Our Research

UPDATED: 4/17/2009 - See UW Math Professor Letter written by Dr. John Lee
UPDATED: 3/14/2009 - See CPM Content Concern Review completed by Dr. Wu-chi Feng
UPDATED: 2/2/2009 - See TIMSS Review
UPDATED: 1/10/2009 - Link to Graphs presented to the School Board

Our research over the past several months has included:

• reading articles and publications on the Internet with regards to

• CPM curriculum reviews

• Implementation and success of the curriculum

• Math education and standards in the US

• reviewing the entire line of CPM textbooks

• reviewing other available math curricula, both reform and traditional

(at Beaverton’s forums for their current math adoption process)

• attending a CPM publisher presentation

• meeting with TTSD teachers, as well as school and district administrators

• discussions with the Oregon Department of Education (ODE)

• observing CPM classroom instruction

• reviewing the TTSD adoption process

• speaking with parents and students

SUMMARY

UNDERSTANDING CPM AND REFORM MATH

Reform math arose out of the 1989 National Council of Teachers of Mathematics (NCTM) standards. The 1989 NCTM standards are derived from a document published by NCTM in 1980, An Agenda for Action. It is these standards on which CPM and other reform math curriculum were developed.

Critics of the NCTM standards say these standards err by not specifying mathematical content and instead focus on how mathematics should be taught.

Read the following: MATHEMATICS “COUNCIL” LOSES HARD-EARNED CREDIBILITY, written by Frank B. Allen, a former President of NCTM. Frank Allen speaks out emphatically against the 1989 NCTM standards and all mathematics curricula that are based on these standards. He sites the fault behind the NCTM “logic”, how it adversely impacts students and its effect on higher education.

Reform math is extremely contentious and has spawned the term “Math Wars” – a phenomenon that has been raging across the United States for many years. For a more in-depth understanding, read “A Brief History of American K-12 Mathematics Education in the 20th Century,” written by David Klein. This article provides some historical context and describes the core conflicts in the “traditional” versus “reform” debate. http://www.csun.edu/~vcmth00m/AHistory.html

At the very center of all reform math curriculum is the radically modified approach to teaching mathematics. The following articles provide a comparison of the differences in teaching between reform math (including CPM) and traditional math. They are authored by leading mathematicians.

“Ten Myths About Math Education And Why You Shouldn’t Believe Them”

“Inquiry Based Instruction vs Example Based Instruction”

Even though CPM is not IMP (another reform math program), the following article, written by Professor Wu from Berkeley, is very insightful on what a mathematics curriculum should contain. IMP has many similarities to CPM in terms of its delivery mechanism.

http://math.berkeley.edu/~wu/IMP2.pdf

CPM REVIEWS & PERFORMANCE

Following are reviews and commentaries on CPM including an unfavorable content review of CPM Algebra 1. The content review was done by Professor Wayne Bishop who was also a member of the California Content Review Panel.

http://www.nychold.com/cpm.html

CPM was identified as one of five “Exemplary Mathematics Programs” in 1999, by the US Department of Education. In response to the USDOE report designating several reform math curricula as exemplary, over 200 accomplished mathematicians and scientists endorsed the OPEN LETTER TO UNITED STATES SECRETARY OF EDUCATION, RICHARD RILEY criticizing these programs and urging the withdrawal of the endorsement. Basically, these mathematicians and scientists accuse these curricula of overemphasizing data analysis with redundant presentations; de-emphasizing the far more important areas of arithmetic and algebra; and creating so-called higher-order thinking projects that are just aimless activities. Overall, they state that these curricula are watered-down math programs where genuine illumination of important mathematical ideas is rare.

California implemented CPM in many school districts in the early 1990’s. After a decade of utilizing this curriculum, many California schools realized CPM was not working and decided to either reject the CPM curriculum altogether or offer an alternative traditional math track. The following are interesting articles about the use of CPM in the California schools. In response to their overall poor performance in the 90’s, California managed to establish state standards for mathematics that rival that of the most advanced foreign countries. They did not use the NCTM standards to develop their new state standards.

http://www.press-enterprise.com/newsarchive/1998/04/26/893547127.html

http://www.ams.org/notices/199707/comm-calif2.pdf

http://www.mathematicallycorrect.com/calif.htm

These are the only performance-related reports we have been able to locate. They are obviously not in favor of CPM. We have not found any empirical data supporting the assertion that CPM actually improves student performance in mathematics or that it prepares students adequately for higher level math.

