In the waters of Lake Michigan beyond Chicago's Navy Pier, tall ships proudly fly their colors as they glide and roll across the waves. In similar fashion, as she opened NCTM's 78th Annual Meeting on April 12 that brought 20,000 of the NCTM's 110,000 members to Chicago, Glenda Lappan proudly unfurled the Principles and Standards for School Mathematics.
During a multi-media presentation to nearly 2300 enthusiastic educators, Glenda explained the reasons PSSM was written, the process by which that was accomplished, the organization of the content, and the expectations for its use. Telling the audience that PSSM extends the vision of the original Standards documents and derives from the need to set higher standards for both our students and ourselves, Glenda remarked thatmore than just talking about coherent goals and the math that needs to be learnedPSSM is a "discussion document meant to raise possibilities with teachers." She added that she hopes educators think of the new document as "an illustrated conversation with teachers about the important mathematics for children to learn."
"My colloquial way of summarizing what this is all about and what we are focusing on is that we should build programs that are developmentally responsive, academically excellent and socially equitable. Students in this country and in Canada deserve no less," Glenda stated.
Glenda challenged educators to continue to help students find success in mathematics by connecting with their mathematics interests, asking for classrooms better equipped with the tools for exploring mathematics, and gaining insight into the sense students are making of mathematics by listening carefully to their ideas, arguments and explanations.
Webcasts of Glenda's address at the opening session as well as Lee Stiff's remarks at the closing session can be accessed at www.nctm.org. The site also tells you how to order print and CD-ROM versions of The Principles and Standards for School Mathematics and the "Outreach Kit" to help others become acquainted with the new document. This fall, to foster a deeper understanding of the new document, a series of two-day professional development institutes will be offered through the brand-new NCTM Academy. And in April 2001, grade-specific support materials called Navigationssimilar to the Addenda serieswill be available. Visit the web site for more details.
Of course, the unveiling of the PSSM was only one of the many exciting things that happened at the NCTM Annual Meeting. In the supplement to this month's Intersection, A Collection of Reflections, you will find short pieces by attendees relating their impressions of the conference.
Those who attended the traditional early-evening reception hosted by the ExxonMobil Foundation during NCTM's Annual Meeting were treated to various delights from a sumptuous, delicious buffet as they visited with friends old and new in a comfortable setting at the Hyatt Regency Hotel.
As well as affording guests an occasion to become acquainted with Bob Witte's successor, Joe Gonzales, the reception also allowed them the opportunity to wish Bob well in his retirement. During a brief program, Joe welcomed guests, made remarks about the launch of the new document, praised the success of project participants, and encouraged future efforts: "Stay the course, stay involved, and look at the attainable achievements."
Following his introductory remarks, Joe invited Bob to the podium. Thanking Joe, Bob addressed the guests: "The gift you've given me is your honesty and your willingness to share the complexity of the tasks you do every day. Many people believe that if parents just turn off the TV, teachers use the materials they've been given, and schools make children behave, we'll succeed. But you know what's right, although it's not easy. You know that children need to know how to think that that's what it's all about."
Next, Joe invited Jean Moon, Pat Hess, and Jean Ehnebuske to the podium to surprise Bob with a two-volume collection of cards and letters relating memories, thanks and best wishes from colleagues and friends across the country. Thanking all, Bob commented that he'd look forward to reading the entries with the careful contemplation and reflection he knows such a gift deserves.
Joe closed the program by rephrasing a common saying: "Those who can, do. Those who can do more, teach." He added, "We entrust you to do more."
Thanks to Dave Ehnebuske for the photos from the reception in this issue. Ed.
The ExxonMobil Foundation will host the Twelfth Annual Meeting of the K-3 Mathematics Specialist Program Teacher-Leaders from Thursday PM, September 21 through Sunday AM, September 24 at the ExxonMobil Global Downstream Headquarters in Fairfax, VA. Following the tradition of the past few years, presessions are scheduled to begin at 2:30 PM on Thursday for those who can make arrangements to attend.
Because space is limited, attendance at the meeting will be by invitation only. Please look for invitations to arrive by mail shortly.
