"More Math For More Students" - The Disbelief Factor
One of the pervasive myths of math education is the belief held by more than a few people that math can only be learned by the few students who "have it." With this belief system, it makes perfectly good sense that:
This "expectation of failure" also makes its believers skeptical when students who do not test in the top ten per cent have successful experiences in math classes. They say, "Why, the book must be too easy," or, "The teacher does not grade hard enough," or, "Maybe the students are cheating." These low expectations and suspicions are exacerbated by the socially acceptable posture of "math illiteracy" for those who readily admit that ,"I was never any good at math," that presently leaves everyone shaking their heads in comforting agreement. These are some reasons why community education is so important.
A second issue that creates confusion for the public - parents in particular - is the perception of what constitutes mathematics. Probably the majority of Americans experienced the approach to mathematics decried by the TIMSS Report: many topics skimmed over with emphasis primarily on procedural and algorithmic skills. For well over two decades, CMC, NCTM, and the math frameworks have suggested that a much more comprehensive math curriculum must be taught to make today's students math literate. Basic skills must be presented in a context that helps students understand what they mean and how, when, and where they are used. Because the world is so open-ended, problem solving skills have joined the list of basic elements in a core math education.
CPM is just one facet of restructuring math education to prepare students for the 21st century. The courses were originally conceived as conservative first steps toward more ambitious restructuring. After eight years in classrooms with over 1,000,000 students, the revised Math 1 and the other courses are models of one way to present a balanced curriculum - basic mathematics, conceptual understanding, and problem solving - that makes mathematics accessible to more students.
More than ever, a good command of mathematics is essential for those who expect to be successful in higher education and the workplace. No one disputes the obvious: the core content of mathematics - the basics - must be present in any math course, K-12. How students learn math, however, needs careful consideration if parents and math educators really want to improve math instruction.
Maximizing Your Chances For Successful Change
One of the best ways to try something new is to do it with other people. From the outset we have recommended that first-time teachers have a partner in their school so that there is the opportunity to plan together, share classroom experiences, and divide the work of preparing classroom materials and assessment devices. Teachers can also build a telephone network of support by exchanging phone numbers with other teachers at the CPM workshop.
Our conversations with teachers over the years indicate that the optimum environment for CPM success exists when all of the CPM teachers in a school have a common time to meet weekly to plan and discuss their CPM courses. When this kind of time is provided, it is important that everyone make a commitment to attend the meeting. These sessions are a kind of oasis from the rush of regular school business where CPM teachers can get and give support to one another. Some schools have team leaders (for the program or by course), others rotate responsibility for chairing the meeting. In general, some time should be given to debriefing what is working and what needs further work, some time for discussing what is coming next in the courses, and usually some time to planning assessment, especially tests, in advance of using them in the classroom.
This team approach can also make the day to day workload lighter for everyone. Members of the team can take turns writing the solutions to the problem sets. Teachers can rotate responsibility for gathering all the manipulatives and copying the resources pages for a unit. While assessment should be collaborative, each teacher can take a turn assembling the test or project for everyone else.
Major Grant Award to CPM Teacher
Congratulations to James Ritchie, who teaches at Yucaipa High School in San Bernardino County, CA. Jim received a 1997 Toyota TIME grant for his project, "Using Quantitative Data and Statistical Analysis to Investigate Water Quality and Health: An Interdisciplinary Approach." Students are currently studying the Santa Ana River from its headwaters to the Pacific Ocean. They will use real data in their chemistry, Algebra 2 (or trig/analysis), English, computer and health classes to study local water quality.
This award is funded by Toyota Motor Sales, (TMS) U.S.A., Inc. and administered by NCTM. The TIME grants represent one of the largest national grant programs ever offered to math teachers. Jim was one of 20 teachers awarded a grant from a pool of almost 1,100 applicants. Jim's grant is for two years.
