Comprehensive School Mathematics Program
The Comprehensive School Mathematics Program, also known as CSMP, was elementary, K-6, math program in the United States of America. It was developed between 1972 and 1984 by the Central Eastern Midwestern Regional Laboratory (CEMRL). In 1984 it was taken over by the McREL (Mid-continent Research for Education and Learning) Institute's Comprehensive School Reform program, who supported the program until 2003. In 1984 it was implemented in 150 school districts in 42 states and about 55,000 students.
Overview
It was designed to teach mathematics as a problem solving activity rather than just teaching arithmetic skills. The program was highly structured using the spiral scheme of program development. It introduced many basic concepts such as fractions earlier than normal but was criticised for lack of emphasis given to calculation. New content in probability and geometry was introduced. There was a range of supporting material including story books with mathematical problems. One character in these books was Eli the Elephant, a pachyderm with a bag of magic peanuts — some representing positive integers, some negative.
The Mini-Computer
One device used throughout the program was a mini-computer. This was a 2 by 2 grid of squares, the squares represented the numbers 1, 2, 4, and 8. Checkers could be placed on the grid to represent different numbers in a similar fashion to the way the binary numeral system is used to represent numbers in a computer.
The mini-computer is laid out as follows: a white square in the lower right corner with a value of 1, a red square in the lower left with a value of 2, a purple square in the upper right with a value of 4, and a brown square in the upper left with a value of 8. Each mini-computer is designed to represent a single decimal digit, and multiple mini-computers can be used together to represent multiple-digit numbers. Each successive board's values are increased by a power of ten. For example, a second mini-computer's squares will represent 10, 20, 40, and 80; a third, 100, 200, 400, and 800, and so on.
Students are instructed to represent values on the mini-computers by adding checkers to the proper squares. To do this only requires a memorization of representations for the digits zero through nine, although non-standard representations are possible since squares can hold more than one checker. Each checker is worth the value of the square it is in, and the sum of the checkers on the board(s) determine the overall value represented. Most checkers used by students are a solid color- any color is fine. The only exception is checkers marked with a caret (^), which are negative.
An example of representing a number: 9067 requires four boards. The leftmost board has two checkers in the 8 and 1 squares (8000 + 1000). The second board has none, as the value has zero hundreds. The third board has checkers in the 4 and 2 squares (40 + 20), and the rightmost board has checkers in the 4, 2, and 1 squares (4 + 2 + 1). Together, these 7 values (8000 + 1000 + 40 + 20 + 4 + 2 + 1) total up to 9067.
This would be considered a standard way to represent the number as it involves the fewest checkers possible without involving negatives. It would be simpler to replace the last board with a positive checker in the 8 and a negative checker in the 1, but this is not taught as the standard.
Arithmetic can be performed on the mini-computer by combining two numbers' representations into a single board and performing simplification techniques. One such technique is to replace checkers from the 8 and 2 squares of one board with a checker on the 1 square of the adjacent board to the left. Another technique is to replace a pair of checkers in the same square with one checker in the next higher square, such as two 4's with an 8.
Study Results
The program received extensive evaluation, with over 50 studies. These studies showed broadly similar results for non CSMP students in computation, concepts and applications. However there was a marked improvement when assessed according to the The Mathematics Applied to Novel Situations (MANS) tests which were introduced to measure students ability for problem solving in novel situations.
References
External links
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