v
Many thanks to new contributor Judy Merchant, elementary math specialist in the Mount Vernon School District, Washington, for this article. An accompanying article by Chris Ohana follows directly after this one. Ed.
As readers of Intersection are well aware, the degree of change necessary by elementary teachers as they implement a standards-based math program is significant. In the Mount Vernon School District, located in Washington, our math leadership team designed a variety of systems to encourage and facilitate this change process following the adoption of the Math Trailblazers program.
An important part of our implementation plan was the allocation of district resources to fund the creation of a math specialist position. One year ago, I was selected to serve in this capacity. Currently, I teach one 90-minute reading block, and then I am released for the remainder of the day to work in this new position.
With the
support of a planning year grant from the ExxonMobil Foundation,
we have been able to augment our professional development
planning and enrich the evolution of this math specialist
position.
In this article, I hope to highlight this evolution, focusing on the conditions that enabled my role to successfully support the professional development needs of our elementary teachers through the significant change process necessary to match the mathematical learning needs of our students.
Recognizing the importance of parent understanding and support, I conducted a Parent Math Night at each elementary school last September. It included an explanation of what standards-based mathematics meant, how it was different from a traditional math program, and why it would better prepare their children for careers of the future. Parents experienced several hands-on activities that were representative of standards-based lessons. They worked in cooperative groups and were encouraged to share their varied strategies. In many cases, there was more than one "right" answer!
Although every attempt had been made to provide all necessary teaching materials before classes began, I spent time in the first weeks of school helping teachers locate "shared kit" materials and correcting order errors or omissions. I also answered questions about the program’s design and philosophy, located resources, made suggestions of how to "bridge" from the students’ basal mathematics background to this standards-based program, and affirmed the beginning efforts of a conscientious, dedicated teaching staff.
I introduced our math tutors to the Math Trailblazer strategies and timeline for learning the math facts as well as the Math Trailblazers philosophy for teaching arithmetic. Tutors learned how to build student understanding of addition and subtraction using concrete materials. They learned meaningful ways to build toward an understanding of the standard computation algorithms. I assisted tutors while they practiced these unfamiliar techniques and provided materials for them to use with students.
Once I began visiting schools in a weekly rotation, I discovered that many teachers were not yet confident enough to invite me into their math classes to observe. I decided the best way to win their trust and confidence was to begin modeling lessons for them in their classrooms. During the next five months, I modeled lessons regularly in first- through fifth-grade classes.
Initially, I focused on modeling effective classroom management techniques for working with manipulatives in a constructivist math classroom. Questioning techniques to clarify, expand, and encourage diverse student thinking were also a major emphasis. Whenever possible, I met with the teachers before I taught the lessons to discuss the major lesson concepts and to suggest specifics to watch for. Having developed a feedback form, I asked teachers to record their reflections as I was teaching. This enabled me know if my modeling had been perceived as useful and what specifics had been gleaned.
Valuable input from Dr. Jean Moon helped me transition from modeling a single lesson for one teacher to team-teaching a series of lessons with several teachers. The ExxonMobil planning grant assisted us in hiring a half-day substitute for the teachers involved. In that half-day, we planned a series of three lessons. We discussed the math concepts, the lesson format, concerns and/or confusion about the lesson, and anything else pertinent to the math program. The teachers overwhelmingly applauded this planning opportunity. Lack of time is always named as the single greatest deterrent to collaboration. This gift of time allowed for the kind of in-depth math conversations that challenged, excited, and energized beleaguered teachers.
As I reflect on the conditions that facilitated my role as the elementary math coach-facilitator, the following stand above:
Time availability, as already mentioned, and accessibility to teachers was crucial. Math conversations can’t be initiated at the end of the day when lesson preparation for the following day is the top priority and teachers are exhausted.
Principal support through encouraging teachers to use me as a resource made a big difference. In buildings where teachers were less confident or reluctant to work with an "outsider," proactive principals opened the doors in a positive, nurturing way. The degree of principal involvement correlated directly with the degree to which the staff used the Trailblazers materials as intended and to my effectiveness in working with them.
