning (SOL) were adopted in June of 1995, and in 1998 students were first introduced to the SOL tests at grade 3, 5, 8 and for end-of-course tests in Algebra I, Geometry and Algebra II. These high stakes multiple choice tests will eventually be used to determine whether or not a child graduates and whether or not a school is accredited. This initiative has put tremendous pressure on administrators, teachers and children across the state. The multiple-choice format and the list of 20-25 objectives per grade level/course have driven some teachers to return to a more skills-oriented curriculum. Our goal in Hanover is to maintain our vision and to base our teaching on documented research that shows teaching for understanding will allow students to be successful on both performance assessment tasks and more traditional multiple-choice tests.
Hanover continues to score in the top 10% of the school districts on the State standardized test measures. Our mathematics teachers have received numerous honors and many have received individual teaching grants for up to $10,000. Many of our teachers serve on the local NCTM affiliate group's board or committees. Representatives participate on State committees to review the SOL test results, and develop support material for teachers across the state.
To provide staff development within the district, the school system has instituted peer-coaching training for all teachers. Designated teachers have also been trained as technology coaches of each school. The school system supports integration across curriculum areas and has supported summer training for this effort. This summer's workshops will include assessment training for administrators and teachers. Bena Kallick and her associates have been hired to assist with this work.
Efforts to integrate content go beyond staff development. For example, mathematics and science resource boxes are being developed for each grade level correlating the physical science strands and the appropriate mathematics at each grade level. Teachers have written integrated lesson plans and provided training for teacher-trainers at each school. Funding for the boxes in 12 elementary schools is about ten thousand dollars per grade level, so corporate funding is being sought. Target has already provided funding for our first grade boxes and the school system covered the cost of the fourth grade. Boxes include such items as magnets, batteries, toy cars, wooden ramps, meter sticks, simple machines, and a variety of grocery store items. Funding will provide for refurbishing of the boxes for the next five years.
To correlate the work of our teachers across all grade levels, a K-12 Mathematics Curriculum Development Committee was formed three years ago. It is composed of the ExxonMobil K-3 mathematics leaders from each elementary school, several upper elementary teachers, secondary mathematics department chairmen, a principal from each level, parents, students, business leaders and four local university mathematics professors. This committed group of individuals worked with teachers across the district to write our mathematics philosophy, study our current needs and set goals based on a cohesive vision. The group led the textbook adoption process last year and oversees its implementation today. The elementary leaders, thanks to the training from ExxonMobil, have played a critical role in this process. Business leaders, parents and students provide perspective and an important liaison with the community. The university professors have provided insight on research and the latest technology. Several have been involved in our staff development. For example, at the elementary level, Dr. Ena Gross of Virginia Commonwealth University is working with the staff at two of our elementary schools on mathematics content and pedagogy. She is also providing valuable parent workshops throughout the year.
Much work still needs to be done, but with the support of dedicated teachers and organizations like ExxonMobil we are excited and encouraged about improvements in mathematics education in the U.S. and feel fortunate to be a part of the effort. We would love to have a visit from any of our ExxonMobil colleagues. We are only two hours south of Washington, D.C. and one hour from historic Williamsburg and the beach. Please e-mail if you are coming this way!
Candance Dolan, a Math Helping Teacher and member of the Kindergarten Team at Short Elementary School in the Arlington (TX) Independent School District sent news that her team has received a $5000 "Innovative Teaching Grant" from the Arlington ISD Education Foundation for their proposal, "Parental Involvement with Four 'Year Long' Kindergarten Projects."
Designed as a means to enhance student learning in math and reading by engaging parents in the education of their children, the project will provide daily, weekly and biweekly activities for kindergartners and their parents to do at home.
Candace writes that she believes that receiving the grant was an outgrowth of the experiences and opportunities provided over the last three years by participation in their Foundation-supported project. She writes: "I want to thank the Foundation for all you do to support teachers in their personal growth and commitment to quality education for our children."
Anne Herndon and Holli Aflatouni, caretakers of the EXXONTNT listserv, collaborated on the item below. Thanks for the article, and thanks for taking such good care of our conversations! Ed.
