September 2001

v

Spreading the Light: Lenses on Learning

Many thanks to Barbara Scott Nelson, Nancy Cole and Susan O’Boyle for contributing the articles that follow.

Barbara is Director of the Center for the Development of Teaching at the Education Development Center in Newton, MA. Until her retirement last May, Nancy worked in Albuquerque, NM, as a math and science resource teacher. Susan is mathematics instructional supervisor for the Houston ISD, Southwest District. Ed

Origins and Impact¹

By Barbara Scott Nelson

In the early 1990’s my colleagues and I had an NSF grant to provide professional development for elementary mathematics teachers.² Like many people with such grants, we invited the principals, district math coordinators, and associate superintendents from the teachers’ schools and districts to be part of the program—visiting the program several times and working with the teachers on mathematics and new instructional ideas, and meeting on their own to talk about how they could support teachers who were in the process of transforming their instructional practice.

These administrators—about 40 of them—were very intrigued with the then-new changes afoot in elementary mathematics, prompted by the NCTM’s 1989 Curriculum and Evaluation Standards for School Mathematics. By visiting the program, they were beginning to develop an appreciation for what puzzling about a mathematical idea might feel like to children and teachers, what it meant to understand a mathematical idea because you had puzzled it out for yourself, what teachers were trying to do as they worked to base their instruction on children’s mathematical thinking, what elementary mathematics classrooms might look like, and so on. But they asked us a question we hadn’t expected. "What," they asked, "was the importance of all this to their own work?" That question—and our attempts to answer it—has involved us in an eight-year journey that is not yet finished. In the process, the Lenses on Learning courses were developed.

What these administrators were sensing was that the work of school administration—instructional leadership, if you will—requires being in close touch with the nature of the teaching and learning that is happening in classrooms. If one is going to be an instructional leader, it is important to understand the nature of the enterprise one is leading. Most administrators were educated at a time when a transmission view of learning and teaching prevailed. Their personal teaching histories, often based on this view, inform their administrative practice. Administrators have specific images of classrooms, teaching, and learning in mind as they make administrative decisions that they intend as supportive. These images, along with the images of management that they have acquired over the years, ground their sense of what it is that is being managed and how it can be supported.

To make this connection clear, consider the example of teacher evaluation. Many administrators have images of mathematics classrooms in which the lesson is presented, students do work at their seats or in-groups, and homework is assigned. The expectation is that the lesson should be tied up neatly by the end of the class period with the facts of the lesson and the homework assignment clear. This image of classrooms is based on the notion that knowledge can be unproblematically transmitted from teacher or textbook to students in discrete chunks that can fit neatly into a forty-two minute class period, and that everyone’s minds can then shift cleanly to the next subject on the agenda. Such an image leads many principals evaluating a teacher’s performance to expect "closure" to the lesson. But evaluating classrooms in which knowledge unfolds through discourse and where interesting questions are not all answered by the end of the class period requires a different image of what knowledge is and, therefore, what should go on in classrooms and how the lesson might end. Traditional notions of closure may not be appropriate. Administrators whose expectations of how a lesson should end based on a transmission view of learning will be out of alignment with contemporary ideas about inquiry- or discourse-based teaching. They are likely to perform the administrative function of teacher evaluation in a way that is not attuned to the intent of that teaching. One principal with whom we have worked described how his expectation for closure to lessons changed:

From a traditional observation’s point of view and a paradigm of the past, most principals, I assume, would go in and look for a total lesson, that the closure would be there…that you wouldn’t leave any cliff hangers to be carried over. [In the lesson on this videotape] there’s a shift to saying, "I’ll carry it on another day." Kids go home and do their follow-up assignment. ... I look for closure in most lessons and I’m not seeing [it] any more and it doesn’t upset me, as it would [have] in the past.

This is not to say that there is now no sensible way for lessons to end, only that the traditional idea of closure may not be appropriate for a classroom environment in which important and hard ideas are being discussed over a long period of time. "Closure" may need to be redefined.

A premise of our work with administrators is that their ideas about the nature of learning and teaching matter. That is, if one is responsible for administering a school or school district, it is not sufficient to employ management techniques without regard to the degree to which they are appropriate to the nature of the processes being administered. Understanding the nature of the organization’s basic processes—in this case teaching anchd learningÿ—is a prerequisite for appropriate management. And so, in our view, it is necessary for administrators to understand contemporary ideas about the nature of learning and teaching in order to take a critical stance toward their own administrative practice and modify it where appropriate. Readers familiar with the Developing Mathematical Ideas curriculum for teachers will see similarities in overall goals and orientation.