Having my role clearly defined as a math facilitator, apart from any connection to evaluation, diminished the threat to teachers of being negatively judged for being open and honest about needs, fears and concerns.
Professional training in group presentation, my speech/debate background, and previous experience working with adult groups prepared me with the necessary skills to inform and field questions with confidence in a large group setting.
Training in coaching techniques allowed me to encourage without intimidating. Asking the teachers to decide how they wanted help, on what lesson specifics they wanted feedback, and when they were most comfortable receiving support built a foundation of trust.
The Mount Vernon staff was fortunate to have easy communication through district e-mail and voice-mail systems. Teaching tips, caution alerts, reminders, resource websites, material needs, inservice opportunities, scheduling changes, questions or concerns, and words of appreciation and encouragement were all at our fingertips.
My district administrative support team was outstanding. Whenever I needed help making a decision, solving a problem, or brainstorming options, an administrator was available.
Although the budget was tight, I was able to assure teachers we would get for them what they needed to teach effectively. The financial commitment for materials was made before the adoption was approved, and it continued throughout the year
Finally, I was encouraged to attend conferences and trainings that increased and supplemented my knowledge and bank of resources. I was able to network with other math specialists sharing materials and resources. Without exception, upon returning after such an experience, some new awareness or knowledge became almost immediately applicable in my role of helping teachers build mathematical confidence and facility in their students.
This year of teaching both children and adults in a subject area about which I am passionate, has been a dream come true. Thank you ExxonMobil Foundation for recognizing the challenges and intricacies of creating an effective new district math role. You have enhanced our ability to improve math education for our students, staff and parent community.
Chris Ohana, Assistant Professor in the Woodring College of Education, Western Washington University, Bellingham, contributed this "companion piece" to Judy Merchant’s. Many thanks, Chris! Ed.
As I teach preservice teachers in their first methods courses, they often struggle over assessment. Yet I hammer them with how important it is to know if a lesson was successful. I can appreciate their struggle as I start a new task: evaluating the success of a new ExxonMobil project in Mount Vernon, WA. How can we gauge the impact we have and how can we make our projects even stronger? How can we learn to gather evidence about the work of our projects that helps us make adjustments and plan for the future—helps us see our way?
This work has become even more critical recently. Evaluation efforts must be strong in order to describe, justify, and improve what we do. The audience for this information is expanding. Districts, faced with funding mathematics specialists, will want to know what the impact of this position is on teaching and learning. School staffs will want to make sure their efforts make a difference and will want to know what can be done better. Parents and other community members will also want to know how well their children are doing and how well school resources are being used. The funder of a project, e.g., the ExxonMobil Foundation, will also want to know how the project worked and how it can inform other mathematics specialist projects.
The evaluation portion of the Mount Vernon project that Judy Merchant described above is growing alongside the project. This has several advantages. First, the information gathered in the report is more likely to be useful to all of the stakeholders if they have a hand in developing it. Second, the evaluation can help the project directors to be realistic and concrete. What does "mathematical power" look like and how can one tell someone is developing it? How will a teacher teach differently after participating in the project? Evaluation can help us make our vision observable.
Given the complexity of teacher change and leadership in mathematics education combined with the multitude of stakeholders, the evaluation of our project will also be complex. Some evaluation tasks seem routine; others will be slippery and demanding. The following is part of a growing list of items we are considering as we develop the project:
Participant satisfaction: In what ways are the teachers (and others) who take part in the workshops or study groups benefiting from these activities? Do we see evidence of transfer of knowledge and skills from these activities to the classroom or to the teachers’ overall professional disposition and practice? What does this evidence look like?
Acquisition of new skills/attitudes: How does the math specialist develop his/her skills? What conditions are necessary for him/her to learn, teach, coach? How can we "grow" new math specialists?