There are many ways our Foundation links people involved in the different Exxon projects nationally. Attending conferences with Exxon folks is one way to connect, as is this newsletter. Another way to actively interact within this family of projects is through the EXXONTNT (Teachers Networking Together) listserv. We thought we would share a sample of one of the recent conversations that occurred on the listserv to give you a sense of the nature of some of the conversations that happen throughout the year.
During a forum with college students, Christopher Kribs-Zaleta, a professor at the University of Texas at Arlington and a member of the Exxon family, was asked the following question by a student, "We often do activities in the classroom that introduce a topic in a constructivist way, where the children are able to work with manipulatives to build their understanding, but then we have to have some way to assess them quantitatively, and all we give them are these worksheets that they have a lot of trouble with. What kinds of substantive assessment tools are there that will work better with the children? We feel a lot of pressure to give grades."
In his message to the listserv group, Christopher commented, "All I could think of was to point my students to a links page on my web site and recommend the NCTM Addenda. Can anyone think of anything else that I can pass along to them?" The listserv allowed Christopher, and those who are a part of the group, to call upon the broad base of expertise and experiences of the listserv members to help gather information, ideas, and support.
To date, two teachers have shared their perspectives with Christopher. Holli, who is a second-grade teacher also in Arlington, Texas says she responded this way: "Christopher, when you teach in a constructivist way, it is a challenge to find a way to get grades that meet the needs of teachers, students, and their parents. My solution is to make the kids 'record' their work. In Investigations it always told them to use words, numbers and pictures to explain their thinking. This seems to work and give an end product that is 'gradeable,' if that's a word. Even when we play card games, I get them to record their number sentences. My students are not thrilled about all the recording, but they do it. It is a difficult and long process to develop their ability to explain their thinking. In the beginning I get a lot of explanations like 'I used my brain,' and 'The answer just came to me,' but through patience and perseverance, it gets much better."
More from Holli: "One complaint I hear a lot from traditional teachers is that doing all these constructivist things is all well and good, but can the students transfer what they know to taking a pencil-and-paper test. I think the key is to give the students enough variety that they can adapt their thinking to any type of assessment. Even though I let my students solve problems any way they want to, I make sure they understand the more traditional ways, too, because I know that in third grade they will be expected to understand it that way. We just say that it's the 'third grade way' and leave it at that. And then I hope that they will retain some of the constructivism that I have hopefully implanted in them."
Martha La Pointe, a third grade teacher from Mapleton, Maine added, "In my classes I always try to do activities that are authentic. I wonder when in the 'real' world one ever has to take a computation test!? It's comforting to know that others struggle with teaching kids to explain their thinking through pictures, numbers, and words. I try to save good examples of student work to show new students a model."
Holli again: "As a classroom teacher, I find that the listserv provides me a place to share my experiences and frustrations without worrying about being criticized about doing something different. It is a place I have found support and collaboration with a group of professionals who all care passionately about how children learn. I think all the subscribers on the listserv, whether they are just lurking or write frequently, benefit from its support system and learn from the experiences of others. It is a peaceful refuge to come home to at the end of a hectic school day!"
If these comments sparked an interest, resonated with your ideas about teaching mathematics, and demonstrated that the listserv is a place to have conversations about mathematics when there may not be that type of support in your school, there is an easy way to become a part of the discussions. Join! To subscribe, send an e-mail message with the words subscribe EXXONTNT in the body of the message, not just on the subject line. The account from which you send your message will be subscribed to the list. Please address the e-mail to major domo@math.byu.edu. After subscribing, you'll receive more information.
Many thanks to Chris Ohana, now teaching at Western Washington University in Bellingham, WA for the review that follows. Until last fall, Chris was involved with the MathCo Project in Iowa. Below, she reviews an article by Susan Ohanian from Phi Delta Kappan, January 2000. Within the review, Chris points readers to a related article written by Robert Linn.
In her recent article in PDK, Susan asks the critical yet neglected questions about standards-based reform efforts such as Goals 2000. Specifically, whose good is being served? Who should have the authority to develop standards and tests? What happens to non-standard children haunted by a standard curriculum?
