Comprehensive School Mathematics Program: Difference between revisions

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{{about|a math curriculum|the Continuous System Modelling Program (CSMP) modeling and simulation language|CSMP III}}

'''Comprehensive School Mathematics Program''' (CSMP) stands for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials.

{{More footnotes|date=October 2021}}

'''Comprehensive School Mathematics Program''' (CSMP) stands for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. in the United States.

Two major curricula were developed underas part of the overall CSMP project,: the Comprehensive School Mathematics Program (CSMP), a K-6K–6 mathematics program for regular classroom instruction, and the Elements of Mathematics (EM) program, a grades 7-127–12 mathematics program for gifted students. EM treats traditional topics rigorously and in -depth, and was the only curriculum that strictly adhereadhered to the ''Goals for School Mathematics: The Report of the Cambridge Conference on School Mathematics'' (1963). As a result, it includes much of the content generally required for an undergraduate mathematics major. These two curricula are unrelated to one another, but certain members of the CSMP staff contributed to the development of both projects. Additionally, (Theresome wasstaff alsoof somethe Elements of Mathematics were also interactioninvolved with the [[Secondary School Mathematics Curriculum Improvement Study]] program being developed around the same time.) The Elements of Mathematics is widely used at the IMACS institute listed below. What follows is a description of the K-6K–6 program that was designed for a general, heterogeneous audience.

The CSMP Projectproject was established in 1966, under the direction of Burt Kaufman, who remained director until 1979, whensucceeded by Clare Heidema became director until 2003. It was originally affiliated with [[Southern Illinois University Carbondale|Southern Illinois University]] in Carbondale, Illinois. After a year of planning, CSMP was incorporated into the Central Midwest Regional Educational Laboratory (later CEMREL, Inc.), one of the national educational laboratories funded at that time by the U.S. Office of Education. (see Final Evaluation Report by Martin Herbert referenced below for more detail) . In 1984, the project moved to Mid-continental Research for Learning (McREL) Institute's Comprehensive School Reform program, who supported the program until 2003. Clare Heidema remained director to its conclusion. In 1984, it was implemented in 150 school districts in 42 states and about 55,000 students.

== Overview ==

The CSMP project employs four non-verbal languages for the purpose of posing problems and representing mathematical concepts: the Papy Minicomputer (mental computation), Arrows (relations), Strings (classification), and Calculators (patterns). It was designed to teach mathematics as a problem-solving activity rather than simply teaching arithmetic skills, and uses the [[Socratic method]], guiding students to figure out concepts on their own rather than directly lecturing or demonstrating the material. The curriculum uses a spiral structure and philosophy, providing students chances to learn materials at different times and rates. By giving students repeated exposure to a variety of content – even if all students may not initially fully understand – students may experience, assimilate, apply, and react to a variety of mathematical experiences, learning to master different concepts over time, at their own paces, rather than being presented with a single topic to study until mastered.

The most influential figure on this project was Frederque’ Papy. This project employs four non-verbal languages for the purpose of posing problems and representing mathematical concepts. They are: the Papy Minicomputer(mental computation), Arrows(relations), Strings(classification) and Calculators(patterns). 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. Itcurriculum introduced many basic concepts such as fractions and integers earlier than normal. butLater wasin criticizedthe forproject's lack of emphasis given to calculation.development, Newnew content in probability and geometry was introduced. ThereThe wascurriculum contained a range of supporting material including story books with mathematical problems., Lessonswith werelessons often posed in a story., designed to feature both real world and fantasy situations. One character in these books was Eli the Elephant, a [[Elephant|pachyderm]] with a bag of magic peanuts —, some representing positive integers, and some negative. Another lesson was titled "Nora's Neighborhood," which taught [[taxicab geometry]].

== Mini-computerMinicomputer ==

[[Image:CSMP mini computer.svg|thumb|right|300px|The number 9067 represented on a mini-computerMinicomputer.]]

