From the Origin provides a forum for lively discussion of issues of importance to the mathematical community. The Michigan Section-MAA Newsletter solicits opinion pieces for publication in this column from anyone in the Michigan mathematical community. In addition, comments on pieces published in earlier issues are welcomed.
Items for From the Origin should be submitted to the editor by the beginning of October to be considered for inclusion in the December issue and by the beginning of February for the April issue. Main opinion pieces should be at most 1800 words long, and responses at most 400. The editors reserve the right to shorten responses, if necessary, in order to fit as many as possible within the available space.
EDITOR'S NOTE: The From the Origin column in the Fall issue was a report from Roger Verhey about school mathematics education reform and in particular how new programs such as Core-Plus would affect the transition students face between high school and college. In this issue, we present first the views of Gregory Bachelis (WSU), who feels that reform is not for everyone, and then a response from that program's directors. We welcome further contributions to this dialog.
by Gregory F. Bachelis (WSU)
This article is a follow-up to Roger Verhey's article in the last Newsletter entitled "Building Bridges in Mathematics Between High Schools and Colleges". The impetus for that article was the "reform math" programs being instituted in many high schools. These programs are usually labelled "Integrated Math" and are mainly the result of the promulgation of new NCTM Standards in 1989. They have many "strands", including the usual high school topics plus probability, statistics or data analysis, and discrete math. Some, such as Chris Hirsch's Core-Plus from WMU, include modeling and simulation. According to the proponents, symbol manipulation and rote learning are replaced by higher order thinking and real world problems.
Now Verhey's article was quite low-key and unobjectionable, so one might wonder what all the fuss is about. Well, to put it succinctly, the math education people, in many of these reform programs, have turned high school mathematics on its head. They have changed the way mathematics is presented, from a deductive discipline to an experimental science, heavily dependent on graphing calculators. They claim that this is better than traditional methods, and that it is suitable for all students, which include those who are college-bound and intend to major in science or engineering. Rather than calling it "reform math", I think a more accurate description would be "deformed math". When Verhey & Co. talk about building bridges, what they want is to insure that students who do well with this deformed curriculum get a warm reception when they get to college.
Well, as far as I am concerned, a bit of rain needs to fall on this parade. Let them play all the games they want with the kids who formerly wouldn't have done well when it came time to get serious about math; that's fine with me. For many of these kids this new approach may in fact be better than the old methods, and in number they may indeed be a majority of the students; but we shouldn't let the reformers impose this masquerade on the kids who need to get serious about math in high school. And we certainly shouldn't let them force a change in the way college math is taught by sending us a bunch of calculator-dependent, algebra-starved students, and expecting us to change our methods accordingly. (If you are thinking of Harvard Calculus at this point, then you will also realize that even it makes regular use of symbol manipulation, as does its pre-calculus younger sibling.) Now I know that all sorts of colleges have endorsed Core-Plus as college-preparatory, so perhaps these endorsements should be revisited, as currently are the endorsements of the NCTM Standards themselves (see next paragraph).
If you think I am just ranting and raving, then I suggest you do the following, as I have done. Read some of the front page articles in leading newspapers about the "math wars" or the "new new math" (for example, Detroit Free Press 10/27/97, Wall Street Journal 11/5/97, Detroit News 11/23/97, New York Times 11/27/97 these also include changes in elementary math education, which I won't get into here), and read the article in the 10/15/97 issue of Education Week. Also read the articles in last summer's AMS Notices, and check out the MAA website, where they publish the minutes of their committee which is reviewing the NCTM Standards. (The AMS also has such a committee.)
After doing all this, I suggest you examine some of the Core-Plus materials, where you can see for yourself how this unhealthy calculator dependence is engendered, and where you will also find misuse of math modeling terminology. See where whole areas of mathematics are galloped through, as if in some giant amusement park. Serious study is replaced by "cooperative learning". (I know, I know; reformers of college math like to stress cooperative learning, real world problems, and the use of graphing calculators; but believe me, the latter are making wavelets compared to the tsunami that Hirsch & Co. have created.)
Then attend some school board meetings in West Bloomfield or Bloomfield Hills, or other places where Core-Plus has been adopted (totally in the former, partially in the latter), where the controversies these adoptions have created unfold. Talk to parents whose children used to like math but are turned off by Core-Plus. I know, many students are thriving, but often they are the ones who wouldn't have liked getting serious about math, so as I said before, let them have their fun. Those who want to pursue mathematics in college will have to be "deprogrammed" after they arrive.
Now, as fast as I can say "standardized tests", some of you are ready to tell me to wait for results from SAT, PSAT, ACT, ITED, etc. to judge how successful Core-Plus is. Well, I have news for you. That won't work. For one thing, the tests are being "fixed" to be more Core-Plus- friendly. For another, many parents in Bloomfield Hills and West Bloomfield, and I'm sure in other "deformed" districts as well, are having their children tutored in algebra, to make up for what they are missing, thus contaminating the treatment group.
