Mile wide and an inch deep

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The new mathematics curriculum adopted by the United States conforming to the standards of the NCTM has been called a mile wide and an inch deep, a phrase coined by William Schmidt of Michigan State University in his analysis of the TIMMS study of international mathematics competency. This terminology had never been applied to traditional texts by creators of the new standards.

National textbooks of nations in Asia such as Singapore concentrate their time on a few basics in great depth. By contrast, many recently adopted American texts cover a very large variety of topics to expose all students to more mathematics rather than single subjects such as algebra or geometry. A meteorology professor from University of Washington^[1] has singled out a widely used high school integrated math series which replaced discrete algebra and trigonometry classes as covering and switching between too many topics in too little depth to be effective. Some texts have even been called "Rainforest Algebra" for filling colorful pages with information on famous persons and the environment rather than mathematics. Standards-based texts in elementary grades often follow guidelines to include statistics, writing and data graphing in place of drill and instruction on basic arithmetic procedures.

Such long lists of topics are a persistent feature of American math texts, partly because the innovation of spiral design of many texts expected to re-teach the same topic each year, not necessarily to proficiency. The textbooks of nations like Singapore, which score highly on international tests, cover far fewer and more basic topics than American texts, lacking treatment of topics given emphasis on the NCTM standards such as multiculturalism, statistics, and data charting. The Singapore books do integrate math topics into a grade rather than distinct classes in algebra and geometry. However, it is their retention of traditional curriculum content levels and standard methods and terminology endears them to parents and teachers who have been put off by radical reform mathematics teaching methods. The recently adopted standards in the United States put more importance on discovery learning and inventing new methods rather than re-learning single efficient traditional methods of arriving at a single, correct answer. Controversy over these methods has led some states and school districts to re-adopt traditional mathematics to either supplement or replace standards-based mathematics.

In countries with fewer topics per year, or in the US before the 1970s, one might spend most of a quarter simply learning how to solve a simple linear algebraic equation. In a newer integrated book, as few as 2 or 3 pages might be devoted to this topic, while topics such as linear algebra and matrix multiplication, traditionally not taught until college calculus, might have a chapter devoted to it as early as the the 8th grade in the Core-Plus Mathematics Project.

[edit] Examples of usage

William Schmidt: "The US by contrast expects second grade teachers to cover twice as many mathematics topics. The result is a characterization of the US curriculum as a mile wide and an inch deep."^[2]

Mathematically Correct: "A mile wide and an inch deep is a catchy slogan. This phrase is used to critique US math education for having too many topics, as suggested by the TIMSS international math study ^[3]

Chicago Catalyst: "Math instruction in the United States is "an inch deep and a mile wide," leaving students with little knowledge because teachers try to cover too much in too little time^[4]