One device used throughout the program was athe ''mini-computerPapy Minicomputer'', named after [[Frédérique Papy-Lenger]] – the most influential figure to the project – and her husband Georges Papy. ThisA wasMinicomputer is a 2 by 2 grid of squares, with the squaresquarters representedrepresenting the numbers 1, 2, 4, and 8. Checkers couldcan 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-computerMinicomputer 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-computerMinicomputer is designed to represent a single decimal digit, and multiple mini-computersMinicomputers 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-computerMinicomputer's squares – placed to the left of the first – will represent 10, 20, 40, and 80; a third, 100, 200, 400, and 800, and so on. Minicomputers to the right of a vertical bar (placed to the right of the first board, representing a decimal point) may be used to represent decimal numbers.

[[Image:CSMP mini computer.svg|thumb|right|300px|The number 9067 represented on a 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]].

Students are instructed to represent values on the mini-computersMinicomputers 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.

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.

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 require fewer checkers 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.

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.

Arithmetic can be performed on the mini-computerMinicomputer 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's4s with an 8.

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.; Howeverhowever, there was a marked improvement when students were assessed according to The Mathematics Applied to Novel Situations (MANS) tests which were, introduced to measure students' ability forto problem solvingsolve in novel situations.

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 Mathematics Applied to Novel Situations (MANS) tests which were introduced to measure students ability for problem solving in novel situations.

==Copyright==

Copyright is currently held by McREL International.

==Current curriculum use==

Burt Kaufman, a mathematics curriculum specialist, headed the team at SIUSouthern Illinois University writing CSMP. In HeJuly 1993, eventuallyhe started the Institute for Mathematics &and Computer Science (IMACS). with IMACShis appearsson toand two colleagues. IMACS useuses elements of the programEM and CSMP programs in their "Mathematics Enrichment" program. For instance, mini-computersMinicomputers and "Eli the Elephant" are present in the IMACS material. IMACS is a private education business focusing on the instruction of students from first grade through high school.{{cn|date=April 2016}}Including online courses, IMACS currently serves over 4,000 students across the U.S. and in over ten countries.<ref>[https://www.imacs.org/home/about/news-us/burt-kaufman.html/ Burt Kaufman: An Appreciation – IMACS]</ref>

CSMP is also used by some homeschooling families either as a core math program or for enrichment exercises.

==Current curriculum use==

Burt Kaufman, a mathematics curriculum specialist, headed the team at SIU writing CSMP. He eventually started the Institute for Mathematics & Computer Science (IMACS). IMACS appears to use elements of the program in their "Mathematics Enrichment" program. For instance, mini-computers and "Eli the Elephant" are present in the IMACS material. IMACS is a private education business focusing on the instruction of students from first grade through high school.{{cn|date=April 2016}}https://www.imacs.org/about/news/burt-kaufman.html

==References==

<references />

*[http://stern.buffalostate.edu/Evaluation/1984CSMPFinalReport.pdf CSMP final evaluation report]

*[http://ceure.buffalostate.edu/~csmp/Evaluation/ReporttotheProgramEffectivenessPanel.pdf Report to the Program Effectiveness Panel]

*[http://www.mathcurriculumcenter.org/PDFS/CCM/summaries/cambridge_summary.pdf Goals for School Mathematics: The Report of the Cambridge Conference on School Mathematics (1963).]

*[gttp://math.buffalostate.edu/~med600/Assignments/GrahamKaylia.pdf]

== External links ==

*[http://stern.buffalostate.edu A comprehensive archive of CSMP materials from Buffalo State]

*[http://www.imacs.org Institute for Mathematics and Computer Science]

*[http://www.mcrel.org MCREL]

*[http://stern.buffalostate.edu/ ACSMP comprehensivePreservation archiveProject ofand CSMParchived materials fromat Buffalo State]

[[Category:Mathematics education]]

*[http://stern.buffalostate.edu/Evaluation/1984CSMPFinalReport.pdf CSMP finalFinal evaluationEvaluation reportReport]

*[http://ceurestern.buffalostate.edu/~csmp/Evaluation/ReporttotheProgramEffectivenessPanel.pdf Report to the Program Effectiveness Panel]

*[httphttps://www.mathcurriculumcentermaa.org/PDFSsites/CCMdefault/summariesfiles/cambridge_summary.pdf/CUPM/first_40years/1963CambConf.pd Goals for School Mathematics: The Report of the Cambridge Conference on School Mathematics (1963).]

*[http://www.imacs.org/ Institute for Mathematics and Computer Science]

*[http://www.mcrel.org/ MCRELMcREL]

[[Category:Mathematics educationcurricula in the United States]]