3rd International Math And Science Study (TIMSS)
Another portion of the TIMSS study was released on November 20. This report is one of the most prestigious and carefully conducted studies of math and science performance available. We reprint William Schmidt's summary at the end of the newsletter and excerpt highlights that are significant for CPM below.
We also agree that stronger, consistent, comprehensive, and coherent standards need to be adopted. We think the California Education Round Table Standards meet these criteria and are worthy of your evaluation and support.
Experienced CPM Teacher Workshops
We are pleased to announce that the first workshop for experienced CPM teachers will be offered next spring. Eventually we will develop a series of workshops for teachers who have attended the first year, eight-day series and who are now teaching CPM for the second or subsequent years. By 1997-98 we hope to offer the series in each region of the state. The first session next spring will focus on assessment. The cost will be $75 for the two sessions, including refreshments and lunch. One quarter unit through U.C. Davis will be optional ($55, pending approval). The two days will run from about 9:00 AM to 3:00 PM. Cities and dates are:
San Bernardino: 2/26 & 4/26
Sacramento: 3/5 & 4/19
Fresno 3/12 & 4/12
We will include specific details on a registration form with the January Newsletter. Space will be limited. If you would definitely like to reserve a space, e-mail Brian at firstname.lastname@example.org and give your name, school, CPM course(s) taught, and the site you will attend. You may also reserve a space by calling Brian's office number during the evening and leaving the same information on his voice mail.
Reflections On The Math Education Debate
Sadly, much of the debate about mathematics education during the past year has been reduced to either/or: you support problem solving math or you favor traditional texts, with nothing in between. This is unfortunate, because CPM has never been an "all or nothing" program with respect to change. In fact, just the opposite is true. During the spring of 1989 the Directors and the Math 1 writing team put constraints on the scope of the program: it had to parallel existing course sequences and it had to be usable by most teachers in most schools.
It makes sense, then, that CPM is precisely the kind of program that recent advisories such as the Math Task Force (9/95) and the State Board of Education Program Advisory (9/96) describe. In terms of content and skills, CPM parallels Algebra 1, Geometry, Algebra 2, and Pre-Calculus. There are numerous practice problems, but they are spread out over weeks and months. CPM emphasizes concepts through its use of developmental problems and its emphasis of several core threads (such as graphing, logical reasoning, ratios, and symbol manipulation) through all four years of the program. Finally, CPM uses a problem solving environment to weave all of this together so that students learn strategies for dealing with mathematical situations as well as develop the skills to solve them.
Not surprisingly, there is no room for extremism in a CPM classroom. CPM classrooms are not the exclusive purview of either/or choices: lecture or study teams, silence or noise, manipulatives or exercises. The effective CPM teacher blends a variety of experiences and methods to make mathematics education understandable and successful for the students. A typical lesson usually includes some direct instruction at the appropriate time, some "lab work" (exploring in study teams), review of past work, clarifications, and summarizing. Some teachers summarize frequently, stopping after every few problems to help students pull things together. Others do so at the beginning or end of most days, while some do so every few days. Teachers have varied ways to help students review previous lessons, but only a small part of class time is spent doing this directly. In short, the CPM classroom blends effective aspects of past teaching practices with additional activities that engage students in ways of learning that lead to success for more students.
We need to be clear about a few things: no CPM teacher (or any teacher, for that matter) should leave the students to work in groups all day every day; no teacher should make an assignment and sit at the desk grading papers; no teacher should lecture the entire period every day, or spend most of the class time reviewing homework. No teacher should refuse to answer student questions, ignore students who are frustrated, or leave loose ends unconnected.
As we listened to teachers at workshops and at the Math 1 dinner meetings last year, we learned why some of the above issues have been confusing for some CPM teachers. First, some have the perception that CPM is saying that there is only one way to teach. Actually, what we have asked is that teachers follow the course and materials the first year they teach CPM, then make adjustments they deem appropriate for their classroom thereafter. Second, because CPM mentors spend much of workshop time talking about how to manage study teams, some teachers have assumed that no other classroom structure is permitted. Not true. Whole group discussion and direction are necessary, particularly to summarize and connect to a larger view. Next, some have interpreted our guideline to answer questions with questions to mean never answer a students 's question. Our issue always has been how you respond to the students. Sometimes a direct answer is appropriate; usually your assessment of the situation cues you as to how to lead students back on track. Finally, some teachers have concluded that the emphasis on guided investigations in the text means that teachers are to remain out of the learning loop. The worst case example is making an assignment and sitting down at the desk. We have written several times about how the CPM teacher needs to be more involved in student work and closer than ever to the individual achievements and needs of the students. Teaching CPM effectively requires active engagement with students, not passive observation.
We hope this short summary helps clarify some of these issues. The points contained here are very important to communicate to students, parents, and administrators so that they avoid similar misconceptions and in fact know how CPM works and what is expected of everyone.