The Lenses on Learning courses were designed to provide this opportunity for school and district administrators. There are two courses: Lenses on Learning: A New Focus on Mathematics and School Leadership, and Lenses on Learning: Classroom Observation and Teacher Supervision in Elementary Mathematics³ The first of these consists of six modules and is intended to help administrators think through ideas about mathematics, learning, and teaching, in the context of several functional areas of their own work. Following an introductory module, there are modules on professional development for teachers, classroom observation and teacher supervision, student assessment, heterogeneity in the classroom, and working with parents. In these modules, administrators have the opportunity to:

v	explore important mathematics topics in the elementary mathematics curriculum;
v	examine and discuss samples of student work in elementary mathematics;
v	view videotapes of a clinical interview with a child about her mathematics thinking and discuss the implications for mathematics teaching;
v	view videotapes of teachers in the process of reforming their instructional practice and discuss with colleagues what is seen;
v	examine and discuss excerpts from teachers’ journals as they work to change their mathematics instruction;
v	read and discuss relevant research-based articles; and
v	be part of a collegial community of administrators with shared interests.

The second course is an eight-session, year-long course which gives administrators the opportunity to learn to focus on children’s mathematical thinking when doing a classroom observation and explore how the teacher’s knowledge and pedagogy support the development of children’s mathematical thinking. They also have the opportunity to rethink what they might want to talk with the teacher about in a post-observation conference and how they might want to have that conversation from the perspective that teachers, too, are the constructors of their own knowledge about mathematics and children’s learning of mathematics. In this course, which is videotape-based, administrators work with a specially-designed classroom observation guide that provides support as they begin to attend to the mathematical ideas at play in the classrooms they observe.

Both of these courses have been field-tested nationally. The first course was field-tested at the University of Washington, Seattle, WA; State University of New York at Cortland, NY; Boston Public Schools, Boston, MA; Greenville County Public Schools, Greenville, SC; Clark County Public Schools, Las Vegas, NV; Albuquerque Public Schools, Albuquerque, NM; Durham Public Schools, Durham, NC; Phoenix Public Schools, Phoenix, AZ; and Mt. Holyoke College, South Hadley, MA. The second course was field-tested at the University of Wisconsin, Milwaukee, WI; Houston Independent School District, Houston, TX; Hamilton County School District, Chattanooga, TN; Clark County Public School, Las Vegas, NV; Portland Public Schools, Portland, OR; and New York City, Community District #2. A number of ExxonMobil sites were involved in these field tests.

Typically, a Lenses course has 15 - 20 administrators enrolled. Often, elementary principals make up fifty-percent of the participants and the rest are a range of central office staff—assistant superintendents, math coordinators, special education coordinators, Title 1 coordinators, etc. There are often one or two teachers who are exploring the possibility of becoming principals.

The field-test was independently evaluated, and we are grateful to the field-test sites, which were diligent in providing the data that the evaluators needed. Data collected included: pre- and post-tests administered to participants; a brief survey administered after every class session; facilitator journals; periodic interviews with facilitators; site visits; and interviews with selected participants.

The results of the field-test were very impressive. The evaluator reported that virtually all administrators developed a deeper understanding of standards-based mathematics instruction and were able to discuss it quite articulately. They were able to provide many more details when they did classroom observations than they had before, and they focused more on the mathematics itself than they had done earlier. Participants tended to view their own administrative work as being increasingly aligned with that of teachers—that is, they began to see themselves as instructional leaders who worked with teachers to improve instruction. Finally, many participants began to see classroom observation as an opportunity for their own learning about mathematics instruction, not just an occasion for evaluating teachers.

The words of one principal at the end of his first Lenses course may make these results come alive and convey a bit of the poignancy many administrators feel when they compare their new understanding of elementary mathematics instruction with their own childhood experiences:

An idea that is particularly salient for me is that of moving teachers into discussing and exploring with their students their understandings of math concepts, beyond the "mechanics" of algorithms. Investigating children’s thinking. Personally, I think this is extremely important and I wish someone had done more of this with me as a student. Little to none of it is taking place in my school right now. Still too much emphasis just on basic skills without enough connection to real situations and exploring individual students’ thinking. … I would like to bring this idea into our discussions around how we want to improve math instruction as we move closer to a decision on an appropriate math program at our school.

A publisher for the Lenses material has been identified and the first Lenses course, Lenses on Learning: A New Focus on Mathematics and School Leadership should be available in the spring of 2002. While the materials have comprehensive facilitator notes and can be taught simply on the basis of the written materials, EDC offered a Facilitator Institute in July 2001 for those who wanted deeper exposure. Field-testers Franny Dever (Albuquerque) and Valerie Gumes (Boston) were among 35 educators from around the nation who attended. Facilitators Institutes will also be offered in 2002 and 2003 for people who would like to be part of a growing national community of people who are interested in the development of administrators’ ideas. Contact Glenn Natali at EDC for more information.

