Guilty! America's Old-Fashioned Math Curriculum: A TIMSS Update
As more parts of the TIMSS (Third International Mathematics and Science Study) Report have been released during the past year, Dr. William Schmidt of Michigan State University, the National Research Coordinator for U.S. TIMSS, has made it abundantly clear that a major culprit in the mediocre math performance of American students is the curriculum itself. (Reminder: the TIMSS study did not include any reform math classrooms in the study.) This point was reinforced by Dr. Schmidt when he spoke to the California State Board of Education on June 13th, just days after the 4th grade results were released. His recommendations? Focus the curriculum each year, make it coherent, set performance expectations that include algorithms with conceptual understanding, establish voluntary national standards, and build the capacity among teachers to accomplish these ends.
TIMSS studied more than 1,500 textbooks, frameworks, and curriculum guides from more than 40 nations. While the United States has plenty of visions of math education (textbooks, assessments, professional associations), there are so many voices that they create a confusing "Babel" of goals that lead to a splintered vision of math education. The textbook analysis showed that the United States crams its textbooks with topics–typically more than 35 in 8th grade texts compared to 5 to 7 in a Japanese textbook–that get brief attention, then are left for the next topic. American textbooks are upwards of 600 pages long; Japanese texts are between 150–200 pages. One explanation for the generally adequate scores of 4th graders but the dismal results of the 8th graders is that after 4th grade the United States continues to focus almost exclusively on arithmetic. The rest of the world, however, shifts its focus to the basics of mathematics; in particular, it incorporates much of algebra and geometry into the curriculum.
Dr. Schmidt noted that when all of this "stuff" reaches the classroom, the result is skipping across topics with a focus on mostly formulas and algorithms. There is virtually no attention paid to problem solving and conceptual understanding. He suggested that if we spent more time on topics, did some exploring, conjecturing, and applying of concepts, students might actually learn the material! Instead, American teachers repeat the same topics each year–plus the new ones they are supposed to cover–in a superficial manner. The predictable result is that not much of anything is learned.
When reading the TIMSS report, one cannot miss the similarities between what seems to work in the rest of the world and the CPM curriculum. Each CPM course focuses on six or seven main threads and spirals them day to day and unit to unit, not year to year like most American textbooks. Lessons are structured to help students think about mathematics and make connections (which Schmidt calls a key feature of mathematics). In addition to problem-solving in each course, the threads of the CPM curriculum are:
Math 1: graphing, writing and solving equations, ratios, geometry, and symbol manipulation.
Math 2: algebra, graphing, ratios, geometric properties, spatial visualization, and conjecture/explanation (proof).
Math 3: representation/modeling, functions/graphing, intersections/systems, algorithms, and reasoning/communication.
Math 4: concepts of calculus, analysis of models, trigonometry, advanced functions, and algebraic fluency and accuracy.
You might also want to compare the CPM curriculum to the California Education Round Table Standards, the Statement of Competencies for Entering Freshmen (UC, CSU, and Community College joint statement), and the Mathematics Content Standards (K-12) recently recommended to the State Board of Education by the Commission for the Establishment of Academic Content and Performance Standards.
As the state and the nation move to improve mathematics instruction and set higher standards, you will find that much of what is recommended as the curriculum for the 21st century is available today in the CPM texts.
If you would like to obtain a copy of the TIMSS Report, call the Institute for Educational Reform at (916) 278-4600, or you may access the report electronically at http://www.csus.edu/ier/materials.html. We suggest that you share this information with your colleagues and the parents of your students.
State Board schedules hearings to discuss California Math Standards
As you are probably aware from media coverage, the Commission for the Establishment of Academic Content and Performance Standards has approved math and language arts standards and sent them to the California State Board of Education. The Board has set hearings for later this month and will discuss the testimony they hear at the November State Board meeting, then vote on the Standards in December. You may review the Standards on the internet at http://www.ca.gov/goldstandards or call the Commission's office for a copy at (916) 323-8013.
