The following article was contributed by Lance Menster, of The Houston Annenberg Challenge, and Susan O'Boyle, mathematics instructional supervisor with the Houston ISD - Southwest District. As project facilitator and project director respectively, Lance and Susan will be working in collaboration to implement the initiative described below. Thanks and welcome! Ed.
Eight elementary schools in the Houston ISD - Southwest District have partnered with ExxonMobil Foundation and The Houston Annenberg Challenge to make a difference in the area of mathematics with on-site math specialists. In September, the math specialists began collaborating with elementary teachers in the project. The goal of the project is to improve student achievement by strengthening teachers' knowledge of mathematics and instructional methods.
The math specialists are working
hand-in-hand with classroom teachers Mondays through Thursdays
through daily co-teaching, coaching, and math planning. Using
recent data analysis, math specialists are targeting number
concepts, measurement and problem solving as the focused effort
of their work.
In an effort to foster collaboration, continuity and the evolution of the math specialist role in the Southwest District, weekly Friday "Think Tank" sessions are in place for reflection, conversation and professional development. Math specialists are active participants in Developing Mathematical Ideas (DMI) sessions investigating Building a System of Tens and are also participating in a Mathematics Critical Friends Group (CFG). As a group, the math specialists will solidify student learning goals, look at student work, explore mathematical cases of student thinking and study how students make sense of numbers.
During the first year of the initiative, the project will target third-graders and focus on the role and work of the math specialist. The Math Initiative has also extended and outreached to involve specialists from neighboring districts including Alief ISD, Ft. Bend ISD and Houston ISD - East District to share professional development experiences.
The announcement was made on Tuesday, October 17, 2000 during a morning ceremony at Foerster Elementary, one of eight elementary schools selected to participate in the project. Many key educators and contributors took part in the ceremony including: Dr. Rod Paige, Superintendent, HISD; Larry Marshall, President, HISD Board of Trustees; Edward F. Ahnert, President, ExxonMobil Foundation; Joe Gonzales, Program Officer, ExxonMobil Foundation; Hugh Hayes, Deputy Commissioner, Texas Education Agency; and Linda Clarke, Executive Director, The Houston Annenberg Challenge.
Many thanks to Bill Nutting, staff development director for the Mount Vernon School District, as well as project director for this newly funded site, for contributing the article that follows. Welcome and best wishes! Ed.
The Mount Vernon School District, located in Mount Vernon, Washington, recently received a planning year grant from the ExxonMobil Foundation. This grant will support improvements in mathematics instruction at our six elementary schools.
With many factors converging, the support from ExxonMobil is timely. Our state is in the process of implementing significant education reforms that feature high-stakes assessments and accountability measures. In contrast to some assessment instruments, the Washington Assessment of Student Learning (WASL) is not a minimum-competency test. This high-standard assessment is a graduation requirement for the class of 2008. Since implementation three years ago, the WASL has significantly challenged our learners.We know that to provide the opportunity for all students to meet or exceed this standard in our district, we must continually improve the teaching of mathematics.
Over the past three years, we have been involved in curriculum adoption work and in an implementation process that has phased in standards-based mathematics from kindergarten through twelfth grade. During the 1999-2000 school year, six elementary teachers piloted Math Trailblazers in preparation for full staff implementation this year. Currently these teacher leaders, in collaboration with our elementary math coach, are providing in-district support, training and leadership to over 100 teachers implementing this new mathematics program. Although the initial implementation has been successful, we know that much hard work lies ahead.
In order to significantly impact mathematics instruction, our district is making a commitment to on-going professional development for teachers.With the belief that quality professional development will result in improved mathematical understandings and improved instructional strategies—and also with the belief that those teaching improvements will lead to student learning improvements—we are optimistic that our efforts will positively impact student learning.
Our Foundation grant affords us the opportunity to plan in three areas. First, our project will work on defining an expanded role of our teacher-leaders and math coach. Recognizing the importance of teacher leadership as well as on-site leadership, we are interested in refining these roles to maximize support for teachers.
Second, we will assess teacher needs for professional development in math. This will occur through both formal and informal means, including the analysis and utilization of student achievement data.
Finally, we will begin planning a menu of professional growth options that will improve both our elementary teachers' mathematical understandings and their instructional skills with mathematics. Our hope is to offer summer institutes, study groups, in-service training, workshops and on-going coaching to our teaching staff.