Notes

¹ The Lenses on Learning work described in this article was supported by grants from the National Science Foundation and The Pew Charitable Trusts. Research on how administrators link new ideas to practice has been supported by the Spencer Foundation.

² Mathematics for Tomorrow, NSF grant # ESI 92-54479.

³ Grant, C. M., Nelson, B. S., Davidson, E., Sassi, A., Weinberg, A.S., & Bleiman, J. (in press). Lenses on Learning: A New Focus on Mathematics and School Leadership.

Grant, C. M., Nelson, B. S., Davidson, E., Sassi, A., Weinberg, A. S., & Bleiman, J. (In press). Lenses on Learning: Classroom observation and teacher supervision in elementary mathematics.

Ayes for Lenses in Albuquerque

By Nancy Cole

At NCTM’s 1999 Annual Meeting in San Francisco, the Albuquerque ExxonMobil teachers attended a session on a math professional development program for principals called Lenses on Learning. The program is comprised of six modules, each one spotlighting an area of mathematics and tailored to the work of an instructional leader at an elementary school. Each module consists of four or five three-hour sessions. The six modules address: the nature of mathematical understanding, the development of children’s mathematical understandings, discourse-based mathematics instruction, professional development for teachers, heterogeneity in the classroom, and assessment. There was an opportunity to field-test the program. So two of us—Franny Dever, a principal at Mark Twain Elementary, and I, a math and science resource teacher for the district—applied for Albuquerque to be a site and were accepted.

The first year, 1999-2000, there were twelve elementary school principals who signed on for the year-long course using three of the modules. The first module was called "So What’s This All About, Anyway?" In this module, administrators engaged in mathematical problem solving—presented at an adult level—in important topics in the elementary mathematics curriculum. Through this work they gained an appreciation for the nature of mathematical understanding that goes beyond algorithmic manipulation. Administrators spent time doing and learning mathematics. Time was spent looking at videos of children explaining their thinking and having conversations around the mathematics they know. Principals then spent time doing the math the children were doing and discussing the mathematics reform movement.

Questions like these sparked interesting discussions: "How is this different from the way you were taught to do mathematics?" "What do these children already know about math?" "What does the teacher have to know about math to conduct this classroom discourse?" "What does a teacher plan for these children next?"

The second module used was "Classroom Observation and Teacher Supervision: Developing an Eye for Mathematics Classrooms." It addressed the issues of developing an eye for reformed and reforming classrooms; developing an understanding of what a teacher’s long-term mathematical agenda might be and the role of such an agenda in teaching; and beginning to rethink their own supervisory and support relationship with teachers. Administrators role-played having conferences with teachers and spent time evaluating their own style. Discussions centered around how to alter a particular style to be more supportive of individual teachers in their shift of mathematical pedagogy. Participants spent time designing questions and record-keeping ideas that would better support their teachers and provide feedback that was useful and child-centered. They also worked on helping teachers learn to self-assess and be continual learners.

The third module was named "From Testing to Assessment." This module provided administrators the opportunity to think about several important aspects of testing and assessment in this time of transition. New approaches to assessment reflecting instruction that emphasizes mathematical thinking linked to standards were explored. Principals discussed what it means for assessments to be "standards- based" rather than "norm-referenced" and looked at connections between new forms of assessment and classroom learning and teaching. They had an opportunity to study various assessments such as criterion-based, norm-referenced and performance-based tests and discussed what each one of these tests reveals about a particular student’s mathematical knowledge and thinking. Principals had a chance to interview a student and compile any assessments given in prior years, and then discuss with a colleague what such information provides about a particular child and what else an educator would want to know.

Throughout the sessions the principals verbalized that Lenses on Learning was the best and most effective professional development they had ever received. The principals shared the articles they read with their staffs and reported that they were not only well received but also inspired mathematical discussions throughout the days and the year. Principals also reported how differently the teachers responded to them when they became aware that "their principal" was attending sessions on mathematical reform and the classroom. Teachers began to come in the office or stop them in the hall to share some child’s work. Teachers now wanted their principal to come to the classroom and see what their children could do mathematically. Principals were excited about the new conversations they were having with their staffs. These discussions spilled over in other content areas, also. As the teachers saw their instructional leaders as continual learners, it inspired them to take risks and become learners, too.

