---
title: "Math wars"
chunk: 1/2
source: "https://en.wikipedia.org/wiki/Math_wars"
category: "reference"
tags: "science, encyclopedia"
date_saved: "2026-05-05T04:18:04.272464+00:00"
instance: "kb-cron"
---

In the United States, math wars are debates over modern mathematics education, textbooks and curricula that were triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.
While the discussion about math skills has persisted for many decades, the term "math wars" was coined by commentators such as John A. Van de Walle and David Klein. The debates focus on traditional mathematics versus reform mathematics philosophy and curricula, which differ significantly in approach and content.

== Advocates of reform ==
The largest supporter of reform in the US has been the National Council of Teachers of Mathematics. They call for a more inquiry-based approach that emphasizes real-world problem solving and understanding the underlying steps, as opposed to merely applying formulas to arrive at a correct answer. Successful implementation of this approach requires a great deal of expertise in educators; some parents and other stakeholders blame educators saying that failures occur because of this lacking expertise rather than a fundamental design flaw in the curriculum.
A backlash, which advocates call "poorly understood reform efforts" and critics call "a complete abandonment of instruction in basic mathematics," resulted in "math wars" between reform and traditional methods of mathematics education.

== Critics of reform ==

Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.
Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or new technology, such as the Logo language. Student innovation is acceptable, even welcome, as long as it is mathematically valid.  Calculator use can be appropriate after number sense has developed and basic skills have been mastered. Constructivist methods which are unfamiliar to many adults, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets that can be completed in minutes, constructivist activities can be more time-consuming. (Reform educators respond that more time is lost in reteaching poorly understood algorithms.) Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with English.
Critics of reform point out that traditional methods are still universally and exclusively used in industry and academia. Reform educators respond that such methods are still the ultimate goal of reform mathematics, and that students need to learn flexible thinking in order to face problems they may not know a method for. Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering foundational skills. Commentators have argued that there is philosophical support for the notion that "algorithmic fluency" requires the very types of cognitive activity whose promotion reform advocates often claim is their approaches' unique virtue. However, such arguments assume that reformers do not want to teach the standard algorithms, which is a common misunderstanding of the reform position.
Some curricula incorporate research by Constance Kamii and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math. Critics have protested some of the consequences of this research. Traditional memorization methods are replaced with constructivist activities. Students who demonstrate proficiency in a standard method are asked to invent another method of arriving at the answer. Some parents have accused reform math advocates of deliberately slowing down students with greater ability in order to "paper-over" the inequalities of the American school system.  Some teachers supplement such textbooks in order to teach standard methods more quickly. Some curricula do not teach long division. Critics believe the NCTM revised its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to some of these curricula (see below).  College professors and employers have sometimes claimed that students that have been taught using reform curricula do not possess basic mathematical skills. One study found that, although first-grade students in 1999 with an average or above-average aptitude for math did equally well with either teacher-directed or student-centered instruction, first-grade students with mathematical difficulties did better with teacher-directed instruction.

== Reform curricula ==

Examples of reform curricula introduced in response to the 1989 NCTM standards and the reasons for initial criticism: