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Many thanks to Katy Early and William Fisher for the article below—one more result of their successful, ongoing collaboration. Ed.
California State University, Chico has instituted an innovative program, connecting the university to the local elementary school district in ways that support mathematics education at many levels. Dr. William Fisher created the Teacher-in-Residence program three years ago. (Please see Intersection, Mar/Apr 1999 Ed.)
As a Teacher-in-Residence (TIR), an elementary teacher is released from regular teaching duties for a period of two years. The TIR then splits his or her time between two positions, one at the university and one at the school district.
At the
university, the TIR teaches mathematics courses for prospective
elementary school teachers. He/she also participates in
department meetings and seminars relevant to the preparation of
elementary school teachers. As an example, last year the
mathematics education faculty at CSU, Chico included several
local elementary teachers in a special seminar series centered on
reading and discussing Liping Ma’s Knowing and Teaching
Elementary Mathematics.
The transition for an elementary teacher to the university staff is made easier by ongoing mentoring, planning, and even team-teaching mathematics courses with university mathematics professors. The TIR has the elementary background and working relationships with the district and can enrich these courses with special areas of expertise. Last semester, a local elementary class came to visit several sections of university mathematics classes for prospective elementary teachers. The fifth- and sixth-grade students paired with university students to work on Mathematics Olympiad problems. They shared with each other how they were thinking about the problems and then explained their solution strategies to the entire class.
The other half of the TIR’s position is with the local schools in the Chico Unified School District. The school-based role of the TIR has shifted this year, in response to California’s changes in education policy. Elementary schools whose children score lower than 40% on the annual Stanford Achievement Tests are designated as Underperforming Schools (UPS) by the state. The ExxonMobil Foundation project at Chico State decided to link directly with schools categorized as underperforming. In conjunction with the district office and with the approval of the teachers at a particular UPS, the TIR works specifically with one elementary campus as a math specialist and resource provider.
Our Math Instructional Partnership is currently with Jay Partridge Elementary School. The Teacher-in-Residence has an office at the school, and is there full days on Tuesdays and Thursdays. Teachers at Partridge collaborate at monthly mathematics inservice meetings, where they have time to plan and to work together, learning more about the mathematics related to their grade levels. The TIR selects collaboration meeting topics of study to coincide with upcoming classroom units of instruction. Each meeting begins with a problem designed to challenge teachers’ understanding of the topic, and then moves to classroom applications. In the final segment of the collaboration session, teachers work together to examine and refine curriculum and assessment for their grade level.
All teachers
at Partridge are involved in the collaboration component of the
ExxonMobil Foundation project. More individualized staff
development takes place when teachers invite the TIR into their
classrooms for model lessons or team-taught lessons. Such visits
have enabled the TIR to become a visible member of the staff, to
develop a direct connection with students, and to support
colleagues engaged in the process of change.
The TIR also becomes a crucial link between the school and university in helping to place prospective elementary teachers from these same mathematics classes in a special mathematics tutoring program at this school. The TIR serves as an on-site coordinator and also team-teaches with a university mathematics professor a biweekly seminar for these tutors. The goals are to provide Partridge with more effective tutors, provide these future teachers more undergraduate classroom experience, and also to bring into the classrooms appropriate supplemental mathematics curriculum and ideas to share with classroom teachers.
This year, the TIR position has been filled by Katy Early, a fifth-grade teacher and member of the Chico Unified Math Task Force for the past eight years. Katy served as a Mentor Teacher in mathematics for five years and as a Teacher on Special Assignment for Mathematics for the district for one year. She first participated in the CSU, Chico Math Project in the summer of 1992, and has remained actively involved with the Project since then. Katy says, "I have always loved mathematics and tried to share my enthusiasm for the subject with my students. Now my students are university level students and my colleagues in the district!"
Carol Brooks, Tucson Unified School District, AZ, forwarded this article about a recent exciting event in her district. The authors are principal Dea Salter and teachers Linda Brady, Luz Elena Howard and Debbie Tindall, Thank you all! Ed.
On the evening of the "Fall in Love with Math" event, families at Harriet Johnson Primary School were greeted at the door by dozens of giant scarecrows and piles of spaghetti that they would enjoy at the end of the evening. Families were invited to view the scarecrow display in the large commons area before going to classrooms. Signs explained how mathematics, literacy and social studies were integrated into the plans that each class made to design its scarecrow. The scarecrows provided a colorful background for lots and lots of photos of parents and students that were taken that night!
