To Ms Colaizzi and the Pittsburgh Public Schools BoE

By Wayne Bishop, California State University at Los Angeles

March 12, 2002

Dear Ms Colaizzi and the PPS Board of Education,

Thank you for the fax of the January 8, 2002, presentation by Dr. Briars entitled "Mathematics Program for the 21st Century". My summary would be that it is misnamed; it is a proposal for a mathematics program of the last couple of decades of the 20th Century, an idea that went belly-up in California and has driven a phenomenon called the Math Wars across California, spreading to Massachusetts, Manhattan, and other places, sometimes under the name "California East," and now seems to have reached you. You have been living with the problem, unaware perhaps, for several years with an elementary school curriculum named Everyday Mathematics and the natural outgrowth of widespread implementation of these ideas has now reached the secondary level.

Thinking that it was your proposed curriculum, I sent you some damning information (and please share with the Board - with the spelling of your name corrected!) in regard to a program called Core-Plus. As it turns out, Core-Plus is not the secondary curriculum proposed for PPS, it is a program called IMP, Integrated Mathematics Program, that originated here in California and that is even worse than Core-Plus. In fact, this is the curriculum that I mentioned in our phone conversation in regard to use in Philadelphia. Although such absolutes are hard to substantiate objectively, it is possible that this is the worst high school mathematics curriculum that has ever been written. The ideologues within the Education and Human Resources division of the NSF, Project 2061 of the AAAS, and the US Department of Education (that deemed both of these curricula "exemplary") notwithstanding, districtwide approval of IMP would be nothing short of immoral. The opportunity of upward mobility through education lost for thousands of children.

The references and supplementary information for the remarks of Cal State Northridge mathematician David Klein given in Washington, D.C., on March 4, 2002,, are informative (my personal favorite is the "Toilet Graph") but so are his actual words (attached below) that began, "No single institution in the United States has caused more damage to the mathematical education of children than the National Science Foundation." That gives you some idea of the true nature of the advice that you have been getting from the Prime-Plus office and of this genre of "reform" be it Core-Plus, CPM, IMP, or others that may not have been deemed "exemplary" or "promising" by the US Department of Education but are, nevertheless, the exact opposite of these impressive sounding adjectives.

One of the long-since discredited ideas that are presented as fact in Dr. Briars' slide presentation is that IMP, or at least "integrated mathematics" of some kind, is the international standard. This stems from a complete misunderstanding of mathematics education in other countries. It is true that their courses are often identified as Maths 1, 2, 3, 4 (the abbreviation is usually taken in the plural abroad) but everyone knowledgeable within a given country knows exactly what topics are studied in which terms of which years. For example, the Singapore secondary curriculum is available, in English, and I recommend it to you most highly, , or the Japanese, that is also available in English, at about $20 a book through the University of Chicago. They are excellent. Real mathematics. IMP is not.

Another misunderstanding is the presumption that it would be wise to conform your curriculum (in any discipline, mathematics included) to the PSSA. The developers of this system of examinations are modeling a philosophy that guided the CLAS exam that California experimented with in 1993 and 1994 but which was such a disaster that it terminated in its second year and Maryland's MSPAP that has followed the same path but more slowly, according to Sunday's Washington Post: The PSSA is tied to the Pennsylvania mathematics standards that I pointed out in my March 9 fax as meriting a D, versus California's of late 1997 that do merit their A (