Lyn Taylor, associate professor of curriculum and pedagogy at the University of Colorado, Denver, is a recipient of this year's Elizabeth Gee Lectureship Award. Bestowed annually upon two female faculty members in recognition of scholarly contributions, distinguished teaching, and advancing women in the academic community, the award includes a $2000 prize.
Specializing in mathematics education, Lyn has focused her work on helping educators recognize the importance of considering gender issues and using gender-inclusive materials. In an article highlighting Lyn's award in Silver and Gold Record, March 16, 2000, Susan Jones writes that Lyn's goal has been to help female students of all ages "be comfortable and skilled in doing mathematics as well as to realize the importance and power that mathematics can bring them." Jones writes: "Taylor is particularly concerned with helping female and minority elementary school teachers develop positive attitudes and meaningful relationships with the field of mathematics."
Congratulations from us all, Lyn! Ed.
Many thanks to Donna Little-Kaumo and to her husband, Brian Kaumo, for submitting the article below about their collaborative work. They are both teachers in the Albuquerque Public Schools. Ed.
Over the last several years, my partner teacher, Brian Kaumo, and I have been teaching fifth-graders in an inclusive educational setting. The composition of our class includes eight special education students who have been identified as learning disabled and eighteen general education students. All students participate together full time in our class. As the general education teacher, I have learned a tremendous amount about mathematical competency for every child to include those who have struggled in our school systems.
Best practice in special education with children who have learning difficulties requires that instruction be presented with a multi-sensory, hands-on approach. Over my years of teaching, I have found this to be true for general education students as well.
The mathematics program in our class can be described as investigative and problem-solving in nature. This approach to learning about mathematical ideas has freed our students of the constraints of routines with traditional algorithms to developing mathematical ideas and making connections that make sense to them.
One of the most amazing events that we have continued to observe each year is the natural interest and flexibility of our special education students to problem-solving. Their past experiences weren't related to mathematics. In fact, according to levels of performance when entering our program, these students were on average three years behind in mathematical performance. However, perhaps because they have needed to develop alternative ways of making sense of their world for quite some time, they were open to assessing a situation and engaging in a common sense approach to developing a solution. These students have provided a huge support system to many of our general education students who have limited comfort in the area of problem-solving.
Over the past three years, we have been fortunate to send several of our special education students to general education mathematics classes in sixth-grade. The joy and success these students and their parents feel is beyond description. As teachers, we feel blessed to have the opportunity to watch and support their amazing work.
We are committed to the opportunities that inclusive education can provide for all children, and continue to explore the mathematical events in our class with the Exxon group participants in Albuquerque.
Now, as doctoral students, Brian and I continue our interest in mathematics instruction with the special needs population and inclusive education. We would love to hear from others who are involved in this type of work. You may contact us by e-mail at SDKWN@swcp.com.
If you're looking for suggestions for summer reading, you'll find some here. Many thanks to all three contributors. Ed.
Author Susan Ohanian forwarded the first review. Susan's most recent book is One Size Fits Few: The Folly of Educational Standards. See Intersection, June 1999, for Cindy Chapman's review of that title. In last month's newsletter, Chris Ohana reviewed Susan's cover article for January's Kappan, "Goals 2000: What's in a Name?" (Read it online at www.pdkintl.org).
What a great title for a book: Learning is a Verb (Holcomb Hathaway Publishers, $18.95. www.hh-pub.com.) Especially in our troubled times, people need to be reminded that learning is a verb, not a melange of nouns to be stuffed into young learners as they move along on a skills conveyor belt from grade to grade. Old friends will rejoice in continuing the conversation with Sherrie from annual Exxon meetings. New friends will find pleasure in joining the conversation. And this slim volume has the feeling of a conversation, with inserted reminders to take a minute and think about a point. There's even spaceand encouragement to jot down a few ideas.
Sherrie reminds us that teaching does not cause learning. She observes that "learning, thinking, and understanding are alive, dynamic, organic processes that can be nurtured and cultivated, but not controlled, measured, forced, or caused." Don't we all have a few state legislators, among others, to whom we could send this statement? The list of people who believe in the control and measure of education is depressingly long.