The original drafts of the Standards (Spring, '97) did not reflect a balanced program, and teachers around the state told the Commission in no uncertain terms that they were unacceptable during hearings and via written comments last June. Thanks to those of you who responded –you did have an impact! The final version sets clear, high standards in the context of a complete math program (in contrast to standards that focus primarily on learning algorithms and definitions as the sum total of math education.) Even though the Commission accepted the math Standards with only two dissenting votes, much of the media attention has focused on the complaints of the dissenters rather than the consensus of the rest of the math subcommittee. In particular, critics from the same groups that have opposed CPM and other math reform efforts are disturbed because they believe that the Standards suggest an integrated approach to algebra and geometry (in contrast to the traditional, segregated sequence). In fact, the standards do not advocate one approach over the other. The content of Algebra 1 is in the 8th grade standards and Geometry and Algebra 2 are in the 9-10 standards. The strands in the standards do, however, help everyone see the connectedness of mathematical ideas.
The proposed math standards have been applauded by the prominent newspapers in California. In fact, on September 21st the Los Angeles Times said: "California's pending educational standards, endorsed last week by the state Academic Standards Commission, will be among the toughest in the nation. Fourth-graders will be required to read extensively outside the classroom, and 10th graders will have to master two years of algebra, a gateway subject to higher learning. California should aim for nothing less."
"There is a war going on in math. We are not solving that war. We kind of come down in the middle."–Ellen Wright, Chairwoman, State Commission for the Establishment of Academic Content and Performance Standards
The next day the San Diego Union-Tribune ran a front-page article about the proposed standards. The chairwoman of the Commission, Ellen Wright, said, "There is a war going on in math. We are not solving that war. We kind of come down in the middle." This comment was in the context of remarks noting that the math standards contain basic skills and problem-solving with some conceptual work. Dan Condron of Hewlett-Packard, the math subcommittee chairman, said that the standards are patterned after those used by Japan, Singapore and other nations with top scores on standardized international tests.
The Union-Tribune also reported that William Schmidt (who was sharply critical of the earlier commission draft), found that "this version of the standards is more reflective of world-class standards, is challenging and rigorous." He noted that the incorporation of algebra and geometry in the eighth grade math classes is "consistent with what most other countries in TIMSS do."
Despite all of the work to draft these standards, there is growing concern that a majority of the State Board of Education may be inclined to rewrite them more along the lines of the minority view. We strongly encourage you to review the standards, then comment in one of the two ways suggested below. The outcome of this debate will influence curriculum materials and assessments well into the next century!
Math 2, Second Edition
The second edition of Math 2 is scheduled for publication in July, 1998. Since the book has been so well received, we do not anticipate changes in the scope and sequence of the course, so schools should be able to replace first edition texts as they wear out on a classroom by classroom basis. In other words, you would not want the two editions in the same classroom. While the course itself will be virtually the same, the visual presentation of the problems and their numbering will be different enough that it will probably be inconvenient to try to use both editions in the same classroom.
Our present plan is to make the book consistent with the style and features of the Second Edition of Math 1. This means adding artwork throughout the text and a four-color cover, objectives on the first page of each unit, tool kit and summary activities to replace the portfolio assignment at the end of each unit, the integration of a student study guide in the first volume, and improved graphics. With respect to content changes, we expect to make the proof thread more explicit, offer extensions of some existing problems, and do spot revisions and edits. Some of the longer days will be shortened, especially in the second semester. Teacher notes will be enhanced.
The preceding paragraph outlines changes we plan based on comments from teachers at workshops, students and parents, and administrators over the past four years. However, as usual, we want suggestions from current classroom teachers about how to accomplish these changes as well as other suggestions you want us to consider. There will be two opportunities for you to respond:
By mail: Everyone in the database listed as a Math 2 teacher will be sent a letter requesting input on revising the text. This will be your opportunity to point out general concerns as well as specific lessons or problems that you think need revision and to make suggestions for the changes. If you want to reply but do not receive a letter within one week of receiving this newsletter, send your reply to: Math 2 Revision, 663 Rivercrest Drive, Sacramento, CA 95831. Deadline to put your reply in the mail is November 12th.