Jim has taught at Yucaipa High, a California Distinguished School, for 20 years. He has taught Math 2 and Math 3 for four years. Jim and his team of teachers initially connected Geometry with Biology and Algebra 2 with Chemistry with the help of a GTE GIFT grant. They will use the TIME grant to expand their interdisciplinary program so that students solve multi-step problems, develop spread sheets and data bases to develop and analyze project data in Computer Business Application classes, write technical reports in English class, evaluate information and statistics from their research and apply these results to the health and welfare of the community in their Health Occupations classes.
Math 1 Preliminary Edition Resources
Many of you are using the preliminary second edition (©1996) of Math 1. Last June we offered to send you updated resource materials; all you had to do was check a box on the database update card. We sent another card to everyone who had not replied to the first request with the September business letter. The resource materials have been shipped. Note that we sent one copy to each school that requested them and a letter to the other teachers from the same school informing them that the package had been shipped.
These resources include copies of all the new problems, including the Gold Medal problems, the new student study guide and where to insert it in the text, both a printed and electronic version of the revised assessment, and a list of changes between the two editions. We are happy to send these materials to each school that is using the preliminary edition. If your school does not have this resource, send a self-addressed mailing label to:
Math 1 Resources
663 Rivercrest Drive
Sacramento, CA 95831-1135
Remember, we are offering one set per school, so please check with other teachers at your school before you request these materials.
Non-English Speaking Homes
We are occasionally asked about making CPM available in languages other than English. Translating the texts is costly and time-intensive. However, we have offered the texts in Math 1 and Math 2 in Spanish, and by next summer we will have bound texts available for Math 1, second edition, Math 2, and Math 3. According to the 1990 census, the following are the top ten non-English languages spoken in the home (per million):
Curriculum Debates: It's Not About Either/Or
Last month's lead article discussed how the existing math curriculum in the United States contributes to low achievement by America's math students. HOWEVER, this does not mean that the content of the math curriculum itself is at fault. Rather, it is how and when the concepts are introduced, and then how they are developed and practiced that is at issue. No one ever said that changing how students learn math meant that we should abandon or skim over core content. In fact, just the opposite is true. As noted last time, TIMSS suggests and CPM incorporates the notion that each course should concentrate on several core ideas (we call them threads) and do them thoroughly.
What CPM finds most troublesome about the math debate - whether national or California's standards and framework development - is that in most cases it has been reduced to either you teach a traditional program or you teach a completely restructured one. CPM was and is committed to producing texts that parallel traditional courses with respect to content. The math is there, but CPM texts also wrap the content in a structured problem solving environment. Investigations and applications strive to help students understand the math. There is no question that the country needs to move forward with improving math education. CPM believes that you do this by building on the past, introducing incremental changes, evaluating the results, and then moving on some more. The second edition of Math 1 illustrates this commitment.
PC Assessment Disk Update
Last month we mentioned that we have had the PC assessment disks reworked. Just a reminder about a few basics. In order to use the disks, you must have Windows 95. The assessment files come to you compressed. When you open the file, it is automatically unstuffed. The file that you see is also a copy of the master, so that you do not accidentally modify the original file. Also be aware that if most of the equations and graphics appear and print okay but a few do not, you probably do not have the font that was used to create the ones that are a problem.
Holiday Gift Suggestion
Brain research about how people learn has been one of the driving forces behind changing how we teach math. You might want to ask for Ronald Kotulak's Inside the Brain - Revolutionary Discoveries of How the Mind Works. (5/96; ISBN: 0-8362-1043-3) It is relatively easy reading on the brain's development and its implications for education. The author also had a Pulitzer Prize-winning series on the brain in the Chicago Tribune.
Math 2 Dinner Meetings
Thanks to everyone who attended the Math 2 dinner meetings to discuss revisions to Math 2. About 75 teachers attended the sessions. We will compile the results this month and report on plans for the revision in the January newsletter.