Chapter 6, Learning as a Condition for Teaching, begins with this quotation: "Teachers act as if teaching causes learning when actually learning should be an occasion for teaching." Kathleen Martin
Sherrie explains that what this means is that "instead of looking at causes as one does in a physical model, we need to think about conditions and constraints, as one does when dealing with living things. It also means that teaching does not and cannot cause learning. Thought is adaptive and responsive to environments. It is dynamic, unfolding, transitional."
This point is explained and illuminated by a discussion of Gregory Bateson, Jean Piaget, Barbel Inhelder, Lev Vygotsky, and Jerome Bruner, among others. Interspersed with the psychological / pedagogical frameworkthat Sherrie makes comfortably accessibleare observations of children reacting to the world around them. Lest this all sound too theoretical for a busy teacher, I would point out that in the middle of the psychology of the matter, the book contains a recipe for gloopand the invitation for teachers to make some and then investigate its qualities with children.
Yes, gloop. I, for one, believe that we'd all be better off if we stopped what we're doing and made some.
Sherrie is concerned about the way we interrupt children regularly, asking them to make sudden and intrusive shifts. Drawing on her experiences at the Fort Worth Museum of Science and Historywhere children are encouraged to pursue their interests, unconstrained by teacher plans or institutional bellsSherrie points to the need "to create conditions for children to develop habits of attending that will serve them well as thinkers and learners." This means that we must slow down our own teacherliness, not be too quick to act too fast.
Sherrie acknowledges that our old teacherly habits, left over from some industrial efficiency model, are hard to break. She suggests one way to learn to change is to watch one child at a time and to take notes. She advises that we should note what the child is doing, without interpreting it. "The most important change is to move from thinking about whether students are 'getting' some idea to just noticing, by what they say and what they do, what they think and what it means to them." This means that we must relinquish our role as leader and, instead, learn to be better listeners. To do this, Sherrie advises, "Practice assuming that you do not automatically understand others."
Sherrie ends the book with a revolutionary suggestion: "If you think you know truth, I suggest that you intentionally seek out someone who disagrees with you and listen to that person's point of view until you understand how he or she can think that way. This doesn't mean you will (or even that you should) change your point of view. It means that your thinking will grow by understanding other perspectives."
I can offer personal testimony at how difficult this is to doand how rewarding. More than a year ago, when I despaired of ever being able to finish an NSF research grant on community dissatisfaction with reform mathematics curriculum, I joined a conservative listserv. Parents' remarks so upset me that I immediately pushed the 'reply' button. Then I was informed by the moderator that this was a parent listserv and they didn't care to listen to teachers disagree with them. So I switched my membership to be one without reply privileges (and thereby saved money). For more than a year I have been forced to listen without talking. I confess it has made me a much better listener. As Sherrie says, it probably hasn't changed my perspective, but certainly my view is broadened. And the good news is that not only did I finish the NSF report, I wrote the January 2000 Kappan cover article too. Neither would have been possible had I not learned to listen.
Tim Martin, El Dorado, AK and Gregg McMann, Albuquerque, NM, reviewed the title above. Thanks to each one! Ed.
Getting Your Message Out to Parents, A K-6 Resource (Sausalito, CA: Math Solutions Publications, 1998), is an excellent guide for new teachers, as well as for seasoned veterans, on methods to bring parents more into the fold of educating children in the learning of mathematics.
Litton provides five chapters of templates and ideas that could be adapted for any grade level. By clearly making parents players in the educational process from day one, she demonstrates simple and practical techniques to help parents understand the learning process of mathematics. For instance, in the appendix to chapter one, she gives examples of the many different methods for discovering how to understand division.
In chapters two and three, she offers suggestions and ideas to be used during a parent conference, and during a Family Math night.
Chapter four pertains to homework and how to keep parents
informed on homework and its purpose. Through letters, she not
only informs parents about homework, but attempts to help parents
to be more prepared to aid their students. With an established
line of communication between parents and the educational process
at hand, parents will feel more empowered to
help their students when homework time comes.
Chapter five addresses the issue of volunteers in the classroom, and ways to enable them to become an integral part of education.