Another positive that emerged from the sessions was how comfortable the principals felt leading site-based discussions on what text book to adopt for mathematics. Out of the twelve school sites involved in the Lenses on Learning professional development, ten of them adopted NSF-funded mathematics materials. Principals stated that they would never have been able to accomplish the adoption as they did if they not experienced the support of the Lenses on Learning course.

The principals were sent to the NCTM’s 2000 Annual Meeting in Chicago using the district’s Title II funds. Each of them stated that the conference was of utmost importance to them and for their staff’s transformation. They could explain to their staffs that this was a national effort and not just centered in Albuquerque.

In the year 2000-2001, there were another twelve principals who inquired about doing a Lenses on Learning course after hearing of the success of the first program from the participants. Once again, principals report that it is an excellent professional development program and they look forward to their meetings. All twelve of the 2000-2001 principals attended the NCTM’s Annual Meeting in Orlando this year. At the conference in Orlando we received information that our district had been selected as a training site and two administrators will receive training at Tufts this year and have support through the year. It is hoped that the Lenses on Learning professional development model will be institutionalized in the Albuquerque Public Schools.

This exciting opportunity could not have been accomplished without the continued support of the ExxonMobil K-5 Mathematics Specialist Program. All of the principals who participated in the original Lenses on Learning group had an ExxonMobil study group at their school. Those teacher leaders were instrumental in encouraging their principals to attend the first sessions. Experiencing the excitement of mathematics from the ExxonMobil teacher leaders and students alike, the principals are aware of a need for their thinking to change also. So, without ExxonMobil, the initial awareness would not have taken place and the Lenses on Learning professional development modules would not have been explored. Thank you ExxonMobil from all of us at the Albuquerque Public Schools.

Focused in Houston

By Susan O’Boyle

In April 2000, while attending NCTM’s national conference in Chicago, I sat in a room with about forty math educators from around the country and listened to Cathy Miles Grant, senior scientist from the Educational Development Center (EDC), as she described Lenses on Learning, a curriculum designed to assist administrators with a framework for supporting reform mathematics in their schools. We watched a short classroom video clip and then used a guide that "framed" our small group responses to the video clip through one of three "lenses"—a mathematics content lens, a mathematics pedagogy lens, and an intellectual community lens.

The discussion that resulted from using the lenses was intense, thoughtful and energizing. At the end of the session, I approached Cathy and asked if she would consider adding a large urban school district to their pilot project. At 220,000 students, Houston Independent School District is ranked as the sixth largest urban school district in the U.S. Within a week, I was e-mailing Michael Foster, the Lenses on Learning grant analyst at EDC, and making arrangements to use the curriculum with our eight grant schools.

In October 2000, our district received a grant from ExxonMobil through the efforts of Houston Annenberg to develop Math Specialists in eight district schools. The importance of the principal seemed to loom as a large and sometimes forgotten piece of the picture of building a different vision for mathematics. As we learned more about the Lenses on Learning curriculum, we decided to require principals who would participate in the grant to attend these eight sessions during the school year.

The principals gladly agreed to participate, but they often arrived at our four o’clock sessions late or distracted by the cacophony of events at their schools. They would begin a session by sharing concerns and food and then settle into the curriculum for the evening. As these principals worked to learn mathematics, they shared how different it felt to work to make sense of a mathematical idea. They began to form a new vision of what a sense-making experience might or should be in a classroom.

Session 5, considered by the principals as one of the strongest, helped them consider how they provide feedback to teachers. The principals shared circle graph estimates of the type of feedback used with teachers and, after much discussion, drew new graphs indicating how they might change the feedback to provide clear support to teachers who are working to teach mathematics more effectively. As part of the Lenses on Learning curriculum, principals were also asked to work with and observe two teachers using a cycle of planning, observing, and debriefing, and to connect their learning from the sessions to work with the teachers in the classroom.

As we begin the second year of the grant, it is easier to see the impact that the Lenses on Learning curriculum had on this group of principals. They are truly in a different place in their thinking about mathematics and how it is to be taught in their schools. We continue as a project to look for ways to provide a similar deep experience for our new principals and look forward to having the resources of Lenses on Learning again in the near future.

Guidelines for Early Childhood Mathematics

This article is another in a series by Douglas Clements and Ann-Marie DiBiase, State University of New York at Buffalo, about the effects of the May 2000 Conference on Standards for Preschool and Kindergarten Mathematics Education. In January 2000, an introductory article about the conference appeared in these pages. The story was continued in the July/August and October 2000 issues and most recently in the June 2001 issue. Ed.

Continuing the Conversation

By Douglas Clements and Ann-Marie DiBiase

"Knowledge of what young children can do and learn, as well as specific learning goals, are necessary for teachers to realize any vision of quality early childhood education."