In person: Once again CPM will host dinner meetings throughout California for Math 2 teachers who want to make suggestions for changes in the text and resources. Similar meetings in the spring of 1996 were instrumental in developing the outline of the revised Math 1 text.
These meetings will be held during the week of November 3rd at a restaurant in your area. Discussion will begin at about 4:30 p.m., dinner will be served about 6:00, and the meeting should conclude by 7:00 or 7:30. CPM will buy your dinner and the Teacher-Leader conducting the meeting will record your ideas. To get the date, time, and location of the meeting in your area and to register, call your Regional Coordinator (listed elsewhere in this newsletter.)
We will schedule meetings in the following areas: Chico, Sacramento, San Francisco, Walnut Creek, San Jose, Fresno, Bakersfield, Santa Barbara, North Hollywood, Torrance, Irvine, Riverside, and San Diego. For Chico, call Bob Hansen (916) 891-3026 (s), or 896-1980 (h). For Santa Barbara, call Kirk Taylor (805) 964-3352. Deadline to call to guarantee a dinner space, is Saturday November 1.
Math 1: Second Edition errata
Despite several rounds of proof-reading, there will still be a few errors in the Math 1, 2nd Ed. student text and several incorrect answers in the teacher edition. For the most part, these errors occur because changes recommended by editors and reviewers of the final draft are entered after some polishing processes have been completed. If you find something that needs to be corrected, or if you have a suggestion to improve a math problem, please fax or e-mail Brian Hoey at (916) 391-3301 (fax) or email@example.com. Corrections will be made in subsequent press runs.
Spanish versions of student texts
Spanish translations of all three student texts–Math 1, Math 2, and Math 3–are currently available. We have bound texts for Math 1, 1st Ed.(©1994) and Math 2. Blackline masters are available for all three texts and both editions of Math 1. Prices are the same as the English editions:
Math 1, 1st Ed. texts: $16.00
Math 2 bound texts: $18.50
Math 1 and 3 blacklines: $20.00
Math 2 blackline: $26.00
Translated resource pages are included with orders for Math 1 and Math 2, First Editions.
We will have bound versions of Math 1, 2nd Ed. (©1997) by August, 1998. The blacklines available this year for the Second Edition are first drafts of the final version. Math 3, Units 1-7, are currently available in first draft form as a blackline master. We expect to have bound copies of Spanish Math 3 by the end of next summer.
PC Assessment Disk Update
During the last school year CPM editors polished and revised all of the assessment files for Math 1, 2, & 3. For some reason, we have had trouble translating these new files from their Mac version to a quality PC product. Consequently, we have had the files translated by a professional software service and now have functional PC disks available for all courses. If you requested a disk exchange after July 1, 1997 and are not satisfied with the PC files you received, send a request for the course(s) you need with a self-addressed mailing label to:
CPM: PC Update
663 Rivercrest Drive
Sacramento, CA 95831-1135.
We will send you a replacement disk by mail. (Remember, the PC disks require Microsoft Word ver. 6.0 and Windows 95.)
Mac Assessment Disk Update
If you received your Mac assessment disk since June, you are aware that the files come "stuffed." The software is included to automatically unstuff the files when you open them. HOWEVER, be sure to copy the file from the floppy disk onto your hard drive before you open the file. Also note that what opens is actually a copy of the file so that when you cut and paste in the test bank you do not inadvertently destroy the master file.
Staying in Touch with CPM
Everyone who receives this newsletter is a new CPM teacher or one who returned the goldenrod postcard we sent in June (and again to some people in September). Thanks for your replies. It is important to have an accurate database so that we can target mailings such as the one described in the Math 2, Second Edition article. If one of your colleagues did not receive this newsletter but did get the September mailing, she/he will most likely get a last request for an update with a postcard in a separate mailing. Update information (name, address, phone number, school, and CPM course(s) taught) should be sent by mail, fax, or email to Jane Bradley (her address appears in the "CPM Contacts" section).