Overall, the book is quite informative and useful. It would be excellent reading for educators and parents alike, to help raise awareness that the learning of mathematics is a complicated process. However, this process can become less stressful for all by establishing clear and open lines of communication among teachers, students, and parents.
Litton's premise for writing this book is that since good math teaching today looks much different than what parents know and did in school, parent education is vital as part of one's teaching practice. The book gives ideas and examples of several strategies that can be used to communicate with parents.
The book is divided into six sections, each of which focuses on a specific strategy for communicating with parents. Each section has both an informative narrative and is supported by numerous samples from Litton's classroom. The first section is about newsletters. Examples are given from throughout the school year in order to get a sense of how the information in a newsletter might change over the course of a year as parents become more familiar with what good math teaching looks like. Ideas that are given include revising a newsletter that a publishing company includes with their materials, sharing classroom vignettes based on actual classroom activities, and once or twice a year discussing mathematical pedagogy.
The next chapter deals with back-to-school nights. Giving demonstrations of manipulative usage and sharing examples of previous years' lessons that develop big concepts and ideas are two ideas mentioned. Litton has also had students write letters to their parents explaining what they do in math class. Litton also realistically discusses how to deal with parents who still have concerns after attending a back-to-school night. She suggests scheduling a private appointment with them and finding out all their concerns prior to the meeting in order to be ready to address all their concerns.
The section on parent conferences includes many, many examples of student work that could be shared with parents. Litton stresses the need to make parents active participants in conferences. One of her strategies for doing this is sending home a letter before the conference in order to give the parents time to reflect and write down questions.
She also discusses scheduling conferences and the type of preparation teachers might consider for conferencing. During the conference she recommends the following schedule. First she begins on a positive note about the student and then finds out what parent information and concerns need to be dealt with. She then shares samples of student work that may highlight issues the teacher has with the student. Finally, if she has done an individual assessment with the student, she will share that with the parents. Another interesting conferencing strategy she shares is to encourage student-parent conferences, which do not necessarily have to occur at school.
Litton next deals with subject of homework by acknowledging that parents have many different expectations in this area. All classroom teachers know that the same group of parents will include some who feel there is not enough homework and some who wish for more. Her most important strategy for homework is to have students prepared to do the assignment and to be in charge of the assignment at home. She also suggests sending home newsletters on the topic of homework in general or a specific series of assignments. This helps prepare parents for what to expect in the way of assignments and may include strategies to help the student.
Litton also has used a homework diary where students, parents, and the teacher can keep an ongoing written dialog going about homework assignments, struggles and successes. The single most important thing a teacher can do to make homework successful is to follow up on the assignment in class. If students see that all that comes of homework is a checkmark in a gradebook, they have little incentive to invest effort in an assignment. Litton suggests following up a homework assignment in class by discussing the work in small groups, using the work (such as gathering data) in a classroom lesson the next day, or having students present their work to peers.
The section on parents volunteering in the classroom has many good ideas for teachers. The most important use of parent volunteers is not to provide help for the teacher but to provide modeling for parents on appropriate instructional interaction with children. Many parents do not know how to discuss mathematics with their children nor how to question them effectively to get at their thinking and understanding. When parents are in the classroom, they are able to see this. Litton suggests using parents to assist in learning centers and small groups. She provides a lesson plan for each group and encourages parents to come early to become familiar with the activity. She also asks parents to stay after the time with students in order to debrief them on what they noticed and how students did with the lesson.
The final section on Family Math gives extensive credit to the program designed by EQUALS at UC Berkeley. Litton's suggestions include using these materials and not feeling obliged to do a Family Math night in any one way. These evenings can be structured or open depending on the parent population and aims of the teacher. She does mention the importance of taking time to process with parents the mathematics that is being used and how the activity helps children's understanding of mathematics.
In her realistic closing, Litton acknowledges how hard it would be to implement all these strategies in one year and how important it is to be realistic in one's expectation of personal time and professional work. This dilemma of all thoughtful teachers is nicely addressed. At the end of the book is a thorough annotated bibliography of related materials for teachers to use.