Development of leadership skills: Do teachers take on new types of tasks or assignments? Do they share their new abilities or insights? What conditions are present that facilitate or obstruct teacher leadership?
Changes in instruction: Does teaching change? How?
Changes in student attitudes and knowledge: How much more do students know after being in these classrooms? Has there been a shift in attitudes about mathematics?T1
Given this evolving set of questions, we are now looking at what evidence we can collect to document the successes and challenges of the Mount Vernon grant. Table 1 summarizes some possible sources of data. Each type of data collection has advantages and disadvantages. Tests, for example, are quick to administer but tough to develop. Care must be taken that the tests assess what the teacher (or project) values. In Mount Vernon we plan to use existing tests that the classroom teachers are, for the most part, already administering (like many communities, Mount Vernon assesses kids often). This will minimize disruption to the classroom.
| Effect/Criteria/Goal | Source and method of data collection | ||||||||||
| Delivery/satisfaction |
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| Math specialist skills/attitudes |
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| Teacher changes—leadership |
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| Changes in classroom |
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| Changes in learning/attitudes |
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| Table 1 2 |
We cannot collect data from all of these sources for each category but we do hope to get multiple lines of evidence. It is dangerous to rely too heavily on any one source of data. For example, surveys are a good, quick way to get immediate feedback about a workshop or class. But the information can be unreliable in terms of classroom impact. Self-reports about change in teaching practice sometimes exaggerate the magnitude of change.
Historically, there has been little attention paid to actual changes in the classroom and in learning. But with increasing demands for accountability, many levels of stakeholders (especially at the district and policy levels) will require us to document improved student understanding. The Mount Vernon school district will be much more likely to fund mathematics specialists if we can show that this role makes a difference in student achievement.
The emphasis on student achievement is perhaps the most slippery piece to document. We all know that there is a huge number of variables that influence student achievement. And there are many different definitions of student achievement. Districts will often define student achievement through standardized tests. Teachers may have a broader, multifaceted perspective on student learning. Our assessments will have to capture the needs of both.
Student achievement is also tricky because it may lag behind the interventions. Will student achievement change immediately or will teachers need time to practice and assimilate new ideas? In our project, we will venture from evaluation to research. If changes in student achievement and attitudes are not immediate, are there precursors of student and teacher behaviors which indicate that positive changes will occur? This would help tremendously as we implement the project and report our findings. If we could point to constellations of factors that predict higher student achievement, we could justify and improve our efforts. We could also beg for something that districts are short of in this high stakes environment: patience.
In the article above, Judy Merchant identified several factors that affect her ability to serve effectively as a mathematics specialist. These issues also need to be addressed by the evaluation. The evaluators (whether it is an internal or external evaluation) should attend to these conditions before the grant is even submitted.
v Time. How does the system support release time for the teachers? Is it one more thing added to the day or are they relieved of some other duties/responsibilities? How can the mathematics specialists structure time? Are they assigned duties that are unrelated to the mathematics program? I was at one school several years ago in which the principal assigned the math specialist (due to his flexibility) to 15 hours a week of yard and bus duty. Clearly that limited the math specialist’s effect.
v How has, or will, the math specialist be prepared to work with adult learners? Not all good elementary teachers make good inservice providers. Does the math specialist have access to training in presentations, coaching, supervising, and mathematics? What are the professional needs of the mathematics specialist and how will they be met?
v Communication. How will teachers and administrators be kept informed? Are there multiple ways to communicate with teachers? Some teachers open e-mail, others do not. Some never look at newsletters. Others do. Will principals help through scheduled time in faculty meetings? Who should be informed? What do they need to know? How will we deliver it?
v Administrative support is critical at the school and district level. Are principals supportive? Do they encourage teachers to participate? Do they structure the time necessary for teachers to thoughtfully participate? District support is also fundamental. Will there be a budget for supplies? Workshops? Substitutes? Is there a district person who can serve as a point person for problems or brainstorming?