Harriet
Johnson Primary School is located in a rural area of Tucson. It
is very culturally diverse, with a large Native American
population. For several years, the staff at Johnson has
participated in the Title 1 Early Childhood Project and the Title
1 ExxonMobil Foundation Mathematics/ Science Learning Community
School Project institutes, workshops and classes.
Johnson recently received an ExxonMobil Foundation mini-grant to develop a Mathematics/Science Learning Community School that fosters success in mathematics and science for their children. (Please see Intersection, Oct. 2000 Ed.) "Fall in Love with Math" was the result of time for discussions in study groups convened at the school and in the school planning time given at a workshop. The teachers’ idea was to design a night that would enhance personal interactions with families while engaging them in cooperative learning and problem solving. They wanted parents to see how mathematics is valued school-wide at Johnson.
During the weeks before the big event, children read and discussed stories about scarecrows. They wrote stories and kept journals that included sketches, plans for construction, and notes on materials used. Discussing proportions, discovering different ways to measure using both standard and non-standard measurement, and using geometric shapes and patterns were some of the mathematics concepts involved. They created categories such as "Most Unusual Scarecrow," "Funniest," and "Most Likely to Scare Away Birds." The children were so excited! They became attached to their own scarecrows but also showed interest in other ones. Conversations took place about why scarecrows were in certain categories and why certain materials were used, etc. Teachers thought that the interactions the displays promoted were wonderful.
Teams of grade-level teachers planned classroom interactive mathematics activities for the families. Kindergarten focused on apples. They made star-pattern bracelets using the star in the middle of the apple, graphed favorite apples, and estimated numbers of apple lollipops in a jar. This led to a discussion about approximation.
First-grade families compared pumpkins. They estimated the circumference and the number of seeds and guessed how many unifix cubes would equal the weight of a small pumpkin.
Families of second-graders solved a problem from Lily Toy Hong’s book Two of Everything: A Chinese Folktale: How many people would we have if everyone in the room fell in the magic pot and two of everyone came out? Teachers observed eager participation and engagement in this supportive environment.
At the end of the activities, all of the families shared a delicious spaghetti dinner prepared by parents and staff. The cafeteria was adorned with math banners, graphs and student work. Even the door prizes were mathematical, such as The Cheerios Counting Book and a box of Cheerios. Everyone felt it was a very fun and successful evening. Johnson is truly a Mathematics/Science Learning Community School.
NCTM will blend voices from across the nation and around the world when mathematics educators convene for the organization’s Annual Meeting—its 79th—from April 4-7 in Orlando, Florida. Currently 110,000 members strong, NCTM is the largest nonprofit professional association of mathematics educators in the world.
At last year’s conference in Chicago, some 20,000 attendees celebrated the release of the Principles and Standards for School Mathematics (PSSM). This year, under the theme "Math World: New Standards for the New Millennium," the celebration will continue with the launch of the Navigations series. Created to help teachers implement PSSM, the Navigations materials will be introduced by NCTM President Lee Stiff at the opening session on Wednesday.
With nearly 1100 sessions to choose from, attendees will have unparalleled opportunities for learning, sharing and networking. To learn about some sessions you’ll definitely want to attend, please see "Star These Sessions" below.
Since 1997, many of you who have had the good fortune to attend NCTM’s Annual Meeting have shared your experiences and your impressions of the conference in "A Collection of Reflections," the annual supplement to the May newsletter.
Any Intersection reader who attends the conference is invited to write about it in these pages. Typically, the reflections have averaged 100-150 words, although some contributors have written 500 or more. What you experience at the conference—in small and large group sessions, at featured presentations, with interactive displays, at the exhibit hall—will clearly interest Intersection readers.
Please send your reflections to the editor by Monday, April 16. And if you take photos, send those, too! Thanks.
Each year, on one of the evenings of NCTM’s Annual Meeting, ExxonMobil Foundation hosts a reception to bring together friends old and new for hors d’oeuvres, drinks and fellowship. This time-honored event will take place between 6 – 8 PM on Thursday evening, April 5, in the Signature II Room at the Rosen Centre Hotel.
The reception is come-and-go, and no RSVP is required. If you are a project/site director, please pass along this invitation to your teachers, teacher-leaders, math specialists, math coaches, and any and all other project participants who will be in Orlando for the conference.
Hope to see you!
The presenters listed below by session number have at least one thing in common—like you, they are all recipients of this newsletter. Of course, you know them best as your friends, colleagues, associates and leaders. If you’ll be in Orlando, you won’t want to miss these sessions!