New Math 1 Student Guide Available
We have been working for several months with Chris Ott from The Learning Connection in Davis to develop a guide that would help students understand what CPM requires of them. Chris has written the guide from a student's point of view in a conversational style. We think that what he has to say is helpful for everyone. Included with this newsletter is most of the text of the guide. We have edited out the graphics, student assignments, and learning profile section so that everyone can see the core of the Guide. You might want to use the Guide in this form, or send for the complete document (52 pages) and reproduce it for the students. While the guide is written for the first edition of Math 1, we think you will find it adaptable to all CPM courses. We expect to have versions for each course by next summer.
To obtain a complimentary copy of "Key to Success: CPM 1 Student Guide," send a self-addressed mailing label to:
Key to Success
c/o 663 Rivercrest Drive
Sacramento, CA 95831-1135
Please DO NOT call Jane or Brian. Distribution will be from a third party by mail only.
Some Ideas To Make The Study Teams Work
At this point in the year you have a fairly good idea about each student's attitudes and behaviors in a team setting. If your study teams are working well as presently constructed, keep using them that way. Another way to arrange teams is to have students work in pairs. Pairs have the advantage of simply sliding one desk next to the other so that each student can see the other's work. Since students are all still facing in the same direction, there is less opportunity for distractions and casual chatter, especially between teams. You can still designate two pairs of students as a team of four for the lessons that require more than two people. A variation on the pairs idea is to let each student pick a partner, then you select two pairs to form each team. In this setting, some students may work in pairs while others work in teams.
A frequently asked question is what to do with uncooperative and/or non-working students. While we are not generally advocates of exclusion, one method of forming teams that has awakened some students is to organize them according to their past effort and contributions. You do not necessarily have to put the hardest workers all on one or two teams, but you do put all the passive students (i.e., those who do little or no work or who just copy what other students do) together. They will know immediately why you have selected the teams. While you must be prudent about using this kind of team organization, experience in several teachers' classes confirms that some students, especially the "sponges," realize that they now must work. Teachers report that they do.
Some teachers have been successful by emphasizing that membership on a team is a privilege that must be earned and respected. Thus, students can lose the opportunity to work with a team, and may be required to earn their way back onto a team.
Getting students started, especially in teams, can be difficult if you just say, "Start!" If your teams take too long to get working (i.e., more than a few minutes), you may want to start the first problem with them. Your role can be as simple as having them form their teams, telling them to get out their books and paper, open to problem AP-37, and then reading the problem with them. Give them enough time to do each part, then say, "Now continue with the rest of the assignment in your teams."
To help keep the students working the entire period, some teachers collect the in-class portion of the assignment at the end of the period each day (or every second or third day--unannounced) and give it a simple check-off grade. Others walk through the room a few minutes before the bell to end class and give credit for progress. It could be similar to the credit you give for doing out of class work.
Finally, we again urge you to make written solutions to each lesson available to the students daily. This method models what you want, is comprehensive, allows students to spend time only on the problems they have questions about, and frees class time for doing the next lesson with one's team (or partner). Some teachers also keep a cumulative binder with solutions in the room. It is useful for absentees to check their makeup work.
Results Of The Summer Textbook Survey
When we updated the database last summer we asked what text each teacher had used before switching to CPM. There were 1,891 responses. About half of you indicated other (311) or none of the above (652). Of the texts and publishers listed, here are the results:
The results are not surprising, since many CPM teachers have made it clear that they were looking for materials that taught math in context rather than isolated pieces. We did take note of the 84 Saxon defections. These 84 teachers represent 58 schools. The late Mr. Saxon had remarked as recently as last March in public testimony before the Assembly Education Committee that he was aware of perhaps two schools that ever dropped his program once they adopted it.
MORE HONORS TO ANNOUNCE
Tahoe-Truckee High School has been designated a California Distinguished School for the second time!
MATH 4 (PRECALCULUS) AVAILABILITY
We will permit experienced CPM teachers (preferably Math 3 users) to use the preliminary edition (1997) of Math 4 during 1997-98. The pilot version table of contents and Units 1-5 (of 9) will be available to preview in January. See details in the January Newsletter.
Discussing Grading In Your Department
Sharing ideas about grading at a department meeting is often effective if there is a common, neutral focus for everyone. Consider giving each department member a copy of a student test (name removed, of course) to grade prior to the next math department meeting. Each teacher decides how many points to give each problem and how to weight them. Everyone brings the graded paper to the meeting. There should be a lively discussion of similarities and differences. The purpose, of course, is for each teacher to stop and rethink how s/he scores tests and to listen for new ideas from her/his peers.
CPM Textbooks And Legal Compliance
Just a reminder that we submitted the Math 1 and Math 2 textbooks to the state for legal compliance review (a prerequisite if you are using state money to purchase the texts) and received approval over two years ago. Likewise, the of University of California (and all other colleges and universities) accepts courses certified by your school as meeting U. C. math requirements that use the program, since the texts are fundamentally Algebra 1, Geometry, and Algebra 2.
Math 1 Second Edition: Where To Look For Test Items In The Original Version Test Bank
If you are using the preliminary second edition, you will find appropriate test problems for each unit in this edition in the unit test folders on the assessment disk listed below.
Units 6 and 7
Units 7 and 11
Units 6 and 7
Units 9 and 11
Units 2 and 11
Units 9 and 10
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