Modifying your program to conform with the specifications of an exam that means nothing outside of Pennsylvania, and that will be dead within 5 years within Pennsylvania, may be education school wisdom but it is not wisdom anywhere else. For example, the IMP people (Philadelphia's Joseph Merlino most notably) have made a major issue out of the fact that Strath Haven High School uses IMP and scored very well in the PSSA. Those affluent folk can and do get to a Sylvan Learning Center, hire tutors, or do whatever is necessary in order to give their children reasonable access to strong universities. More relevant than PSSA data, however, is the fact that the application forms to both Penn and Penn State (wisely) never mention the PSSA but they do ask for SAT or ACT data. For example, Penn wants the ACT or both the SAT I and three of the SAT II subject tests. Penn State's application information indicates that a SAT I in the1160-1340 range is normal for successful applicants at University Park but 950-1140 will do at all other campuses, or an ACT of 26-30 at University Park but 20-25 at all other campuses. This is the kind of information that creates opportunities for well prepared students, not stupidly forcing them all (italics original) "to pass Integrated 1&2" and with its strong emphasis on technology instead of the conceptual understanding and computational competence that they would need for success in university mathematics. That will leave back the stronger students with an interest and ability in math based work an amazing three years! See the comments below in regard to Stuyvesant High for confirmation. Instead of encouraging and supporting preparation for and completion of algebra in grade eight, these unfortunate students would be forced to stay in IMP's silly project-oriented classes for another two years after arriving in high school!

The truth is that IMP correlates with falling SAT mathematics scores, especially SAT II and ACT, for college entry. I've forgotten the specifics, although I could look them up for you if it were helpful, but this much I remember "off the top". The two IMP pilot high schools in Los Angeles Unified School District, starting in or about 1993, were Marshall High and Roosevelt High and their experience was typical of other schools across California. Substantial pressure was exerted from central administration (with assistance from the NSF in the form of substantial Systemic Initiative funding - think Prime-Plus) for other schools to adopt IMP as well, and some did. By the time the IMP kids got to be seniors and were thinking about college, substantially fewer students (somewhere in the 30% range) even bothered to take the SAT (few out here take the ACT), and those who did take it scored markedly lower on average. Finally, both schools dropped their IMP curriculum and returned to a more conventional mathematics program, as have most other schools here in California that had adopted IMP with great fanfare earlier. Again, this pattern has been repeated in district after district across California.

Some of the information that was presented on January 8 can only be fairly identified as religious proselytizing or outright lie. Ignorance used to be a third option but not for years; the California evidence has been too strong in regard to IMP specifically but the same can be said for the genre, such as the Core-Plus information that I already sent you. As an example, P. 9 says that the program, "Contains the same algebra and geometry content as the Algebra 1, Geometry, Algebra 2 sequence." If this statement is even close to being true, you need to see what kind of abomination has already occurred in these courses because it simply is not true for traditional mathematics courses with those names and a traditional final exam in any of them would confirm it for you. That is "reason" for the need of the so-called "New Standards" of line 15 of page 13 of Draft 7 of the PPS Strategic Plan. Give a real algebra test or a real geometry test and the results will be reflected in that Austin MN article that I sent, "We gave our students a diagnostic test and they were doing awful."

As a concrete example of this phenomenon, one of the strongest public high schools in the nation, Peter Stuyvesant in Manhattan, has had to institute a new policy, a requisite placement exam for incoming students to ascertain the proper first course, all as a result of the fact that many children are now coming from NCTM's (so-called) Standards-based programs (Core-Plus, CMP, Math in Context, ARISE, IMP, etc.) instead of a strong, traditional, first year algebra. The irony of the term "Standards," in this context, is that there are no identifiable standards in the NCTM Standards! These kids will not have a shot at the highest level courses offered at Stuyvesant because they are going to have to start at a lower level, having not taken 1st year algebra, which in past years was fulfilled in middle school for all of those more advanced students who had the slightest reasonable hope of getting into prestigious Stuyvesant. Algebra is algebra. IMP is not.

Finally, the commitment of $355K this year and $887K next year would be worse than a waste of scarce resources. Better to use the old dog-eared mathematics books, buy a few for replacement if needed, and continue to educate the college bound appropriately, independent of their gender, race, or family background. Male/female, black/white/Hispanic/Asian, rich/poor, etc., are all irrelevant. If money is available, use it to replace the elementary school curriculum, Everyday Mathematics, that is helping to make your secondary problem worse, not to buy and to train teachers for IMP. Mathematics is mathematics. IMP is not.

Wayne Bishop, Ph D
Department of Mathematics
California State University, LA


Please note also the subsequent letter to the Pittsburgh Board of Eduction (April 10 2002).

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