Tutors for Your CPM Students
Several teachers have reported success with peer tutoring at their schools. Students in Math 3 and Math 4 work with students enrolled in Math 1 and Math 2. This approach also fosters better attitudes by the younger students with respect to expanding their view of mathematics and how to learn it. By the way, several of last year's Math 4 teachers reported that their students were also tutoring students from another class: AP Calculus! It seems that the AP students were lost in the details of the theorems, but the CPM students filled in the understanding part.
Veteran Teacher Workshops
This fall, CPM will be offering workshops for veteran CPM teachers in your specific region. These two-day workshops will discuss how to get study teams to work more effectively, the TIMSS report, assessment ideas (including rubric scoring), questioning techniques, and an overview of the CPM Supplemental Materials. If you are interested in attending, please contact your Regional Coordinator regarding scheduled dates and costs. We will also publicize local dates and times in subsequent newsletters.
New and Improved CPM Web Site
The CPM Web Site is going through some major revisions and enhancements in an ongoing effort to better serve your needs and to help provide you with current, useful information. You can find us at http://www.cpm.org
Summer Leadership Institutes
By Carol Jancsi, San Diego
In 1992, CPM began sponsoring Summer Leadership Institutes for all prospective and continuing CPM Teacher-Leaders. These have always been fully funded by CPM at no cost to local districts or workshop sites, in an on-going effort to improve and update the eight-day local workshop series. Due to increased needs in the state, CPM expanded to two California sites three years ago, one in Northern California and one in the south. This past summer, a third Institute was held in Philadelphia, PA to accommodate the many out-of-state workshop site leaders.
More than 80 CPM teacher-leaders from all over California (and even one from Texas) came together at the two Institutes held in Sacramento and Santa Ana, led by Chris Mikles and Carol Jancsi. They met for three days and focused mainly on CPM workshops for the 1997-98 school year. Chris and Carol spent one day with the new teacher-leaders, studying techniques to get study teams to work well and reviewing the workshop agendas.
During the next two days, both new and returning teacher-leaders discussed many of the issues facing teachers in California today. One main item of discussion was the TIMSS report and its impact on the teaching of mathematics in the U.S. They also looked at rubric scoring, community education, the assessment handbooks and changes in the workshop curriculum.
Several of the veteran teacher-leaders provided expert help to lead the group through another vintage "Dr. Sallee" math problem, and they also offered suggestions to make our efforts in the classroom more effective. As always, the Teacher-Leaders who attended enjoyed the chance to share ideas and the opportunity to grow professionally, with respect to both the upcoming local workshops and their own classrooms.
Thirty-five CPM teacher-leaders, representing workshop sites in Washington, D.C., Philadelphia, PA, Wisconsin, Illinois, Florida and Rhode Island, met in Philadelphia for the first out-of-state CPM Summer Leadership Institute. Dr. Tom Sallee, Brian Hoey, and Chris Mikles conducted the workshop. As in California, they met for three days to focus mainly on CPM workshops for the 1997-98 school year and the topics previously mentioned.
A special feature of the Philadelphia workshop was the opportunity to work with a representative from the Education Trust, located in Washington DC, specifically focusing on issues related to urban schools. This time together helped the Teacher-Leaders build a national network of support for CPM teachers.
Change takes time and effort. Our local workshops are a critical piece of that change process for many teachers. CPM Educational Program would like to applaud all of the teachers who dedicated part of their summer to becoming more effective workshop presenters.
Thanks to Outgoing Regional Coordinators
The Directors of CPM would like to thank Carol Jancsi and Irene Eizen for all of their efforts to help make CPM successful in their regions.