In the article published here in June, we stated this conclusion, which was drawn from the expertise shared at the Conference on Standards for Preschool and Kindergarten Mathematics Education. We also stated how important it is to carefully consider the way you organize and state this knowledge. We rejected the notion of rigid standards—but how else do you communicate this knowledge if not as rigid standards? We decided to structure the knowledge as curriculum standards—descriptions of what programs should enable children to know and to do. We believe that mathematics curriculum standards for early childhood education should be flexible guidelines along learning paths for young children’s mathematical learning. These guidelines should meet the following criteria:

1. Guidelines should be based on available research and expert practice.

We know a lot! Young children possess an informal knowledge of mathematics that is surprisingly broad, complex, and sophisticated. Whether in play or instructional situations, children engage in a significant level of mathematical activity. Preschoolers engage in substantial amounts of foundational free play¹. They explore patterns and shapes, compare magnitudes, and count objects. Less frequently, they explore dynamic changes, classify, and explore spatial relations. Importantly, this is true for children regardless of income level and gender. It is just as natural for young children to think mathematically as it is for them to use language, because "humans are born with a fundamental sense of quantity" (Geary, 1994). Young children can learn more interesting and substantial mathematics than is introduced in most programs.

2. Guidelines should focus on the big ideas of the mathematics of children.

For our purposes, we define the big ideas of mathematics as those that are mathematically central and coherent, consistent with children’s thinking, and generative of future learning. Research and expert practice identify what is challenging but accessible to children, especially at the PreK to Grade 2 levels, and thus allow us to describe these big ideas.

3. Guidelines should represent a range of expectations for the child outcomes that are developmentally appropriate.

This is consistent with the notion of developmentally appropriate as challenging but attainable for most children of a given age range and flexible enough to respond to inevitable individual variation. That is, expectations may have to be adjusted for children with different experiential backgrounds.

We specified big ideas for each of the five main topics of the PSSM (see Figure 1). The content standards are surrounded by a connected ring of process standards, which relate to all that they enclose. We believe that these big ideas will help early childhood teachers keep focused on the main mathematical objectives. So, the first contribution we made to building on the PSSM was to specify, at a higher level of generalization than the PSSM’s "expectations," the big ideas of mathematics for PreK to grade 2.

Our second contribution was on the other end of the continuum. That is, we knew that expert teachers, curriculum developers, and others also needed more specificity. For the finest level of detail, we created tables of developmental guidelines. The goal of these is to illuminate potential developmental paths, and also to encourage teachers to provide their children with activities appropriate to their abilities—attainable but challenging for each child. Figure 2 presents a small portion of only one of the topics, number.

We caution readers that the competencies in these tables are developmental guidelines, not detailed "directions" for curriculum, teaching, or assessment. The activities in which children engage to learn these competencies should provide rich, integrated experiences. These experiences should facilitate children’s development of several competencies simultaneously—including those that go beyond those in the table! For example, consider the "Double Trouble" activity from the Building Blocks project². The teacher tells a story of Mrs. Double, who is throwing a birthday party for her twins. The twins like their cookies to have the same number of chocolate chips. Pretending rugs are cookies and children are chips, the teacher has children act out situations such as one group of students making a rug cookie with some number of chips (e.g., four children pretending to be chips) and another group makes a cookie with the same number.

There are several follow-up activities. The "Double Trouble" computer activity has numerous levels of difficulty. In one, the on-screen character Mrs. Double asks children to make a "twin" cookie with the same number of chips as a cookie she made. A later activity is similar, but Mrs. Double makes a cookie…and then covers it with a napkin!

Another group of follow-up activities consists of "Cookie Games" that children play on a "mat" which contains a picture of a dinner plate at the top and cookies with no chips below. Player 1 rolls a die and puts that many chips, let’s say 6, on her "plate." Player 2 must agree that she is correct. If so, player 1 puts the chips on her cookies, trying to get 4 (or whatever number the children are working on that day) on each. For example, if she rolled 6, she could put 4 on one cookie and start another cookie with 2. Players take turns. The winner is the first player to get 4 chips on each cookie. We usually have all children be "winners," one after another!

These are simple activities, appropriate for preschool. Nevertheless, they meet multiple goals. For example, the "Cookie Game" involves most all of the goals in Figure 2. Children make small collections, nonverbally if they prefer (e.g., seeing 2 on a die and putting 2 chips on their plates). They "subitize" or quickly see a group and tell how many. They count by ones. They need to know that the last counting word tells "how many." They count out, or produce, a collection of a specified size. To check each other, they identify whether collections are the "same number." In this way, all good activities, whether planned, such as these, or the equally important incidental, informal activities of the day, should help children develop several skills and concepts.