The answers to these questions are important. Every district may have a different approach but the important thing is that there should be a plan that makes sense in the local context. Mount Vernon has a different set of needs than the large districts I taught in. While the solutions may differ, the questions are important to anticipate.
As the Mount Vernon project moves from planning to implementation, the evaluation efforts will help provide feedback about successes or challenges. It can help the math specialists do the most effective job possible. In our case, I will provide a different perspective. I cannot call my role "external" because I have been involved almost from the beginning. But I do not have the day to day knowledge of the grant that the math specialist has. Both perspectives are important to the evaluation; it should be a team effort. Evaluations can also serve to help other projects as they develop. Although evaluation can be time-consuming, even messy, we think it will pay off in the end.?
Note: Several excellent evaluation papers may be found at www.horizon-research.com.
1 After Frechtling, J. (2001). Emerging trends and current challenges in the evaluation of professional development programs. Paper presented at the Annual Meeting of the National Association of Research on Science Teaching, St. Louis, MO.
2 After Lawrenz, F. (2001). Evaluation of teacher leader professional development programs. In Nesbit, C., Wallace, J., Pugalee, D., Miller, A. & DiBiase, W. (Eds.). Developing teacher leaders in: Professional development in math and science.. Columbus, OH: ERIC Clearinghouse.
This article, subtitled "An Experiment in How to Build a Self-sustaining Professional Learning Community," was contributed by project director Bonnie Tank and project evaluator Mary Haywood who work with the ExxonMobil Project in the San Francisco Unified School District. Many thanks! Ed.
At the annual ExxonMobil Foundation meeting in September 2000, Carol Brooks presented a session on a unique aspect of the Tucson project design called "Mini-Grants." For Bonnie Tank, the idea of providing a mini-grant to some of her "veteran" ExxonMobil schools became an exciting possibility. The mini-grant application process requires that an ExxonMobil school’s Math Team write a proposal that includes a guiding research question, goals and a set of activities for the year that are designed to continue to improve mathematics teaching and learning within the school.
Back home in San Francisco, Bonnie discussed the idea with teacher leaders and with Mary Haywood, project evaluator. They suspected that mini-grants might help address a challenge they faced: Once a school becomes an active partner with the ExxonMobil project to improve mathematics teaching and learning, how can the project help schools develop the in-house "math conscience" needed to sustain continuous learning and improvement across the school?
In this year’s grant, we
customized Tucson’s mini-grant idea to fit the needs of San
Francisco’s ExxonMobil schools. In San Francisco’s
mini-grant guidelines, schools that have participated in our
project for at least three years are eligible to apply for an
ExxonMobil Mini-Grant. The purpose of the grant is to provide
support to members of the school learning community so that they
may develop the structures and processes needed to assure a
continued focus on mathematics improvement. By partnering with
schools through the mini-grant process, we hope to begin to
answer the following guiding question:
What does it take to sustain and renew the professional learning community to assure consistency and quality in the mathematics program and to maintain the focus on continuous improvement?
Mini-grants offered approximately $225 per teacher or between $4,000 - $5,000 per school. Four ExxonMobil schools were awarded grants. To date, only one of the four schools, Grattan Elementary School, has completed its documentation for the year. Their successful work together was shaped through a proposal that included the following guiding question:
How does examining student work on a regular basis improve or guide our teaching practice?
Proposed plans for the year at Grattan included five after-school meetings and a half-day release day. The Math Team used this time to guide peers in selecting appropriate open-ended problems for each grade level, learn how to collectively examine student work to determine levels of mathematics understanding, and reflect on student performance, collective standards and teaching practice.