Web Site Update
If you looked for the "new and improved" web site last month, you most likely were disappointed. Some last-minute technical problems delayed the changes. The new page is up now, and we plan more changes in the near future. We will soon have several resources available for downloading: workshop registration forms, teacher and school agreements, and the Parent Guides for Math 1 and Math 2. We'll keep you posted about other additions as they become available. You can find the CPM Website at http://www.cpm.org .
Encouraging Community Education
Classroom, Workshop Visitations
For several years CPM has included articles in the newsletter for you to distribute to parents, administrators, and peers. While written information is helpful and necessary in any community education effort, the most effective methods are those that engage people personally. "Math Information Nights," whether part of a school-wide event or limited just to math, give you the opportunity to demonstrate concretely both what is different and what is the same about CPM math. You can have parents do a problem or two, then talk about how the problem and its solution process illustrate the various goals of the program and your class.
One area of community education that we think is under-utilized is classroom visitations. Parents often make assumptions or hear rumors about new methods, study teams, manipulatives and the like that raise their anxiety level. In addition to telephone conversations with concerned parents, we think you should invite them to visit your classroom so that they will see first-hand what the class is like. Be sure to discuss general information about the course and particulars for the day with the parent before the visit. It is best during any visitation that you teach the class as if the visitor was not present. Other than perhaps a brief comment now and then, save discussions for a debriefing conversation after the visit. In particular, you want the visitor to see you moving around the room interacting with the students as you would on any other day. Just as most parents are supportive after an information night, most visitors should have a better appreciation for how you use class time and see that your methodology is a blend of direct teaching, discussion, guided investigations (study team time), and individual help.
A similar approach can be taken with administrators, other teachers and off-campus tutors. Certainly you should invite them into your classroom. However, you might also want to arrange for them to attend one of the local CPM workshop sessions. In the case of tutors, they might want to enroll in the series of workshops if they have several clients who use CPM. Call your regional coordinator to arrange a workshop visit.
Mastery Over Time: An Update
Last May we featured an article about mastery over time by Michelle Chenal-Ducey. We wanted to remind you that a commitment to this aspect of the CPM program means changing both expectations and behaviors with respect to assessment. We know that some students will understand an idea as soon as it is introduced. However, our goal is for most, if not all, of the students to understand an idea. Thus, we must first accept the fact that some - even many - students will not master an idea by the end of a unit, even though they may have worked with many good problems. Second, we must modify the structure of unit tests to emphasize older material and to include only fundamental ideas from the new material.
We do expect that students will improve over time. Given that mastery is often an individual event, it is hard to set specific guidelines for when students "should" have mastered an idea. Certainly the Distributive Property, for example, should take less time than ratios. You will need to decide when it is reasonable to see mastery of topics in your class. Consider the end of the semester as a "snapshot" of work-in-progress. Students need to receive grades that honestly reflect their work to date. Keep in mind, however, that core topics like functions and ratios are developed over the four years of the CPM curriculum, so be certain that your assessment is appropriate for the stage of development of an idea in each course.
There are several ways to foster mastery after a topic has been introduced. Obviously there are the post-problems spread throughout the remainder of the text. There are also more practice problems in the Supplements for Math 1 and Math 2. Perhaps more important, especially in Math 1, is for students to use the Study Guide to learn how to organize their learning. This means that they must work hard on unit summaries and keep a thorough, current tool kit. The same is true in other CPM courses.
Mastery over time will work, but you must have patience with the students and persevere with those topics that cause them difficulty.
New Regional Coordinator Named for L.A. Region
CPM would like to thank Edna Murphy for several years of service as the Regional Coordinator and Peer Coach for Torrance/Central Los Angeles/San Fernando/Santa Barbara (CA). Edna was one of the original workshop presenters in Riverside, CA as well as in her local area. For the past two years she has worked half-time for CPM, making new contacts with schools and districts and responding to needs of existing schools in the greater Los Angeles, CA area.
Micheal Marsh from Culver City High School has assumed Edna's duties effective November 1. You may reach him at school at (310) 842-4200 or evenings at (213) 654-8402 or at firstname.lastname@example.org.
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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