Already our relationship with the ExxonMobil Foundation has informed our planning. Both Chris Ohana and Jean Moon have been instrumental in helping us think through our next steps. We recognize the long-term commitment required to impact teaching and learning in our school district. We are excited by the challenge and are very appreciative of the ExxonMobil Foundation's support to enhance the on-going work in mathematics instruction in the Mount Vernon School District.
Thanks to Anne Herndon at the Fort Worth Museum for letting us know about this honor. Congratulations! Ed.
The Hands On Science Learning Laboratory at the Fort Worth Museum of Science and History was chosen as an Exemplary Partnership in the state of Texas during the Texas Alliance Legislative Conference on Science, Technology and Mathematics Education held in Dallas recently. This conference is held every two years and brings together leaders from business, education, government and local communities to focus on one central topic—improving the capacity and quality of math and science education in K-12 schools and institutions of higher learning.
Partnerships from around the state were invited to submit proposals outlining the ways they support mathematics and science in their communities. Ten partnerships were chosen as exemplary and were asked to present during the conference. In addition to the Hands On Science Laboratory, two of the other Exemplary Partnerships are also supported by ExxonMobil Foundation. The Museum was grateful to be highlighted at this conference and, of course, grateful for the support of the Foundation that makes this work possible.
Inspired by the presentation of Tom Carpenter and Megan Franke at September's meeting of the ExxonMobil Foundation/NCTM K-5 Math Specialists, Holli Aflatouni shared on the listserv what she tried with her second-graders in Arlington, TX. Note: If you haven't yet subscribed, what follows is representative of the substantive ideas posted on this particular listserv. Please join! Ed.
Here are problems that I wrote on the board:
9+5=14
9+5=13+1
9+5=14+0
9+5=0+14
I asked the students, "Do you agree or disagree?"
On the first problem, everyone agreed. Mark even told us that he knew it was right because he double checked on a counting chart. On the second problem, everyone disagreed except Sandy. The disagreeing faction said that 9 and 5 make 14, not 13. Sandy said that you have to add 1 and it makes 14, but everyone else said no, it says 9+5=13; you add 1 later and it still doesn't make it true. Sandy would not change her mind, but she could not think of another way to explain. She said she would think about it.
On the third problem, everyone agreed it was true. One child explained that 9 and 5 is 14 and 0 doesn't do anything. That explanation seemed to satisfy everyone. On the last problem, all disagreed except Jeff and Sandy. Jeff went up to the board and explained that 9+5+0=14. Then some kids said he couldn't do that because he was changing the problem. I asked him if he could use his method on 9+5=14+0 and he said, "No it won't work on that one." He decided maybe his way wasn't quite right. Sandy wanted to explain her thinking again. I could sense her struggle with the words, so I wrote on the board what I thought she was trying to say. She said 9+5 is 14, but 0+14 is also 14. So I wrote:
9+5=0+14
14=14
She got very excited and said, "Yes! Yes! That is what I am trying to say!"
Most kids tried to tell Sandy that is not what the problem means. You have to do 9+5=0 first, then add 14. Since 9+5 is not 0, then the problem is wrong. They said the answer always goes after the equals sign. So, I asked if a problem could be written like 8=5+3. Sandy said it could and some others began to wonder. Then I wrote 5+_=9. I asked what the answer was. Everyone quickly said 4. I asked, "Why isn't it 9?"
They looked at me like they thought I had finally lost it. "Because 5+4=9," they said. I told them they just told me the answer is always after the = sign. I had successfully created some real doubts in their minds about what they thought and the language we were using. No one offered that the answer they were referring to after the equals sign was actually the sum.
I then asked, "What does the = sign mean?" I got a variety of answers. Most kids said that when you see the =, you know the answer is the next number. I had some kids stand up. First I said, "If you take 1 student and add 2 more students, how many students do you have?"
"Three," they replied. Then I took 2 students and added 1 student. They again said 3.
I asked, "Are these two groups of students equal?" They said yes.
Sandy, getting frustrated with the other kids, said, "Well, that is the same thing the problem is saying!" There were murmurs among the class so I decided we would revote on the problem. When asked how many agreed that 9+5=0+14, about half the class now agreed with Sandy. The other half looked semi-perplexed. We stopped there and agreed to revisit it again another day. I found it interesting that not one student ever asked me what the answer was. Maybe they weren't convinced I knew!
Since it had been a few weeks, I decided to bring up equality again. Here are the problems that I wrote on the board:
3+5=8
8=3+5
3+5=2+6
3+5=5+3
8=8
I asked them if they agreed or disagreed.
Everyone agreed with the first problem. Some agreed with the second, but not many. Tony said, "It's just like the first problem, it's just backwards. The = can be in the front."