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Many thanks to Babs Margolies, a teacher in the Montgomery County Schools, MD and to Pat Hess, retired project facilitator for the Foundation, Albuquerque, NM, for forwarding the two reviews that follow. Ed.
Reviewed by Babs Margolies
Math Matters: Understanding the Math You Teach, Grades K–6 by Suzanne H. Chapin and Art Johnson is another outstanding mathematics resource book from Marilyn Burns’ Math Solutions Publications (September 2000, 256 pages).
The book is based on the authors’ experiences with the U.S. Department of Education-funded Partners in Change Project. It helps to fill the gap between research and practice by clarifying ideas presented in the NCTM Standards, linking those ideas to activities that enhance student and teacher thinking and learning, and enabling teachers and other mathematics educators to better understand the mathematics they teach.
The book consists of thirteen chapters, each dealing with a specific mathematical topic studied in the elementary grades. Each one begins with a brief introduction followed by numbered sections that address different aspects of the topic. These sections contain in-depth yet "teacher friendly" explanations of math concepts basic to particular topics and subtopics; introduction to and definitions of terms related to each concept; and activities which can be used in the classroom to promote concept and skill acquisition.
After each activity are "Things To Think About," including very helpful tips on why some students have difficulty understanding specific ideas or learning particular skills. Furthermore, information from current research on how children learn is correlated with a discussion of why particular topics need to be included in the elementary mathematics curriculum.
Each chapter is chock-full of insights and provides ample opportunities for stretching one’s mathematical thinking in new ways. For instance, Chapter 2 (Computation) and the related chapters on Addition and Subtraction (Chapter 3) and Multiplication and Division (Chapter 4) really clarified for this reviewer the interrelated nature of mathematical operations. The "Teaching Computation" section pointed out that "Students need to understand a variety of approaches to solving problems in order to choose the most appropriate method based on the numbers involved and the complexity of the procedure." It goes on to say "… another fact that affects our choice of algorithms or procedures involves the context of the problem." Following this logic through Chapters 3 and 4, one cannot ignore the importance of helping our students look beyond the memorization of solution steps in the traditional way. Instead, students must chose an algorithm based on their understanding of what the numbers and operations represent.
Each chapter of Math Matters presents opportunities for new knowledge. Chapter 1, Number Sense, develops the notion of what it takes for a student to become numerically powerful, and the importance of the teacher’s understanding about number and number systems in this process. Find out, in this chapter, how activities involving even and odd numbers and activities surrounding rectangular dimensions and factors aid in the process of understanding numbers. Worried about helping students develop a thorough understanding of our place value numeration system? Chapter 1 can help with this, too!
Computation means more than memorizing algorithms. Check out Chapter 2 for why and how to address teaching computation. Explore the importance of mathematical properties and how they relate to the "basic facts." Discover ways to encourage flexible thinking.
Chapters 3 and 4 deal with the four interrelated mathematical operations: addition, subtraction, multiplication and division. Consider the various meanings of the operations. Help your students connect concrete objects and their manipulation to the written symbols, and then to the abstract ideas inherent in the operations. Look at the larger picture: How does operation sense lead to later understanding of multi-step problems, and to topics such as rational numbers and integers?
Want to know about the basic concepts underlying instruction of fractions, decimals, and percent? Check out Chapters 5, 6, and 7. Learn why, when she read the activity, "Does It Terminate?" Marilyn Burns began thinking about why some fractions convert to terminating decimals while others convert to repeating decimals, and how allowing students to look at patterns in this type of activity aids them in understanding mathematical relationships. Marilyn eloquently states in the introduction to Math Matters how, with this discussion, the book "…reminded [her] … of the importance of being a lifelong learner, that it’s never too late to learn."
Algebra, "the fundamental language of mathematics," and its incorporation through the elementary grades is dealt with in Chapter 8. The concepts of equality, patterns, variables, rules and relationships, and representation are discussed in great detail.
In Chapters 9, 10, and 11, mathematics educators will find alternatives for worn-out instruction that emphasizes procedures and definitions for Geometry, Spatial Sense and Measurement. Learn about the levels of geometric thought and the idea of spatial sense. Excite your students with activities that bring understandings about points, lines, angles, and polygons. Use spatial visualization and orientation to investigate reflections, symmetry and structures. Gain a greater grasp of understandings surrounding measurement relationships. Reflect on the components of Metric and English measurement.