NATIONAL MATHEMATICS ADVISORY PANEL (NMAP)

The NMAP was appointed by President Bush in 2006, to make recommendations on the best use of scientifically based research to advance the teaching and learning of mathematics. The final report was issued in the fall of 2008. The National Council of Teachers of Mathematics (NCTM) issued their response to the panel’s report in essence agreeing with the recommendations as the next step in preparing America’s students not only to excel in mathematics, but to become leaders in the fields of science, engineering, and research.

Link to: Final NMAP Report

Many of the recommendations from the panel are in direct contradiction to CPM’s methodology of teaching math. For example, the NMAP states that, “Any approach that continually revisits topics year after year without closure is to be avoided.” The report stresses the importance of mastering skills the first time rather than relying on repeated reintroduction to material. Math is a sequential subject that absolutely requires success on one level before advancing to the next. CPM’s use of spiraling is in direct contradiction to the NMAP recommendations.

TIMSS

For over 10 years, the Trends in International Mathematics and Science Study (TIMSS) has been the world’s largest assessment of international achievement. TIMSS provides reliable, timely data on the mathematics and science achievement of U.S. 4th- and 8th-grade students compared to that of students in other countries. Historically, the US has not ranked well when compared with other countries – especially in terms of the number of students that score at the advanced level.

One clear benefit of the TIMSS study is the ability to review and analyze the math curriculums of top performing countries (typically referred to as A+ countries) and contrast their characteristics with the US math curriculums.

A review of the TIMSS report, reported by the director of the U.S. National Research Center for (TIMSS), defined US math curricula as unfocused, highly repetitive, not very demanding, and incoherent when compared to the A+ countries - thereby establishing that our curriculums are “A Mile Wide and an Inch Deep”.

This slogan has become one of the most used, yet least understood phrases coming from the early TIMSS report. Many have taken the “mile wide – inch deep” statement to mean we teach too much – we must simplify. But what does it really mean? Do we truly teach too many topics overall? Apparently, it’s not all that black and white. But it looks like it’s not about how many topics we teach overall – it’s more about when and how often we choose to teach them. While the US teaches far more topics in the early years, in reality, we introduce far fewer topics in the middle school years (which coincidentally, is when our performance begins declining rapidly). In the US, we tend to introduce many topics early on, never expecting mastery and then reintroduce them again in the following years. The duration of teaching a specific topic is nearly twice that of the A+ countries with a significant number being covered for 8 continuous years.

In other words, “We introduce topics early and then repeat them year after year. To make matters worse, very little depth is added each time the topic is addressed because each year we devote much of the time to reviewing the topic… In the middle-school years, when the relative performance of U.S. students declines, the rest of the world shifts its attention from the basics of arithmetic and elementary science to beginning concepts in algebra, geometry, chemistry, and physics. We continue to address elementary topics that were not mastered early on… Math is really a handful of basic ideas; but in the United States, mathematics standards are long laundry lists of seemingly unrelated, separate topics.”

The following article, A Coherent Curriculum, sheds light on the issues facing US math curriculum. It compares the US with the A+ countries and provides some insight into the “mile wide – inch deep” statement.

Also coming from TIMSS are video recordings comparing US and Japanese classrooms (Japan is considered one of the A+ countries). There has been much controversy regarding this comparison and what the tapes actually show. For an interesting assessment of Japanese classrooms, read “Telling Lessons from the TIMSS Videotape…”

The recently released 2007 TIMSS report shows slight improvement, though not the radical change the US was hoping for. This article explains why.

http://www.forbes.com/2008/12/10/timss-nclb-minnesota-oped-cx_dr_1211ravitch.html?partner=email

On the positive side, Massachusetts and Minnesota, are seeing improvements at a greater rate than the rest of the nation. Why? Both states rewrote their educational standards stressing the mastery of math facts and algebra.

As stated in the Forbes article: “If we want to see genuine improvement, we should pay attention to Minnesota’s dramatic ascent over the past decade. That state adopted a coherent, focused, grade-by-grade math curriculum… Minnesota competed in the TIMSS study and saw its scores jump from mediocre to world-class. Any state could do what Minnesota did. All it requires is implementing a well-designed, coherent curriculum in mathematics and science.”

From Massachusetts:
http://www.tommyduggan.com/VP060705stotsky.html
Sandra Stotskya co-author of the National Mathematics Advisory Panel (NMAP) final report, released in March 2008.

From Minnesota:

http://edaction.org/2004/120204.htm

http://rationalamerican.com/rp.org/archives/math.html

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“Inquiry Based Instruction vs Example Based Instruction”

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