©2004 Kathleen Kelly
La Salle University
RETURN
edited 4/12/09
Stereotypically, educator talk about mathematics is boring. However, for at least the last decade, there has been a dispute simmering and then heating up again as to what should be taught in mathematics classrooms and how it should be taught. Commonly known as the "math wars," this controversy employs sloganistic phrases and centers around misunderstandings of language, fact and value.
Each side has its own interpretation of what mathematics truly is which leads to the underlying issues with the present national curriculum of the subject. This controversy is fueled by two opposing sides, apparently set in their beliefs and values. Yet, there are signs of math educators which have reached a "middle ground" and are now trying to get their message out to all members of the mathematics education community in hopes that, someday, there will be an end to this controversy. When this happens, everyone may then be able to focus attention on what is undoubtedly most important  the education of the students.
This essay will attempt to present the issues involved in the "math wars." Both sides of the controversy will be described, and the paper will then analyze the controversy according to the criteria set forth by Clabaugh and Rozycki (2003) in Chapter 1 of Analyzing Controversy.
Background/PreAnalysis:
The phrase, "math wars," describes a serious debate in California in which the methods used in classrooms to teach mathematics are being questioned. Is a "traditional" approach to teaching mathematics better than a "whole math"/reform approach? As with any controversy, opposing views have emerged  those of the traditionalists and those of the reformists. Consisting mostly of parents and more experienced teachers, the traditionalists fear reform math will be detrimental to the students because it lacks rigor. That is, in the past, skills were learned through memorization and then repetition and practice until they were automatic. It is a traditionalist's belief that "children must develop basic math skills before they can understand concepts" (Walbert, 2001, p. 1). According to Linda Starr (2002), parents who support the traditionalists view fear that their children are being shortchanged by an educational experiment that is politically correct and mathematically incorrect.
On the other side of the controversy stand the reformists. Judith Sowder (1998) characterizes them as:
advocating an emphasis on understanding mathematics, and claim that learning happens more quickly and more easily when understanding is the focus of mathematics instruction. They say that they want to produce citizens who can use mathematics, who can solve problems, who can work cooperatively on mathematics and communicate mathematically, who can 'make sense' mathematically of the world around them. They claim that although computational skills remain important, these skills should not be the whole focus of the curriculum in the elementary grades. They prefer a curriculum that develops 'number sense' and reasoning and problem solving skills. (p. 2)
Content Analysis:
Problems of Understanding
At this point it is necessary to note that problems of understanding include definitions upon which there seems to be consensus among groups, terms that are considered sloganistic (because they are vague enough to mean different things to different people) and reifications. This last term refers to a word or phrase that has been used in such a way that it obscures the importance of individual differences within groups (Clabaugh & Rozycki, 2003).
To begin, there are two terms in this controversy which both sides seem to agree upon their definition. They are "traditional math" (sometimes referred to as "the basics") and "fuzzy math" or reform math. As previously mentioned, "fuzzy math" involves a type of curriculum intended to help children discover, understand and integrate knowledge through the independent exploration of mathematics (Starr, 2002). Stated by Van de Walle (1999), "fuzzy math" is also about how children learn and how to enable students to reach the content goals that are set for them by their teacher. This term "fuzzy math," is sloganistic because of its vagueness. It is hardly ever described as a math curriculum which initially allows students to discover mathematical concepts on their own and then reinforce them with repetition and practice. It has garnered a broad but shallow consensus among the two sides of the controversy and has obviously become a point of conflict.
The other term, "traditional math" also coined as "parrot math," is strictly seen as the old "kill and drill" that was common when today's adults and elders were in school and suggests that children mimic mindlessly what teachers model with the hope that somehow the mimicry will lead to learning (Van de Walle, 1999). Like "fuzzy math," the teaching style that this term refers to has clearly become a point of conflict in this controversy and also has a broad but shallow consensus among the differing sides.
In this heated debate, reifications have developed in regards to how one side views what the other really stands for. For instance, among the reformists is a subgroup of "extreme reformists" which have really painted the worst picture about reform mathematics. It is important to note that this is the image that the traditionalists have come to associate with reform math. These "extreme reformists" have the desire to make math fun and interesting  so much so they lose sight of the math that needs to be learned. They let technology, manipulatives, group work/cooperative learning and the use of realistic situations act as the ends rather than the means to the end. Therefore, "they leave the public with a false impression that [all] reformers believe that there should be no drill and practice, that no skills need to automatized that getting right answers does not matter" (Sowder, 1998, p. 2). Because of this subgroup within the group of reformists, parents and traditionalists have taken the stance they have in believing there is no place for "reform math" in a mathematics curriculum.
Similarly, reification exists on the traditionalists' side. Reformists group all traditionalists as those who have the same view as the "extreme traditionalists." These people believe that any change is bad and that mathematics should be taught the traditional way  because that's how they learned it so "their children and grandchildren should learn it the same way. They [extreme traditionalists] also feel that widespread testing on computation skills will keep us on the straight and narrow path" (Sowder, 1998, p. 2). Hence, the individual differences of all traditionalists have been obscured and the reformists believe that all traditionalists have no place for problemsolving of realworld situations in a mathematics curriculum.