Thus, we can see that this particular activity addresses numerous mathematical goals in Figure 2. Similarly, it is critical to note that while the Figure provides guidelines for practitioners, creative activities should always synthesize across the curriculum content areas, concepts, ideas and skills, building on children’s existing mathematical knowledge base.

Expert teaching does not begin and end with "developmental paths." Further, research has much more to offer regarding how to teach such developmental concepts. More important than knowing what age most children acquire specific mathematical concepts is knowing how these mathematics develop and how we can enrich and deepen children’s concepts. In our next issue, we’ll take a deeper look at this learning process by considering a specific developmental or learning continuum. We’ll show how such a continuum can help facilitate developmentally appropriate teaching and learning—that is, how they can help generate activities that are attainable, but challenging, for each child.

Notes

¹ Such everyday foundational experiences form the intuitive, implicit conceptual foundation for later mathematics. Later, children represent and elaborate these ideas—creating models of an everyday activity with mathematical objects, such as numbers and shapes; mathematical actions, such as counting or transforming shapes; and their structural relationships. We call this process "mathematization." A distinction is necessary to avoid confusion about the type of activity in which children are engaged (c.f. Kronholz, 2000).

² Building Blocks is a National Science Foundation-funded project developing and evaluating an innovative curriculum for early childhood education, preschool to grade 2. The Building Blocks program incorporates both old and new technologies, from blocks and puzzles to multimedia computer programs. Preliminary evaluations show the program’s approach of finding the mathematics in, and developing mathematics from, children’s everyday activity allows children to learn and do more mathematics than previously assumed.

References

Geary, D.C. (1994). Children’s Mathematical Development: Research and Practical Applications. Washington, DC: American Psychological Association.

Kronholz, J. (2000). "See Johnny Jump! Hey, Isn’t It Math He’s Really Doing?" The Wall Street Journal.

Author Note

Time to prepare this material was partially provided by three grants, two from the NSF, ESI-98-17540: "Conference on Standards for Preschool and Kindergarten Mathematics Education" and ESI-9730804, "Building Blocks —Foundations for Mathematical Thinking, Pre-Kindergarten to Grade 2: Research-based Materials Development" and one from the ExxonMobil Foundation, with the same title. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of either foundation.

EM M³

A Formula for Success

With funding support from ExxonMobil, The Children’s Museum of Houston (CMH) has introduced the new ExxonMobil Math Path and ExxonMobil Magnificent Math Moments (EM M³).

The ExxonMobil Math Path will be added to five museum exhibits, identifying for children how they use math skills in their favorite activities every day. EM M³ features any of 120 hands-on math exploration activities including games and puzzles to help children become more comfortable with mathematics operations and understand their relevance. All activities will be featured in the bi-lingual ExxonMobil Math Path Activity booklets, which will be distributed to families and classrooms and may be purchased at the museum for a minimal price.

The programs are designed to strike away the fear most Americans feel towards math and use hands-on activities to give children and their caregivers an understanding of how frequently they use math and how easy it can be.

"ExxonMobil is delighted to support The Children’s Museum of Houston and encourages children to embrace mathematics at an early age," said Terry Koonce, president, ExxonMobil Production Company. "We believe these math concepts and programs will serve as a foundation for our children’s future success."

Discovery Guides will show kids how they can use math in their daily lives—from playing soccer with friends to cooking with Dad, playing an instrument, planning their day or almost anything else. Plus, they will learn some new measurement and math games at three Junktion tables in the CMH McGovern Kids’ Hall.

New mathematics programming in Spanish and English resulting from the grant begins July 2001 at the museum as well as at museum outreach events hosted in conjunction with local schools, universities and community service organizations.

"Thanks to this latest partnership with ExxonMobil, we can engage our young visitors in mathematics learning by getting the children and their parents excited. These new programs also serve as teacher professional development tools, giving teachers new options for the classroom," Tammie Kahn, CMH Executive Director, said. "Math can often be intimidating, but through the ExxonMobil Math Path and EM M³, the processes of math will be presented in an exciting and comfortable way for everyone to learn together."

ExxonMobil has been a supporter of the CMH since 1984, funding several educational programs prior to this one. The company was an early supporter of the capital campaign to build the Children’s Museum, as well as a supporter of the Museum’s inaugural archeological exhibit Dig It: Houston’s History Underground. ExxonMobil support of the Museum’s Bubble Lab exhibit helped children to learn science principles in an innovative setting.

This latest contribution allows CMH to expand educational programming with an emphasis on mathematics and its processes, with hands-on experimentation and exploration.