The San Francisco ExxonMobil Project’s reflection on Grattan’s experience suggests that certain elements of the mini-grant and attributes of the Math Team may help assure the effectiveness of the grant at a school site. First, Grattan’s grant application was brief, clear, explicit and easy to follow. To assure that the plans would be implemented, it included a timeline and pre-scheduled meeting dates. Second, the Math Team was self-selected and respected by peers as a group of "good" and experienced teachers who displayed positive attitudes, excitement and motivation to learn. Third, the Math Team knew when to ask for help and support from the ExxonMobil project director. For example, the team requested help to plan the mini-grant itself, and again to develop the agenda and activities for the initial all-staff meeting. Finally, the Math Team documented the work diligently, making records of each agenda, all peer learning activities, discussion summaries, examples of assessed student work and rationales for scoring. This information was shared with the teaching staff and collected as a summary document for the project.
According to teachers at Grattan, what has been most valuable about the mini-grant process is the opportunity to learn together as a community. The Math Team was excited to extract the following points from the whole school’s reflective discussion:
v Students need multiple experiences with a concept before assessment occurs.
v Appropriate selection of the problem is critical to success.
v Clear performance expectations for each problem must be identified in advance, so that teachers can communicate clear expectations to students before the problem is given. This is how to achieve realistic but high standards.
At Grattan Elementary next fall, mathematics improvement work will start with a review of this year’s learning and build on the wisdom of practice gained through the important, collective, professional learning experience sponsored by an ExxonMobil Mini-Grant.
This article was submitted by Douglas H. Clements and Ann-Marie DiBiase, State University of New York, Buffalo. It is another installment in a continuing story about the Conference on Standards for Preschool and Kindergarten Mathematics Education and the results of that meeting. An introductory article about their work appeared in Intersection, January 2000. Subsequent articles followed in the July/August and October issues. Many thanks to the authors. Ed.
Previously, we wrote about the exciting results of the May 2000 Conference on Standards for Preschool and Kindergarten Mathematics Education. This historic event was the first conference to have brought together such a comprehensive range of experts in diverse fields relevant to the creation of educational standards. According to the participants, the conference was a resounding success. Presentations and panels were lively and informative and discussions among the participants from different fields were especially productive and enjoyable.
Following the main conference, ExxonMobil Foundation hosted a follow-up meeting in October 2000. ExxonMobil kindergarten teacher-leaders collaborated with mathematics educators and researchers, representatives from state departments of education, and early childhood policy makers ( including a representative from NAEYC.) This group worked on Part One of the final report. It consolidated recommendations from the conference that were based on an initial draft that we wrote. This constitutes a set of guidelines that will assist individuals responsible for framing and implementing early childhood mathematics standards to develop consistent standards rooted in current research, practice and policy. Part Two of the report contains chapters from presenters at the conference. Part Three will contain reactions from teachers and educators. We are happy to announce that the report—including these three parts—will be published as a book with Lawrence Erlbaum Associates.
The book has its roots in the initial conference, which emphasized mathematics education for the youngest children. However, because many of the speakers and participants discussed NCTM’s full range of preschool to grade 2, the standards and recommendations the book provides cover all these ages.
Part One, "Major Themes and Recommendations," consists of conclusions drawn from the expertise shared at the conference and specific recommendations for mathematics education for young children. These recommendations are intended to facilitate the creation of standards and curriculum materials that are consistent and inclusive, rather than incoherent and confusing. They are developmentally appropriate—attainable yet challenging—for young children. Part One includes sixteen recommendations and specific guidelines for mathematical content which are organized into a small number of "big ideas." These big ideas are elaborated into detailed developmental guidelines for each age range, 2 – 8, across several distinct mathematical topics. Part Two includes a compilation of papers written by the invited presenters and introductory notes by the editors introducing and connecting these papers.
Both parts are organized into the same five thematic sections:
Standards in Early Childhood Education deals with general policy and pedagogical issues related to the creation and use of standards for young children, including different types of standards and the advantages and disadvantages of standards for the early childhood years.
Mathematics Standards and Guidelines includes research summaries about young children’s development and learning of specific mathematical topics. This knowledge base is extended to describe the "big ideas" of important mathematical topics—at four progressive levels of detail—designed for different audiences.