Finally, in Chapters 12 and 13, discover how to help your students understand and interpret statistics and use counterintuitive thinking to determine the probability of certain events occurring. See how elementary students can present information in sophisticated ways including spreadsheets and graphs.
Whether the reader is an experienced teacher, a new teacher, a pre-service education student, or a teacher educator, this book is a must for your bookshelf. It is one that you will refer to often, and one from which you will gain new insights with each reading.
Reviewed by Pat Hess
Day-by-Day Math: Activities for Grades 3 - 6, a math resource book by Susan Ohanian, published by Marilyn Burns’ Math Solutions, is a collection of anniversaries of two events for each day of the year. In the preface, Marilyn Burns states that these events suggest a mathematical problem, investigation or activity that is suitable for students in grades 3 through 6.
There are common mathematical investigation themes throughout the book: how long ago did this happen; how can you collect, organize and graph data; how can you figure the cost of things, and how you can measure.
This book is an excellent and unique resource book for both students and teachers. The best thing about the collection is its ability to spark the interest of children and give them a jump-start in continuing their investigations. Susan has provided resources for children’s further exploration. For example: "July 21, 1985. After searching for sixteen years, treasure hunter Mel Fisher finds the wreck of the Spanish galleon Nestra Senora de Atocha, valued at 400 million dollars. The galleon sank off the coast of Key West, Florida in 1622. This and other shipwrecks are described online at www.melfisher.org. Mental Math: How did long did the galleon lie in the ocean undiscovered?" This entry definitely interested me so I’ll go to that web site and find out more about shipwrecks.
In my opinion this book would be a helpful resource for first- and second-grade teachers. Some schools have science and math fairs and many of these entries would help children begin the process of developing their projects. I also think that any child would delight in exploring the entry for his/her birthday.
There are many entries that I’ve marked with post-it notes. March 5, 1853 tells about the immigrant Steinweg brothers who Americanized their name and opened a piano-making business. You are referred to www.steinway.com to see how pianos are built. Another is April 28, 1975, World Whale Day (all children love whales) with the web address provided. One more is May 8, 1924 when Tana Hoban, future photographer and author, is born. This last entry needs to have a referral to Chuck Walter or Robert Speiser at Brigham Young University to see what children in their project have photographed.
This book is a great resource for teachers and would make a thoughtful gift for your teacher buddy.
For ordering information on both of these titles, please visit www.mathsolutions.com.
This reminder is thanks to Norma Sakamoto at WestEd. Ed.
Mathematics Case Methods Seminars are being offered once again in late May at the WestEd Office in Oakland, CA.
These sessions present cases about real classroom situations and include dialogue and student work. Participants will learn how to examine the math, student thinking, instruction and language in a case; how cases are facilitated; how to practice the techniques (if you volunteer), and how to introduce cases to others.
Option 1 (2 days), May 18-19, costs $350. Option 2 (Option 1 plus 1 day advanced training), May 18-20, costs $450. The fees cover all materials and breakfast and lunch each day. Participants will receive a "Getting Started Handbook," instruments for reflecting on, assessing and improving the quality of discussions; "Fractions, Decimals, Ratios and Percents," a casebook and facilitator’s guide; and starter problems for the cases. For more information, call Norma Sakamoto at (510) 302-4206 or e-mail her at nsakamo@WestEd.org.
The deadline for registration is April 16. Please send your name, address, phone number, fax number and check (made payable to WestEd) to Carne Barnett, WestEd, 300 Lakeside Drive, 18th Floor, Oakland, CA 94612 by that date.
Here’s another title you can own if you review it for Intersection—Susan Ohanian’s most recent release, Caught in the Middle: Nonstandard Kids and a Killing Curriculum. Just published by Heinemann, Susan’s stories from her own classrooms are both poignant and provocative. This one will move you, alternately, to tears of anger, sadness and joy. Please contact me if you’d like to volunteer. Thanks. Ed.
"Communicate, impart, tell, lay on one <nonformal>, convey, transmit, transfer, send, send word, deliver or send a signal or message, disseminate, broadcast, pass, pass on or along, hand on; report, render, make known, get across or over; give or send or leave word; signal; share, share with." That’s from Roget’s International Thesaurus. And that’s what you’re invited to do!
Thanks to all who submitted articles for this issue. Deadlines? For the April issue, it’s Monday, April 16. May’s will be Monday, May 14. Please send contributions to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; e-mail, jean@intersectionlive.org; phone, (512) 689-1580; fax. (512) 869-8477.
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