Serving more than 500,000 people annually, The Children’s Museum of Houston is the highest-attended youth museum in the country for its size. It is committed to the mission of learning by providing hands-on exhibitions in the areas of science and technology, history and culture, health and human development, and the arts.

Cathy Kinzer Named Awardee

The week of March 6-10 found Cathy Kinzer of Las Cruces, NM, in Washington, D.C. to be recognized as a Presidential Awardee for Excellence in Mathematics and Science Teaching from the state of New Mexico.

The award is described by the National Science Foundation as "the nation’s highest commendation for K-12 math and science teachers."

Currently a doctoral student and instructor in elementary math methods in the College of Education at New Mexico State University, Cathy also works in Preparing Tomorrow’s Teachers Today, an NMSU initiative to develop the use of technology in the classroom. She is on leave from Mesilla Park Elementary School where she has taught for seven years. As a result of her award, her school will receive a $7,500 grant for promoting math and science education.

Cathy commented: "For too long elementary mathematics has been a focus on arithmetic, memorizing arbitrary rules and procedures without understanding the mathematics. Math should involve thinking, reasoning, problem solving, making conjectures, developing strategies and offering explanations.

"I really think that having a love of learning and a passion to empower students through helping them develop their abilities and keep their hearts and minds safe in a wonderful learning environment helped me maintain a proactive approach to teaching in these challenging times. Actually, my wonderful students, their parents, and mentors in my life are all stakeholders in this award."

Congratulations from us all, Cathy! Ed

News from Maryland

Skip Fennell sends word that the September 2001 issue of NCTM’s Teaching Children Mathematics features on page 20 an Investigation authored by Laura Cline, a teacher in his project. In addition, readers can find on pages 44-48 responses from participants in Skip’s ExxonMobil Elementary Mathematics Leadership Project.

Also of interest is the Maryland Mathematics Commission Report entitled "Keys to Math Success." Skip reports that one of the commission’s recommendationsc—the creation of a certificate for elementary mathematics specialists—was accepted by the Maryland State Board of Education. You can read the full 76-page report in pdf format.

Reviews by Readers

Many thanks to Cornelia Tierney and Christine Thereault for reviewing this recent title by Susan Ohanian. Cornelia is currently a senior scientist at TERC. Christine is a math specialist at Stedwick Elementary School in the Montgomery County (MD) Public Schools. Thanks to each of you! Thanks also to Victoria Merecki at Heinemann for providing the copies of the book for review. Ed.

Caught in the Middle

Cornelia Tierney’s Review

In Caught in the Middle: Nonstandard Kids and a Killing Curriculum (Heinemann, 2001), Susan Ohanian tells stories from her time as a seventh- and eighth-grade remedial reading teacher in the 1970’s in a "disadvantaged poverty" middle school where teachers teach by the manual as they are expected to do, and are bewildered that many of their students become disenchanted with education. Some blame and punish the students who "fail"; others are puzzled and seek advice.

As Ohanian describes it, "This book is about noticing small things. It is about a teacher doing what she can, a book about trying to keep one’s eye on the needs of students in a system run amok, about not giving up but coming back everyday to continue the fight." She tells us that "Standardisto blueprints are unsatisfactory guides because they write about schools the way Hemingway wrote about Africa: without noticing the natives."

Her stories are about students whose strengths, needs, and eccentricities expose the glaring ineptitude and inequities of schools ingrained in practices that make no sense in a particular situation or no longer make sense at all, if they ever did.

Exclusion by tracking begins before first grade. A Kindergarten teacher invites children who can copy a paragraph perfectly into a club and to her house for a party, but leaves out the other students.

Property is valued more than people. An electric typewriter required for a boy with cerebral palsy and purchased exclusively for him must be signed out for each period and returned to the special services office at the end of every period.

Manners are valued more than intelligence, curiosity or ambition. The principal and faculty recommend a student for scholarship at a private school because of her manners and family acceptability whereas girls with high reading levels in spite of little family support are denied chances for scholarships.

Students who read the assigned texts critically are measured only by their poor performance on the end of chapter tests. Students point out the discrepancies between what they read in their social studies text (e.g., "one passenger car for every 4 persons") and what they know to be true for their families.

Ohanian tells of working with other teachers to help them reach unusual students and allowing students to stay in her classroom for much or all of the day because that is where they feel safe and can learn. She gives up her lunch period to run a writers’ workshop in which students find their voices; she types up for school publication the work of all students, not just the best. She assigns Langston Hughes’ poetry and other literature that her students can connect with. She puts on a Christmas play that students make theirs.

To involve the students in reading, Ohanian offers a large variety of adult and children’s fiction and non-fiction, reference books, reading skills programs, film-strips, and she even creates a program where students can buy books to own. She works with the librarian to offer a question of the day to get students reading for information.

