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If one could make a case against the perpetrators of reform math—complete with arrests and jail time—showing that such programs are a form of child abuse, the math wars would cease in a matter of days.  As it is, however, reasoned arguments from those who oppose the reform programs haven’t seemed to carry much weight, as the programs seem to proliferate in school after school across the U.S.  And in a recent Education Week column, Mr. T.C. O’Brien seems quite content to skewer those who criticize the reform programs, resorting at times to borderline name-calling, and laying blame in large part on mathematicians.  It seems that mathematicians’ call for math to be in math textbooks and that such math be correct is an artifact of purism and backwards thinking.

Ordinarily I would ignore such a diatribe.  But I believe there have been too few rebuttals to this type of op-ed which Education Week seems only too happy to publish.  Take for example this statement: “The National Mathematics Advisory Panel, established by the Bush administration in April of last year, has been meeting to discuss the improvement of achievement in mathematics in the schools.  A good portion of its members have no experience in mathematics, no experience teaching children, or both.”

Putting aside the fact that panels typically draw from a number of disciplines, of the 17-member panel two are well-respected mathematicians (Wilfried Schmid from Harvard, and Hung-Hsi Wu from U.C. Berkeley); one is a middle-school math teacher who teaches in the traditional style reviled by Mr. O’Brien and many of whose gifted students end up at universities like MIT (Vern Williams); one is a former principal of a school in California who turned it around to become a top performing school (Nancy Ichinaga); and one is a former math teacher from China who wrote a book about how good math teaching requires a thorough understanding by the teacher of the math they are teaching (Liping Ma). I could go on.

What’s really on Mr. O’Brien’s mind is the point of view of the panelists which he characterizes as “the disdain and/or lack of knowledge [they] have regarding the past 20 years of reform in K-12 mathematics”.  He finds these panelists representative of the class of “anti-reformists” who, he says, “emphasize what they see as ‘basic’: Don’t figure things out. Don’t make sense. Act rapidly and obediently. Copy what the teacher says and give it back at test time.  Be pure.  Those who wish innovative programs to disappear seem to have ignored people (especially children) in their education manifestos, and thus it seems reasonable to label their wares “Parrot Math,” a term I have used in my writing since the late 1980s.”

This is a variation on a theme I have seen repeatedly and relies on the dichotomy that “if it isn’t innovative, it’s traditional” and also relies on the canard that “traditional math does not work”.  The charge against the traditional approach is that facts and skills are learned in isolation and students don’t connect them with solving problems.  I don’t doubt that there are traditional math books that are badly written; I’ve seen them.  But I’ve seen just as many that are good; and in fact, I used them when I was in grade school.  I have them, courtesy of the Internet.  Addition and subtraction facts are presented along with word problems to show just how these concepts are applied.  Multiplication and division are clearly explained with examples of how they are used: Three boxes of apples with 6 apples in each box totals how much? 6 + 6 + 6 which is 6 three times, or 6 x 3.  Seems connected.  I also seem to recall problems for which we were asked not to calculate the answer but to tell whether multiplication or division was needed to solve the problem.

I fail to understand how Mr. O’Brien finds such approach as a manifestation of “Don’t make sense.”  Achieving mastery to the point of automaticity is the goal, to free the mind to solve more complex problems.  I and others I know are products of what he terms “Parrot Math.”  Somehow we learned enough in grade school and high school using traditional texts to be able to major in mathematics.  I could go on.

He then looks to California to bolster his argument.  California instituted standards in 1997 to ensure that basic skills and concepts are mastered on a grade-by-grade basis.  What good are such standards, he asks, given that “last year, research from the California department of education showed that 23 percent of coursetakers are proficient at Algebra 1, and 25 percent at Algebra 2. But the number of coursetakers for Algebra 1—707,000—dropped to 214,000 in Algebra 2.”  He does not mention that there are some districts in California which refused to adopt textbooks and programs that conformed to the standards.  If the California data were disaggregated to show the results of the conforming districts versus the districts that stayed with the previous curriculum, one wonders what the results would be.  One can get an inkling by reading a paper by Bill Hook, Wayne Bishop and John Hook that presents the results of a five-year study for two cohorts totaling over 13,000 students, from four urban districts in California that adopted texts that conform to the math standards, and where 68% of the students were economically disadvantaged.  The results show a transition from far-below to above-average learning performance of these students over the 1998–2002 period.  I could go on.

Finally, Mr. O’Brien offers what he feels is the final nail in the coffin for traditional math by showing that in a study he did in the 1980s of children who were able to provide correct answers to multiplication problems such as 6 x 3, that these same children were unable to provide a corresponding word problem for that fact.  “A large proportion of the children said something like this: “On Monday, I bought six doughnuts. On Tuesday, I bought three doughnuts. How many doughnuts did I buy altogether? Eighteen, because six times three equals 18.’  “

The students he asked were in the 4th, 5th, and 6th grades.  I can say from my experience in working with some sixth grade children in an inner-city school in Washington DC that I encountered the same thing.  In fact, I encounter the same thing with my own daughter.  In my experience, I’ve noticed that the children I’ve worked with have a tough time making up word problems.  The same kids I worked with in the DC school, (as well as my daughter) were able, however, to be able to tell how to solve a word problem requiring multiplication if you gave it to them. If I ask them how many donuts have I bought if I buy three a day for six days, they can identify that 6 x 3 is how it is solved. O’Brien does not disclose whether he asked them questions like that and how they answered.  I could go on.

Finally, let’s look at the crown jewel of O’Brien’s treatise. This one, in the realm of “research shows”, goes to the Piaget-linked view that children construct their own knowledge. O’Brien gets a bit philosophical here and hearkens to refrains of “What is knowledge?”, stating that we all construct our own realities.  His view of a Yankees game may not be the same as yours.  Maybe not, but I would hope that when he multiplies 6 x 3 he gets 18.  He is, of course, heading in the direction of the “constructivist camp” which holds that children should be given the opportunity to discover math concepts for themselves rather than to be saddled with “parroting” which in his view is preventing true learning.  From where I sit, “research shows” the opposite.  To wit: “When students have too much freedom, they may fail to come into contact with the to-be-learned material.  There is nothing magical to insure that simply working on a problem or simply discussing a problem will lead to discovering its solution.  If the learner fails to come into contact with the to-be-learned material, no amount of activity or discussion will be able to help the learner make sense of it.”  (From “Should There Be a Three-Strikes Rule Against Pure Discovery Learning?” by Richard E. Mayer, U.C. Santa Barbara, Janua

ry 2004, American Psychologist, Vol. 59, No. 1).  There are many other such peer-reviewed studies.  I encourage you to read them.  I could go on.

Barry Garelick is an analyst for the U.S. Environmental Protection Agency and lives in the Washington D.C. area. He is a national advisor to NYC HOLD, an education advocacy organization that addresses mathematics education in schools throughout the United States.