Barry McGhan is the K-12 mathematics coordinator for an urban Midwestern school district with an enrollment of 26,000. He has also taught middle school, high school (in traditional, alternative, and vocational programs), and college mathematics.
Some will be bothered by his references to the National Council of Teachers of Mathematics’ “math sophisticates’’ and to “the N.C.T.M. and its ilk,’' both of which might be interpreted as pejorative. Such references, we may imagine, can be explained by Mr. Finn’s lingering animosities over difficulties with his 4th-grade math teacher.
Others will be bothered by Mr. Finn’s apparent lack of knowledge about the content of the N.C.T.M.'s Curriculum and Evaluation Standards for School Mathematics (1989) and its Professional Standards for Teaching Mathematics (1991). For example:
- He accuses the N.C.T.M. of being high-handed about its recommendations for change (a criticism that never bothered him when he was reorganizing the U.S. Education Department’s research operations). But he appears unaware that it is not just the “sophisticates’’ at the N.C.T.M. who have expressed a need for curriculum change. In fact, leaders of business and industry have often expressed the need for changes favoring greater attention to developing problem-solving and thinking skills.
- He seems not to know that the new N.C.T.M. standards cover both curriculum for, and evaluation of, students, as well as professional training and retraining for teachers. His implication that the N.C.T.M. is silent concerning performance standards ignores the fact that the 1989 Standards contains a section on evaluation, and that the N.C.T.M. supports the development of a common curriculum in which all students will be successful.
- He is concerned that problem-solving is being taught as something apart from obtaining the right answer. He seems oblivious of the notion that good recommendations can be poorly implemented despite the intentions of the original designers. I imagine he must be surprised when well-designed bridges or buildings collapse through contractor or workman error.
- His concern over proceeding with program changes without incontrovertible research evidence (his example is the unsettled debate between whole language and phonics proponents) seems at best, naive, at worst, uninformed. The debates that spring up around different research methodologies and conclusions are often fueled by competing and incongruent paradigms. When the art of education becomes a science we will then have the luxury of making changes after research has identified those which are best.
Still other mathematics educators will be concerned by the shallowness of Mr. Finn’s view of what mathematics is. He speaks about the satisfaction that students “get from knowing things; precise, definite things that they know they know’’ (such as 5 x 11 = 55). Wouldn’t students get satisfaction from knowing that they have command of the strategies that make them successful problem-solvers? Wouldn’t they get satisfaction from understanding mathematics as the science of patterns, in the same way we expect them to find satisfaction in knowing their rights as citizens, how to communicate effectively, or how to express themselves creatively?
To all these irritations I say to my colleagues, “Keep the faith, baby.’'
It’s natural for conservative thinkers to hearken back to the good old days. The depth of Mr. Finn’s antediluvian thought is revealed in his endorsement of Siegfried Engelmann’s complaint that problem-solving is the cause of student’s not knowing long division. This is the age of computers and calculators, isn’t it?
Mr. Finn’s concerns about the N.C.T.M. Standards are perfectly normal to those conservative educators who honor the lower-order thinking skills embodied in such approaches to curriculum as E.D. Hirsch’s “core knowledge’’ proposal. It’s a simplistic strategy. One buries one’s head in the sand of the past and thus avoids the responsibility for estimating what kind of education students might need to meet the future. In this way, one also avoids taking any steps to change the traditional system into something likely to be more useful.
There’s another point to keep in mind about conservatives--teaching thinking skills and problem-solving strategies to a wider-than-usual range of students scares the bejesus out of them. If such an effort succeeds, it might destabilize the current social order a bit, which really makes them nervous.
My career as a mathematics teacher began at the height of the “new math” era in the early 60’s, and I agree with Mr. Finn that the Standards published in 1989 bear some resemblance to the old “new math.’' To which I say, “It’s about time!’'
- The essence of mathematics is problem-solving.
- The best way to produce problem-solving ability in students is through student-centered practice (today it’s called “constructivism’'; in the 60’s we called it “discovery learning’’).
This time, we need to stay the course.