I asked him why he thought it was okay for the equal to be in the front and someone else said, "Because you told us it could."
I said, "I never said that, but I think someone else did." It didn't matter to Tony who said it; he was positive it didn't matter where the = was.
Jimmy then said, "Well, I disagree." I asked him why. "Because the = is like a stop sign—you know like the period at the end of the sentence. It is where you stop and it has to go at the end of the problem." I asked him how he knew that and he looked bewildered.
"Oh, I learned that in first grade, I think." I asked for a volunteer to go up and draw what 3+5=8 meant. Walt went up to the board and drew 3 circles with 5 circles under them. Everyone agreed that represented the problem. Jimmy went up to show us what 8=3+5 meant. He drew 3 circles with 5 circles next to them.
Someone said, "That is what Walt drew."
Jimmy said, "Oh, well I didn't draw it right. I need more circles." He couldn't figure out what to do, but Tom offered to help. Tom drew 8 circles, then 3 circles, then 5 circles. Jimmy looked relieved. I asked Tom how many circles he drew and he said 16. I asked if that was right and most weren't convinced but couldn't really explain why.
The next problem was 3+5=2+6. Almost everyone disagreed. Winnie said, "I don't understand why there is an equal sign in the middle." No one could explain it to her. Jimmy offered, "3+5=8 and there is no 8 in the problem." Then he said, "2+6=8 but it is not the same." I asked it someone could show us what the problem meant with cubes. Tom went up and took 3 cubes then 5 more. Alice took 2 cubes and 6 more. Tom said, "We both have 8. Then I agree that 3+5=2+6." Jimmy said no. Most were unsure.
The next problem was 3+5=5+3. Tony and Hal and several others immediately agreed. Hal said, "It is just backwards." There were several who agreed with Hal. I asked about 8=8. Everyone agreed, no problem. Tony said, "Well, 3+5=5+3 is just like 8=8 since 3+5 and 5+3 both equal 8." Jimmy agreed that 3 and 5 are 8 and 5 and 3 are 8, but he said that is not what that problem is saying. He said that it is saying 3+5=5 and then add 3 more. Jimmy said it is wrong because there is no 8.
Hal said, "Yes there is, 3+5 and 5+3 are both 8." Kirk said the = cannot go in the middle. So I asked where the = can go. The end? They said yes. The middle? Some said yes. The beginning? Some said yes.
Jimmy is getting really annoyed at this point. He said, "Some people voted more than once!!"
I said, "It is because they think the = can go all those places." He looked troubled.
As we cleaned up, we heard Jimmy mumble, "Well, I am sure about the first and last problem, but now I am not sure about the rest." Sandy, who was vocal last time, was quiet today. She came up to me afterward and told me, "You know, I agree with all those." I said to her, "I knew you would." She smiled.
NCTM has just announced the election of four new board members as well as a president-elect. Among them is Cindy Chapman, whose peers have elected her to a three-year term as "Director, Elementary School Classroom Teacher." Her term will begin in April 2001.
Currently a second-grade teacher at Inez Science and Technology Magnet School in Albuquerque, NM, Cindy has been involved with Foundation-supported projects for several of her twenty-eight years of teaching. A Presidential Awardee and a NM fellow with FAME (Fellows for the Advancement of Mathematics Education), Cindy has presented at regional, state and annual conferences of NCTM and also served on various professional committees at all levels. Somehow she has also found time to be a frequent contributor to this newsletter.
Commenting about her election on the listserv, Cindy wrote: "Your support has meant so very much to me in my teaching and learning of mathematics. I never in my wildest dreams thought that I would end up serving on the NCTM Board. I never knew mathematics would come to bring me such incredible joy. How my life has changed since I became a New Mexico FAME fellow 10 years ago—I never would have dreamed! I guess what's most important is how my teaching has changed. Thank you all so very much."
Johnny Lott, professor of mathematical sciences at the University of Montana, was elected president of NCTM. He will serve a one-year term as president-elect beginning April 2001. He will then begin his two-year term as president in April 2002. The other three board positions were filled by Carolyn Kieran, Westmount, QC, Canada; Mark Saul, New York, NY; and J. Michael Shaughnessy, Portland, OR.
Congratulations, Cindy!
Thanks to Chris Ohana, assistant professor in the Woodring College of Education at Western Washington University in Bellingham, for writing the review below. Ed.