The standards-based reform efforts have an unsavory genealogy. A Nation at Risk begat America 2000 which begat Goals 2000 which spawned a plethora of state standards. Now all states (except dear, sensible Iowa) have state standards. Fifteen years ago, Susan found the original documents of A Nation at Risk and America 2000 to be annoying but ignorable. These texts thrashed and bashed but had no muscle. But times, as Susan points out, have changed.
The new standards come complete with a powerful ally—high-stakes tests. The market metaphors used by education critics are not new. Education critics have applied business efficiency concepts to education since the turn of the century. Schools are compared to conveyor belts on which students travel from grade to grade. At each stop they are stamped with the information necessary for the next station. None of this is new. It drove the development of modern structures of schooling. Despite these structural changes, teaching has remained remarkably stable. So why worry now? The difference is in the development of high-stakes testing.
Susan describes some of the more inane examples of high-stakes tests: Quick, who was William Tyndale? What was the major economic consequence of the Blizzard of 1888? Writers of Trivial Pursuit questions seem to have guaranteed job security through test-writing. Some questions that may not be trivial compensate by requiring stupid answers. Susan presents a test question which forces students to choose acoustical properties over the structural integrity of a concert hall. I will add my own example of a NAEP test item that claimed the correct answer to a question about the life cycle of a butterfly was "egg - caterpillar - cocoon - butterfly." Wrong answers included "butterfly - egg - caterpillar - cocoon." Test writers seemed to have answered the age-old question of which came first.
Susan goes beyond describing examples of flawed test items to look at a much more critical issue: Who writes these tests and how will they be used? Should testers in the exclusive beach community of Monterey have the authority to write exams for New York third-graders? Why would the Virginia school board purposely choose a test that 97% of their schools would fail? This testing lunacy affects real kids and their families as the New York disaster demonstrates. A friend, a man from Norway, told me that his daughter came home and solemnly reported her news. She had to prepare for The Test. She would need to get rest, eat right, and practice. When, my friend asked his daughter, is this test? "In three months, and we are already behind." He asked me if it is customary in the U.S. to spend three months preparing eight-year-olds for a test.
What agenda would drive these events? Susan suggests that,"Once the high-stakes tests drive a standardized curriculum into the schools, politicians and their corporate cronies can claim they have equalized education— regardless of the shameful inequalities of facilities and resources" (p. 352). If all kids have the same standards and take the same tests, then we can assign blame to those schools and teachers whose students fail. Enter vouchers and the privatization.
Is there hope? Susan offers some glimpses. There have been some small anti-test rebellions in many communities. Perhaps as parents are confronted with some of the consequences and hidden costs, more will resist the testing frenzy. She also admires the organizational skills and activism of the Radical Right, "Liberals grouse and grumble; conservatives set up web sites" (p. 354). Clearly, the assumptions of high-stakes testing need to be challenged by groups of organized, knowledgeable educators and parents.
One start might be low-tech. I suggest that we nail a copy of Susan's manifesto to the doors of the state capitols. I do not suggest this as a way to impose my views but rather to return to a reasoned discussion of why and how we educate.
What if policy-makers do not listen to Susan's stories and common sense? I'd recommend a companion piece to Susan's— "Assessment and Accountability"—that appeared in Educational Researcher, Volume 29 (2), March 2000. In his extensive review of high-stakes tests, author Robert Linn concludes that "Assessment systems that are useful monitors lose much of their dependability and credibility...when high stakes are attached to them" (p. 14). State policy-makers are attracted to high-stakes tests because they:
In short, high-stakes tests are political junk food—they are accessible, cheap and satiate without nourishing. Of particular note is the pattern of scores in the implementation of any test system. The first scores are low. As students and teachers learn and teach to the test, scores rise dramatically before stabilizing within a few years. This pattern is classic. The improved scores tell us nothing about teaching or learning beyond skills at test-taking. But the initial low scores followed by dramatic gains make any ambitious politician drool.
This article contains a wealth of detail that would be of interest to those who are involved in policy decisions. But first brew a pot of strong coffee. If only academic researchers could write like Susan Ohanian!
When did your article last grace these pages? Readers would like to know what's going on with your project. This is the place to share that.
Many thanks to those who submitted articles this month. Contributions for the April issue are due no later than Monday, April 24. 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.