Even a cursory glance at the reform math curriculum by anyone who has taught its various strands at the college level, as I have, reveals that this is just too much material to cover in four years of high school in a serious way. So what do I suggest doing to remedy this situation? Well, you can forget about waiting for the evaluations of the NSF grants these reformers have. The evaluators are on the same team, after all. Now Senator Robert Byrd of West Virginia has denounced "rain forest algebra" on the floor of the U.S. Senate, so maybe we could politicize this battle even more than it has been. What I suggest is that traditional math be kept as an option in every district where Core-Plus or other programs of its ilk are adopted, and that all of us serious mathematicians support such efforts wherever we can. And also, as I mentioned above, we should look carefully again at Integrated Math programs individually, because there is such a wide variation to see which ones are really college-preparatory.
And for those of you who are ready to dismiss what I say as merely anecdotal, let me end this harangue by paraphrasing the late Senator Everett Dirksen of Illinois. "A few anecdotes here, a few anecdotes there pretty soon you're talking about real statistics."
Standards-based Reform:
Moving Beyond Rhetoric
by Christian R. Hirsch (WMU), Arthur F. Coxford (UM-Ann Arbor), James T. Fey (U of Maryland), and Harold L. Schoen (U of Iowa)
This article is a response to Gregory Bachelis's attack on Standards-based curriculum reform. At the January Joint Meetings of the American Mathematical Society and the Mathematical Association of America, U.S. Secretary of Education Richard Riley, called for "an end to the shortsighted, politicized, and harmful bickering over teaching and learning of mathematics" that has characterized the so-called "math-wars" in California and elsewhere (including, it would appear, Bloomfield Hills). He urged the mathematics community to begin a more "civil and constructive discourse" based on facts. In that spirit (and with all due respect to the late Senator Dirksen's standards of evidence), we offer the following facts for consideration.
- The NCTM Curriculum and Evaluation Standards for School Mathematics published in 1989 were developed over a three-year period, reviewed and endorsed by 15 mathematical sciences organizations including the AMS, CBMS, and MAA. As planned, the Standards are being revised, and will continue to be, in response to advances in the practice of mathematics, in technology, and in research on teaching and learning.
- The Core-Plus Mathematics Project (CPMP), funded by grants from the National Science Foundation, has completed work on a Standards-based three-year mathematical sciences curriculum for all high school students. Research and development is in progress on a fourth-year course that continues the preparation of students for college mathematics. Our work has been guided by an international advisory board and informed by consultants from the mathematics community, including Kenneth Ross (U of Oregon), David Smith (Duke U), and Paul Zorn (St. Olaf College).
- Each year the CPMP curriculum advances students' mathematical thinking and skills along four connected strands: algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. An over-arching goal is to develop student ability to reason and communicate mathematically and to solve problems involving data, shape, change, and chance. Examination copies of the published texts are available from Everyday Learning Corporation (800-322-MATH). A careful review of these materials will show that symbolic reasoning and manipulation as well as proof have not been ignored and are, in fact, central ideas in Course 3 and in Course 4.
- Each CPMP course was carefully developed with teacher input over a three-year period and field tested in 36 high schools in 11 states. (Bloomfield Hills Andover volunteered to be a pilot and field test site.) Eleven of the field test sites volunteered to pretest and posttest students enrolled in traditional, comparison classes.
- As measured by the mathematics subtest of the Iowa Tests of Educational Development (ITED), compared to students in traditional mathematics courses and to those in the nationally representative norm group, students in CPMP courses after one year, two years, and three years demonstrated better understanding of, and ability to reason in, quantitative situations. At the end of Course 2, mean ITED performance of CPMP students was at the twelfth-grade level. (Harold L. Schoen and Steven W. Ziebarth, Mathematical Achievement on Standardized Tests: A Core-Plus Mathematics Project Field Test Progress Report (U of Iowa, 1998a))
- On CPMP-developed posttests for Courses 1 and 2 which measured content that both CPMP students and control students had an opportunity to learn, CPMP students showed a greater understanding of, and ability to apply, algebraic and geometric concepts. (Harold L. Schoen and Steven W. Ziebarth, Assessments of Students' Mathematical Performance: A Core-Plus Mathematics Project Field Test Progress Report (U of Iowa, 1998b))
- On a composite test of items from the twelfth-grade NAEP assessments, performance of end-of-Course 3 students was considerably higher than the NAEP national sample across all five content areas and across the three process categories. (Schoen and Ziebarth 1998a)
- The CPMP three-year curriculum is accepted as a college-preparatory mathematics program at universities across the country, including UM-Ann Arbor.
- Course 4 materials will be field tested during the 1998-1999 school year. Thus, students completing field-test (not final) versions of the complete CPMP four-year curriculum will first arrive on college campuses in Fall 1999.
- The out-of-school tutoring referred to in Bachelis's article is a historical and cultural artifact of the community. The practice was common before the NCTM Standards and CPMP.
For further information about the goals, content, and effectiveness of the Core-Plus Mathematics Project curriculum, visit our website (www.wmich.edu/math-stat/cpmp/).
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