Curriculum, Learning, Teaching, and Assessment includes descriptions of approaches to curriculum, instruction, and assessment that have been supported by research and expert practice.
The Professional Development section describes research and expert practice that addresses the dire need for better preparation of teachers and childcare workers.
Finally, Towards the Future: Implementation and Policy, presents issues and recommendations that we believe must be considered when putting all these recommendations into practice.
Here, we will highlight a few salient themes.
With the varied backgrounds of the participants, it is unsurprising that there were many different perspectives. Equally surprising, however, was the degree of consensus for most issues. One important question was this one: Should there be standards for young children? Those connected to NCTM’s Principles and Standards for School Mathematics (PSSM) were in favor of standards and wanted to elaborate on those in the PSSM. On the other hand, several people—particularly teachers—were concerned about the notion of standards for early childhood. Discussion revealed that the two groups Pwere often talking about two different types of standards. This led to the following conclusion:
"There is a substantial and critical difference between standards as a vision of excellence and standards as narrow and rigid requirements for mastery. Only the former, including flexible guidelines and ways to achieve learning goals, is appropriate for early childhood mathematics education at the national level."
A related issue arose that there might be standards for programs and teachers, standards for children, or both. Sue Bredekamp, one of the creators of the ideas of "developmentally appropriate practice," answered the question by saying, "We need both." After discussion, we reached consensus that standards for programs and teachers were essential. Such standards protect children from harm and contribute to their development and learning.
The issue of standards for children is more complex. Historically, early childhood educators have been resistant to specifying learning goals for very young children. A major concern is that because children develop and learn at individually different rates, no one set of agerelated goals can be applied to all children. A specific learning timeline may create inaccurate judgments and categorizations of individual children. In addition, specifying learning outcomes may limit the curriculum to those outcomes and lead to inappropriate teaching of narrowly defined skills. This concern mirrors the "teach to the test" phenomenon for older students. Catherine Sophian suggests that "Even the best-motivated set of instructional objectives can be counterproductive if the emphasis shifts from engendering particular kinds of understanding to eliciting correct performance on particular tasks." In general, there is concern that the learning outcomes will be limited to a few academic areas without adequately addressing the development of the "whole child."
These concerns warrant attention at all phases of creating and implementing new visions or standards. Most, however, are based on assumptions, such as that the mastery goals that are set will be the wrong goals. The participants came to agree that these disadvantages result, to a large extent, from misuses of standards. Avoiding such abuses sets the stage for realizing the advantages of specific goals. First, such standards can de-mystify what children are able to do. Second, they can provide teachers of young children needed guidance about appropriate expectations for children’s learning. They can focus that learning on important knowledge and skills, including critical thinking skills. Third, standards can help parents better understand and provide appropriate experiences for their children. Fourth, in the classroom and home, such goals can help "level the playing field," achieving equity by ensuring that the mathematical potential of all young children is developed throughout their lives.
Teachers have welcomed more specific guidance on learning goals linked to age/grade levels, such as those published in a recent joint position statement on developmentally appropriate practices in early literacy (by NAEYC and the International Reading Association). The fundamental question for teachers is what to teach and when to teach it. For goals to truly be useful guides, they need to be more closely connected to age/grade levels than are those in NCTM’s visionary PSSM. This assertion—voiced by Sue Bredekamp and others—ckwas echoed by most participants throughout the conference. In summary, quality standards can provide a foundation upon which to build a program that is coherent with the K-12 system students will enter. We therefore came to the following conclusion.
"Knowledge of what children of each age are capable of doing and learning, and specific learning goals, are necessary for teachers to realize any vision of quality early childhood education."
Finally, creating standards may be politically wise. Standards for young children are politically inevitable. If we "do not create these standards, someone else with far less expertise will" as Jeane Joyner suggested. We want to do this in a way that balances higher expectations with the aim of preschool to foster a love for learning, a feeling of success, and the joy of being a child. Specific suggestions about how to develop standards that minimize disadvantages and realize the advantages are discussed in a section in our book denoted as Mathematics Standards.
