Mile wide and an inch deep
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The standards-based mathematics curriculum adopted by the United States in the 1990s has been called a mile wide and an inch deep. Compared to nations in Asia such as Singapore which concentrate spending a lot of time on a few basics in great depth, American texts such as integrated mathematics cover a very large variety of topics to expose all students to more mathematics. Mathematics curriculum frameworks typically list a a very broad range of learning outcomes to be achieved at each grade level.
Such long lists of standards are a common feature of standards based education reform, which set out to have government agencies higher achievable world class standards of what every student should know and be able to do. Ironically, such world class standards bear very little resemblence to the standards of any one nation like Singapore, which publishes math books which cover far fewer topics than American standards.
In traditional mathematics, learning in incremental and sequential, one topic at a time. One might spend most of a quarter simply learning how to solve a simple linear algebraic equation with repetitive simple practice problems as an algebra class. An integrated approach might cover linear algebra, geometry, statistics, and problem solving over the same period of time in the context of projecting a complex model of environmental change, while spending one page rather than a quarter of a entire book on solving a problem of the form ax + b = c as would have been done in the 1970s.
[edit] Examples of usage
- 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 [1]
- 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[2]