Math Solutions Publications has released a second edition of Marilyn Burns' About Teaching Mathematics, first published in 1992. This edition retains much of the content and organization of the original. The book contains four sections. The first three sections represent an updating of the original edition. The single major difference is the addition of a new 50-page section in which the mathematics of 40 lessons in the book are discussed and extended.
Part I, "Raising the Issues," defines Burns' approach to the mathematics classroom. It includes basic, quick overviews of such topics as how children learn mathematics and how to include problem-solving in mathematics classes.
For instance, Burns presents some common arithmetic errors and offers a brief interpretation of them. If children are asked, for example, to find the missing number in 3+X= 7 (a problem similar to ones we examined at ExxonMobil Foundation's K-5 Director's meeting), they may answer that X must be 10. Burns suggests that a child may see it as a "plus" question. You have a 7, a 3, and a plus sign. Add 'em together and the answer is 10.
This example speaks both to the strength and weakness of this book. The strength is that the book addresses many issues familiar to mathematics educators. In this case, we all have to diagnose and understand student thinking. The weakness is that since the book is so inclusive and broad, the discussion tends to be somewhat cursory. In the section on cooperative learning, the reader gets a very broad view of working with groups (though not really cooperative learning), but does not get enough to actually choose cooperative tasks, design an assessment and manage cooperative groups.
In Part II, Burns provides a host of lesson ideas in each of the strands of mathematics. She describes sample lessons with clear and concise instructions. These types of lesson are the foundation for the phenomenal success of Marilyn Burns. Each of the lessons is followed by a series of activity extensions that incorporate problem-solving. For example, a lesson on body ratios is followed by activities on foot perimeter and other measurement ideas. Her lessons on probability and statistics are particularly welcome since children often lack enough experience with this strand.
There has been a substantial revision to Part III, Teaching Arithmetic. As a result of Burns' recent experience teaching fourth and fifth grades, she added a section on extending multiplication and division. This section presents whole class lessons on extending multiplication and division to large numbers. Several games and menu (independent) suggestions are offered as well.
The most dramatic change in the book is the addition of a discussion section (Part IV) in which the mathematics in many of the activities in the book is discussed in some depth. This is a significant improvement. There have been many occasions on which I have seen Burns' lessons taught or presented but the mathematical point was not made clear. The point becomes much more explicit with this section. In fact, while I found myself skimming through the first three sections, I spent significant time reading and re-reading Part IV. It was almost as if I were eavesdropping on Burns as she thought about these lessons.
The first edition had a broad audience. Many people still use it to teach mathematics methods classes. Many of us grew to rely on Marilyn Burns' books as our new understanding of teaching mathematics grew. This book seems particularly appropriate for beginning teachers and others (like that favorite administrator in your life who needs a general perspective on mathematics) who do not want or need detailed discussions of mathematics education. For those folks, this book can serve an important and useful function.
To learn about purchasing this title, visit www.math solutions.com.
Patricia Baggett in the Department of Math Sciences at New Mexico State University extends this personal invitation. Ed.
I am writing to invite you to attend the Fourth Annual Mathematics Education Institute to be held in Las Cruces, NM, Saturday, March 17 - Tuesday, March 20, 2001. The Institute is sponsored by NMCETP, the New Mexico Collaborative for Excellence in Teacher Preparation, an NSF-funded project. We have some funding for attendees to help defray expenses. Details about the Institute, and an on-line registration form, may be found at math.nmsu.edu/ breakingaway/.
There are two main purposes for the Institute:
Las Cruces, a beautiful multicultural city in southern New Mexico, is delightful in March! I hope you will attend!
Thanks to Virginia Bastable for this information about summer 2001 sessions. Ed.
The DMI (Developing Mathematical Ideas) Leadership Institute Program is designed for teams of staff developers, teacher-educators, teacher-leaders and others who support teachers' professional development in mathematics, K-7. Participants will work in a community of peers to inquire into the goals of professional development for elementary and middle school mathematics, reflect on the kinds of structures and activities that can support those goals, and become familiar with DMI as a tool to forward the mathematics education agenda at their home sites.
Two modules of DMI are now available: Building a System of Tens and Making Meaning for Operations. Three new modules will be available in the summer of 2001. Two of these are based in geometry: Examining Features of Shape and Measuring Space in One, Two and Three Dimensions. The third module is about statistics: Working with Data.
DMI L1, based on Building a System of Tens (BST) and Making Meaning for Operations (MMO), is appropriate for educators who are new to the DMI materials. DMI L2 will build on the work of DMI L1 and also include sessions in which participants delve deeply either into one of the three new modules or into rational number issues as presented in BST and MMO.