Carol has been the San Diego coordinator for several years. In addition to her regular duties of scheduling workshops and providing local support for Teacher-Leaders and local CPM instructors, Carol has served as a presenter for and assistant director of the Summer Leadership Workshops in California. She will continue to work as a consultant to prepare and conduct a new workshop series for veteran CPM teachers.
Irene has provided support for the CPM teachers in the Philadelphia Public Schools. In addition, she has introduced the CPM program in several other districts and school systems and represented CPM at the AFT QUEST conference in Washington, D.C. last summer.
Back to Basics–Wrong Answer for Math
By John Dossey, San Francisco Chronicle–9/5/97
A cellular phone company offers customers two plans. The first charges a $25 monthly service fee and 45 cents per minute, while the second has a $50 monthly service fee but charges only 25 cents per minute. Which is the better deal for you?
Answering this question requires knowing some basic arithmetic, but it also involves more sophisticated mathematical thinking. That's because the answer depends on how many hours a month you are likely to use the phone.
Such problems are typical of the real-life math challenges that schools must prepare students to handle. The question of how teachers can best do this is a source of controversy.
Some people back a clear-cut focus on "basics." All responsible educators agree that students must master fundamental math skills. But "basics" is also used as a code word for classroom methods biased toward memorizing, rote learning and downloading of information from an active teacher to passive students.
This approach has been tried and has failed. Long-standing reliance on "drill and kill" methods is a major reason why U.S. students have fared so poorly in international comparisons of student achievement. It is the demonstrated failure of this approach that has inspired the movement to improve math teaching in American schools.
Also, although students need the basics, they also need much more. Not only should they know how to solve story problems in a book, but more important, they should learn how to apply their knowledge to solve a myriad of everyday challenges. In the phone problem, for example, memorization of procedures and arithmetic skills will not by themselves allow a student to calculate that 125 minutes is the point at which the second plan becomes more economical. Before doing the calculation, students must first figure out what to multiply and divide in the first place. In other words, they must know how to "think" mathematically.
Beginning in 1989, the National Council of Teachers of Mathematics has worked to set standards for teaching and assessment. The NCTM standards emphasize problem-solving rather than rote learning, active rather than passive learning, and the need for students to be able to articulate the mathematical principles with which they are working.
The council's standards have slowly made their impact felt in U.S. classrooms. Research carried out as part of the Third International Mathematics and Science Study found that most eighth grade math teachers in the United States knew of the new standards, agreed with them, and had taken steps to incorporate more elements, such as problem-solving activities. And several high-quality texts exemplifying the standards are now on the market.
In the eight years since the standards were released, U.S. students' performance has risen. Data from the National Assessment of Educational Progress, which samples the performance of fourth, eighth, and twelfth-graders, show progressive improvement in all three grades between 1990 and 1996, the gains have been particularly strong in knowledge of math fundamentals between 1990 and 1996; the proportion of students performing at or above the basic level increased. These figures should silence any claims that U.S. schools are neglecting to teach basics.
U.S. math students are also faring better in relation to their peers in other countries. The Third International Mathematics and Science Study [TIMSS] showed U.S. fourth graders, on average, scored higher than those in 26 other countries.
However, we still have a long way to go. Given the gains of recent years, it would be tragic if, instead of pushing to further implement standards-based math instruction, schools succumbed to those who want to roll back the clock, barred textbooks that reflect the new approach and condemned U.S. students to discredited forms of teaching.
John Dossey, an Illinois State University math professor, is past-president of the National Council of Teachers of Mathematics (NCTM), and author of several secondary-school math programs.
How to Order Supplements
We need your help to expedite orders for supplements and parent's guides. Basic ordering information and prices appear below. Please copy this information and distribute it to interested parents. If you, your school, or district wish to order in quantity, please use the regular CPM order form. Note that the parent guide to the Second Edition of Math 1 is part of the Math 1, Second Edition supplement. Other parent guides are not sold by CPM; they are included in every Teacher Edition. Duplication and distribution are left to each teacher/school/district.
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