This informative and easy-to-read book contains a wealth of information and strategies for elementary teachers to inform and communicate with parents. Many of the ideas could easily be transferred to middle school and high school educators as well. For a teacher looking for ways to communicate with classroom parents, this book will prove an excellent resource.
You may have as your own one of the following new titles if you'll review it for this newsletter.
The first is notable because it is the first-ever joint publication by NCTM and NCTEMath is Language Too by Phyllis and David Whitin.
The other, donated by Susan Ohanian, is Introduction to Problem Solving, Strategies for the Elementary Classroom by Susan O'Connell. Please contact yours truly if you'd like to volunteer. Ed.
Many thanks to Nihad Ziad at NCTM HQ for calling attention to these wonderful opportunities! Ed.
Over the summer, why not spend some time preparing a grant proposal for one or more of the many funding opportunities offered through the Mathematics Education Trust (MET)? Established by NCTM, the MET awards support special projects that enhance the teaching and learning of mathematics.
Since applications for most of the awards are not due until December 2000and some not until January 2001if you begin this summer, you'll have plenty of lead time. To learn more, please visit www.nctm .org/about/met or call NCTM at (703) 620-9840, x 2113.
Christina Perez recently made this announcement on the listserv. Many thanks! Ed.
Weaving Gender Equity into Math Reform (based at TERC in Cambridge, MA) at www.terc.edu/wge seeks to assist staff developers, curriculum writers, and workshop leaders in expanding the equity content of their workshops, videos, and written materials for teachers. Our project is investigating the specific question of gender equity in math reform, as well as the larger equity issues that these reforms pose for students from various academic, socio-economic, and linguistic backgrounds.
Visit and you'll find information on the project and our partners; links to other organizations concerned about equity in education; articles on equity in education; an annotated list of research articles, books, and electronic resources; and a list of equity workshops around the country.
Thanks to Christopher Kribs-Zaleta for forwarding this information. Ed.
The DIMACS program at Rutgers is providing NSF-funded two-week summer institutes on discrete mathematics for math teachers and specialists, K-8. Discrete mathematics, like number theory, deals with a variety of interesting problems that are accessible to learners at a wide range of ages (e.g., handshake problems, traveling salesman, map coloring).
There will be a residential institute at Rutgers and commuter institutes in Greenville, NC; Auburn, AL; Houston, TX; and Worcester, MA. Participant costs are covered by NSF, and graduate credit is possible. Visit dimacs .rutgers.edu/lp/institutes/ for details.
Christopher adds: " I really enjoyed their presentation at NCTMunfortunately it was in a hidden-away room in the Sheraton basement on Saturday afternoon."
From Jerry Becker comes the following announcement. Thanks! Ed.
The Beijing Academy of Educational Science (BAES) and the Organizing Committee on "Mathematics Education, History of Mathematics, Cultural History of Mathematics, Informatics and Learning Obstacles" will host an international conference in Beijing,China, July 24-27, 2000.
With the advance of the information-communication oriented society, the research in the fields of Mathematics Education, History of Mathematics, Cultural History of Mathematics, Informatics and Learning Obstacles are greatly advanced in all the world. The conference provides a forum for researchers to exchange and discuss their ideas, views, and findings in those affairs and to set a direction for establishing international links and future research.
For further information, please contact the Secretary General, as follows: Mr. Zhang Shin, President's Office, Beijing Academy of Educational Science, No. 7 West Chang'an Avenue, Beijing 100031, P.R. of CHINA; ; phone, (+86)-10-66067158; fax, (+86)-10-66075470; e-mail email@example.com .cn.
Visit www.intersectionlive .org and view all past issues of Intersection from January 1999 to the present. Please tell your friends and colleagues to check it out, too!
In a few scant weeks, some of you (especially if you teach in Texas) will be out for a well-earned summer vacation. But as you sit poolside, hike that trail, or author the Great American Novel, please remember that Intersection readers would love to hear from you! Please take a moment to reflect on the year just past, jot down your thoughts, and send them to the editor.
Thanks to all who contributed to this issue. The deadline for the May issue will be Monday, May 22. Please send contributions to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; phone, (512) 869-1580; fax, (512) 869-8477; e-mail, firstname.lastname@example.org. Thanks!
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