Two levels of DMI Leadership Institutes will be offered in the summer of 2001. The two-week programs will be conducted from July 22 through August 3 at Mount Holyoke College in Massachusetts. The program fee of $1700 includes room, board and four graduate credits in mathematics education.
The application deadline for the DMI Leadership Program is March 1. Early applications are advised since the institutes may fill before that date. Also, early applicants to DMI L2 will be more likely to receive their first choice of modules.
For more information, please call (413) 538-2063 or e-mail smt-dmiinfo@mtholy oke.edu. To learn more about DMI, visit www.edc.org/LTT/ CDT/DMIcur.html.
Thanks to Nihad Ziad at NCTM HQ for this reminder of a deadline you don't want to miss! Ed.
There is still time to prepare a grant proposal for one or more of the many funding opportunities offered through NCTM's Mathematics Education Trust (MET). Proposals for all but one of the awards are currently being accepted and must be postmarked no later than December 5, 2000 to be considered. The Toyota TIME award deadline is January 10, 2001.
Readers will recall that Betty Erickson, mathematics coordinator for the Kearsarge Regional School District in NH, was a recipient last year of a $10,000 Toyota TIME award for her proposal "Creating Mathematically Rich Classrooms Through Teacher Training" (Intersection, May 2000). Let Betty's success inspire you!
To learn more about the possibilities, and to view "Ten Tips for Writing Successful Proposals for MET Grants," visit www.nctm.org/about/ met/.
One of these new books can be yours "for keeps" if you offer to review it for the newsletter. Think of the books as holiday gifts with "ribbons"—not strings—attached! Interested? Please contact me. Ed.
In Sensible Mathematics, A Guide for School Leaders, published recently by Heinemann (126 pgs; $17.00), author Steven Leinwand provides practical suggestions and strategies to help educators make the case for change in mathematics education. The content is closely aligned with PSSM to help educators communicate the basis and necessity for change.
In the opening paragraph of the introduction, "Helping People Change," the author writes: "Changing people's behavior is one of the most difficult aspects of leadership. We know that people cannot do what they cannot envision. People will not do what they do not believe is possible. People will not support what they do not understand. And people will avoid those changes whose consequences are uncertain or feared So it is with school mathematics as we enter the twenty-first century."
Leinwand remarks in the introduction that school leaders must be the ones who take on the difficult task of helping others envision, understand, accept and support change. To that end, his book provides a "toolkit." He writes: "It [the book] is designed to provide reasonable and cogent answers to many of the questions that educators face when they are called upon to deal with a school or district's mathematics program." For more, visit www.heinemann.com.
Susan Ohanian's new book, Day-by-Day Math: Activities for Grades 3-6, a Math Solutions Publication (184 pgs.; $19.95), presents in a January-through-December format a fascinating and rich collection of stories, anecdotes and facts paired with suggestions for follow-up activities.
In her introduction, Susan begins with a quotation from mathematics professor and author Ian Stewart, "The story of calculus brings out two of the main things that mathematics is for: providing tools that let scientists calculate what nature is doing, and providing new questions for mathematicians to sort out to their own satisfaction." In this book, Susan provides a year's worth of starting-points to inspire teachers and children to explore interesting mathematics. She writes: "I hope this book inspires curiosity-driven classroom explorations." No question it will. Two samples:
Two elephants arrive in Turin, Italy. They have walked 500 miles (850 kilometers) in 21 days, following the same route taken by Hannibal in his famous journey across the Alps from France.
Investigate: Mental Math: About how many miles do the elephants walk each day?
Time how long it takes you to walk half a mile. How many miles do you think you can walk in a day?
Author Daniel Pinkwater is born. In Pinkwater's story The Hoboken Chicken Emergency, Arthur's mother sends him to the store for a chicken. He gets the best poultry bargain—a 266- pound super chicken, for six cents a pound. The seller lends Arthur a collar and leash so he can get the chicken home.
Investigate: How much did Arthur pay for this super chicken?
Visit www.mathsolutions .com to learn more.
Wouldn't you like an article about your project to appear in the very first issue of the brand new year? Simply send your contribution by Monday, January 8 to Jean Ehnebuske, 105 Hideaway Cove, Georgetown, TX 78628; e-mail, jean@intersec tionlive.org; phone, (512) 869-1580; fax, (512) 869-8477.
Thanks to those who have filled these issues so meaningfully all year with your articles, reflections, reviews and photos. Best wishes to all readers for joyful holidays and for peace and happiness in 2001 and thereafter.
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