One of the themes Ohanian illustrates again and again is that it makes little sense to measure students by their learning and regurgitation of particular "core knowledge." However, we must hold expectations for all students that they can learn if they work hard and that even the weakest students should have available the resources and tasks to engage with exciting and complex ideas. We need to look at what we are asking of each child; how is the task different for the child who can read than for the student who must learn only by listening? How is it different for the student who critiques what she reads than for the one who answers the questions at the end of the chapter as expected?

Caught in the Middle illustrates convincingly that universal anything—high stakes tests, the newest textbooks, reading assignments—will not improve the schools. Ohanian makes clear the need to base educational decisions at all levels on worchking closely with students in their unique situations.

We need flexibility in programming instead of tracking. Teachers working as a team with a reasonable number of students could take time to discuss students needs and strengths and flexibly make program decisions. Across the program and within each class we need to offer a variety of tasks with many entries and work with students to find out what works best for them. All students deserve to find ways to learn and feel glad at what they do, learn and produce.

Reading and rereading Caught in the Middle provokes me into reconsidering much about my own teaching and about what I believe about public policy. I recommend it as a highly readable, humorous book, that will leave you better informed and deeply puzzled.

Christine Thereault’s Review

Caught in the Middle: Nonstandard Kids and a Killing Curriculum is a truthful look at our teaching profession. Susan Ohanian’s book offers readers a view into her middle-school classroom and into the lives of her students whom she endearingly refers to as "rotten readers." These students are "nonstandard kids" and despite how many challenges they face, in or out of school, they are expected to meet the requirements of the curriculum. The curriculum doesn’t happen to hold a lot of meaning for these "nonstandard kids." Although the author addresses the politics that often influence what happens in our classrooms that can be maddening at times, she does it in a way which is comical, critical, honest, and unfortunately, realistic.

Sound like a bummer? On the contrary! This reader found it to be refreshing. Although this teacher was constantly reminded of how difficult her job was, she never let the obstacles get the best of her. She remained focused on what was important to her—her students. (She explained that she put the curriculum guides aside in order to meet the individual needs of her students. Ohanian stated, "Let the politicians and the educrats make the pronouncements about ‘all students.’ For me, being a teacher means taking pride and pleasure in the particular. One student on one day." She found faults in the school system, the administration, her colleagues, and herself. She openly admitted and learned from her own mistakes.

This book helped me to feel justified in some of the feelings that I have throughout the school year. As teachers feel the pressure to adequately prepare children for tests, they sacrifice the teachable moment—something Ohanian believes is important. This affects the mood in a classroom where we want to facilitate a love of learning. We want our students to have an optimistic attitude about learning since they will be the future leaders in our country, parents in our community and, potentially, the teachers in our schools. Caught in the Middle helped remind me why I became a teacher and refocus on what an important job I have to do!

To order this title, visit www.heinemann.com. Ed.

Call for Reviewers

Thanks to Toby Gordon at Marilyn Burns Education Associates, there are two new books from Math Solutions Publications looking for reviewers. They are the first two in a new ten-volume series called Teaching Arithmetic. One is Lessons for Introducing Fractions, Grades 4-5, by Marilyn Burns; the other is Lessons for Extending Multiplication, Grades 4-5, by Maryann Wickett and Marilyn Burns.

Remember, if you request, read and review a title offered here, it’s yours! Anyone interested? Please contact me and I’ll mail you one or the other right away. Thanks! Ed.

Call for Presenters

The annual joint conference of the New Mexico Council of Teachers of Mathematics and the New Mexico Science Teachers Association is slated for October 11 – 13 in Taos, NM. NCTM President-elect Johnny Lott will be the keynote speaker, and many sessions are planned about activities for connecting mathematics, science and art. And what could be a better setting for exploring those connections than Taos?

Proposals for presentations are still being accepted, although not for too much longer. On-line information and registration and proposal forms are available at the New Mexico Council of Teachers of Mathematics website. Don’t delay—visit today!

Mailing List Additions, Updates

If anyone knows of individuals to be added to the mailing list for Intersection, please forward their names and addresses so that they may be subscribed. Also, please forward mailing list changes or corrections as well. See contact info below. Ed.

Scare up an Article for Halloween

Treat newsletter readers by sending along an article now about what’s happening in your project. Contributions are always welcome.

The deadline for the October issue is Monday, October 1. For the November/December issue, it’s Monday, November 5. Please send submissions to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; e-mail, jean@intersectionlive.org; phone, (512) 869-1580; fax, (512) 869-8477. Many thanks!