What should the form of these standards be? We rejected rigid, prescriptive guidelines and instead created flexible developmental guidelines. Next time, we’ll share an example of these with you.
Last month’s issue announced that the Thirteenth Annual Meeting of the ExxonMobil Foundation/NCTM K-5 Mathematics Specialist Program will be held September 20 – 23 at the corporation’s headquarters in Irving, TX. Invitations have been mailed to those who will represent various projects. Next month’s Intersection will provide information about presenters, sessions, and activities.
As in the past, a presession will be offered on the afternoon of the first day of the conference. This year’s presession—scheduled to begin promptly at 2:30 PM on Thursday, September 20—will focus on project evaluation. It will be led by Rose-Ann McKernan, director of research and evaluation for the Albuquerque Public Schools. Rose-Ann has been intricately involved with the design and implementation of the Albuquerque mathematics specialist project evaluation for many years. She is well versed in identifying comprehensive data-gathering strategies that are also productive and reliable as sources of information for ongoing project planning. Rose-Ann’s familiarity with ExxonMobil Foundation’s K-5 program will allow her to lead a relevant "working session" designed to help participants formulate evaluation questions as well as look at possible evaluation/research strategies for gathering data in response to those questions. She will also help participants explore the productive use of student achievement data as a means of exploring project strengths and weaknesses.
To help her plan an effective presession, Rose-Ann will be e-mailing all invitees who indicated on their response forms that they’d like to attend. You’ll hear from her soon.
Thanks to Susan Ohanian for forwarding this review of a light-hearted book you may want to ask your school librarian to order next fall. Better yet, get one for your own classroom! Ed.
Reviewed by Susan Ohanian
A Burst of Firsts: Doers, Shakers, and Record Breakers, written by J. Patrick Lewis and illustrated by Brian Ajhar (Dial 2001) is a book after my own heart.
I discovered the power of Guinness Records very early in my teaching career. I made great use of them in Day-by-Day Math: Activities for Grades 3-6 (Math Solutions, 2000). (Reviewed in March 2001 Intersection. Ed.) Now here comes one of my favorite poets using these same records in lively poems that will provoke much fun, frolic and further mathematics investigation.
A few poem titles give you a glimpse of the mathematics possibilities provided in this upbeat volume: "The Biggest Bubble- Gum Bubble Ever Blown," "First Non-Japanese Sumo Wrestler," "#1 Lunch Choice of School Kids," "First House of Cards with More than 500 Decks," "First Person Who Jumped Rope More than 14,000 Times in One Hour," "First Man to Lead the NBA in Scoring for Ten Years," "First American Woman in Space,"
The opening of "First House of Cards" gives you an idea of some of the mathematical possibilities in this volume:
"There was a young man who built him a house,
And this was the house that Jack built.
It had 83 stories
With 83 doors
and 83 ceilings,
So how many floors
Of twos-by-twos
And threes-by-fours?"
Share this volume with your students to show them that mathematics can be fascinating. Lewis says the volume was inspired by the fact that as a young child he witnessed Roger Bannister break the world’s first four-minute mile record. Start your students with these verses of "firsts" which contain numbers and then send them looking for more.
As you probably know, the ancient Romans believed that Sirius—the "dog star"—added its heat to that of the Sun to make mid-summer days the hottest of the year. That’s why they were called the "dog days."
Escape those so-called dog days. Find the shade of a tree or a blast of A/C, pour a tall glass of lemonade, and retreat into memories of last year. What stood out? What was most meaningful? What connections did you make? What professional books impressed you? What did you learn? What will you do differently next year?
Please consider contributing an article about your experiences during this past year. The deadline for the July/August issue is July 23; for September’s, it’s August 27; for October’s, it’s October 1. Send items to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; e-mail, jean@intersectionlive.org; phone, (512) 869-1580; fax, (512) 869-8477. Thanks very much to all who contributed to this issue!
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