One underlying issue in this controversy, which can be seen as a problem of understanding, is what each side is using as their definition of mathematics. It is worthwhile to note that Clabaugh and Rozycki declare that an indicator of an issue of facts is when "different parties to the dispute make conflicting statements about the same thing" (2003, p. 9). Therefore, this difference in definition will be discussed as an issue of fact.
Problems of Fact
Each party in this dispute uses conflicting statements/definitions of mathematics. Sowder (1998) perceives the two sides differing in the following ways: "They hold different beliefs about what mathematics is, different beliefs about how mathematics is learned, different understandings of what it means to know mathematics, and different ways of interpreting what research has to tell us on these issues" (p. 2). Traditionalists believe mathematics to be a set of rules, skills and facts that need to be learned, maintained, and drawn upon when and if necessary. Other traditionalists understand mathematics to be "a unified (but static) body of knowledge, with all the parts logically connected, there to be discovered by humans" (Sowder, 1998, p. 3).
However, according to Thompson (1992), the reformists view the idea of teaching mathematics as "one in which students engage in purposeful activities that grow out of problem situations, requiring reasoning and creative thinking, gathering and applying information, discovering, inventing, and communicating ideas, and testing those ideas through critical reflection and argumentation" (p. 3). In essence, the traditionalists support the behaviorist theory of learning which is based on stimulusresponse theory. Hence, the teaching is very directive and the classroom is extremely teachercentered. On the other hand, the reformists advocate the cognitive theory of learning. Because of this, their teaching is very indirect and the classroom is notably studentcentered. In addition to the Nation's Math Report Card from the U.S. Department of Education, a "source" authority that is accepted by both sides of the controversy is the Third International Mathematics and Science Study (TIMSS).
Problems of Value
In this debate, a few issues of value exist which actually center around the parents of the children who are falling victim to the "math wars." The parents claim that the teachers in favor of "reform math" are trying to force a politically correct and mathematically incorrect educational program on their students and using them as their "guinea pigs." In essence, the parents believe the reform teachers are giving the impression that their reform experiment is more important than the education of their students; thereby, giving students and parents the feeling that the teachers' values are not appropriate. Yet, these same parents are not using a suitable value system themselves. Walbert (2001) reports that "many parents, teachers, and interested citizens insist that if drill and practice in computation was good enough for them, it is good enough for today's children  ignoring the fact that they themselves often never mastered the basic math skills in question" (p. 2). So whose values should really be in question? Most certainly not just those of the reformists.
Metaanalysis
In short, first, there is a problem with consensus in regards to the definition of mathematics. As a matter of fact, there is no consensus among the differing sides about it. Secondly, this conflict is a prime example of the conflict model of society. Clabaugh & Rozycki (2003) define it as a model which "assumes societies are arenas in which various groups struggle for contradictory goals and compete for limited resources. . . Like the consensus model, the conflict model relies on reifications; but the conflict model reifies oppositional societal groups" (p. 63). Clearly, one can see that each side of the "math wars" has contradictory goals when compared to the other side. In addition, it has already been discussed how both the traditionalists and the reformists are both guilty of reifying the other group because of the extremists.
Summary
The "math wars" have been going on for well over a decade and still continue to rage. Each side has a firm stance on what they believe mathematics is and how is should be taught. However, within each group there are people (teachers, parents, legislators) that are beginning to reach a middle ground and understand how the goals of each group can be met. It's called compromise. What is so unique about this compromise, if it were to ever happen, is that, from the personal experience of the author of this paper, that is the way mathematics should really be taught. Unfortunately, until the misunderstandings of language, fact and value have been recognized by both groups, this controversy will continue.
See, also, "Logical Structure (of Math Curriculum)"

References
Clabaugh, G. K. & Rozycki, E. G. (Fall, 2003). Analyzing controversy: 2^{nd} edition. Oreland, PA: New Foundations Press.
Sowder, J. (Spring, 1998). What are the "math wars" in California all about? Reasons and Perspectives. Retrieved November 30, 2004 from www.mathematicallysane.com/print.asp?p=mathwars
Starr, L. (2002). Math wars! Retrieved December 1, 2004 from www.educationworld.com/a_curr/curr071.shtml
Thompson, A. G. (1992). Teachers' beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (p. 127146). New York: Macmillian.
Van de Walle, J. A. (1999). Reform mathematics vs. the basics: Understanding the conflict and dealing with it. Retrieved December 1, 2004 from www.mathematicallysane.com/analysis/reformvsbasics.asp
Walbert, D. (September, 2001). The math wars and the case for problemcentered math. Retrieved December 1, 2004 from www.learnnc.org/index.nsf/doc/editor0402?OpenDocument