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.
63-572: Two major curricula were developed as part of the overall CSMP project: the Comprehensive School Mathematics Program (CSMP), a K–6 mathematics program for regular classroom instruction, and the Elements of Mathematics (EM) program, a grades 7–12 mathematics program for gifted students. EM treats traditional topics rigorously and in-depth, and was the only curriculum that strictly adhered to Goals for School Mathematics: The Report of
126-513: A type or hot-lead printing character. The original 1963 version of the ASCII standard used the code point 0x5E for an up-arrow ↑ . However, the 1965 ISO/IEC 646 standard defined code point 0x5E as one of five available for national variation, with the circumflex ^ diacritic as the default and the up-arrow as one of the alternative uses. In 1967, the second revision of ASCII followed suit. Overprinting to add an accent mark
189-459: A " circumflex "; the Unicode standard calls it a "circumflex accent", although it is no longer practicable for that purpose. On typewriters designed for languages that routinely use diacritics (accent marks), there are two possible ways to type these: keys can be dedicated to precomposed characters (with the diacritic included); alternatively a dead key mechanism can be provided. With the latter,
252-703: A broader range of mathematical ability. Computer programming on time-shared computer systems was included in the curriculum both for its own importance and for understanding numerical methods. The first course introduced flow charts and the notion of algorithms . The beginning portion of the fourth-year course was devoted to introducing the BASIC programming language, with an emphasis on fundamental control flow statements, continued use of flow charts for design, and numerical programming applications. Interactive teletype interfaces on slow and erratic dial-up connections , with troublesome paper tape for offline storage,
315-424: A core of fundamental concepts and structures common to all. For example, as the courses progressed, the concept of mappings was used to describe, and visually illustrate, the traditionally disparate topics of translation , line reflection , probability of an event , trigonometric functions , isomorphism and complex numbers , and analysis and linear mappings . Traditional subjects were broken up, such that
378-628: A couple of high schools) in the United States. Fehr did not do much curriculum development himself, but rather recruited and led the others and organized the whole process. Graduate students from the Department of Mathematical Education at Teachers College also served each year in various capacities on the SSMCIS program. The central idea of the program was to organize mathematics not by algebra, geometry, etc., but rather to unify those branches by studying
441-499: A major concern of parents and students and teachers. A 1973 report compared the test performance of such students with those from traditional mathematics curricula. It found that the SSMCIS students did better on the mathematics portion of the Preliminary Scholastic Aptitude Test (PSAT) , even when matched for background and performance on the verbal portion. It also found that SSMCIS students did just as well on
504-479: A mark is made when a dead key is typed but, unlike normal keys, the paper carriage does not move on and thus the next letter to be typed is printed under the accent. The ^ symbol was originally provided in typewriters and computer printers so that circumflex accents could be overprinted on letters (as in ô or ŵ ). The incorporation of the circumflex symbol into ASCII is a consequence of this prior existence on typewriters: this symbol did not exist independently as
567-441: 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 Minicomputer is designed to represent a single decimal digit, and multiple Minicomputers 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 Minicomputer's squares – placed to the left of the first – will represent 10, 20, 40, and 80;
630-463: A single topic to study until mastered. The curriculum introduced many basic concepts such as fractions and integers earlier than normal. Later in the project's development, new content in probability and geometry was introduced. The curriculum contained a range of supporting material including story books with mathematical problems, with lessons often posed in a story, designed to feature both real world and fantasy situations. One character in these books
693-569: 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. Students are instructed to represent values on the Minicomputers 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
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#1733086196154756-412: Is a 2 by 2 grid of squares, with the quarters representing the numbers 1, 2, 4, and 8. Checkers can 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 Minicomputer 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,
819-648: Is a description of the K–6 program that was designed for a general, heterogeneous audience. The CSMP project was established in 1966, under the direction of Burt Kaufman, who remained director until 1979, succeeded by Clare Heidema. It was originally affiliated with 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
882-498: Is currently held by McREL International. Burt Kaufman, a mathematics curriculum specialist, headed the team at Southern Illinois University writing CSMP. In July 1993, he started the Institute for Mathematics and Computer Science (IMACS) with his son and two colleagues. IMACS uses elements of the EM and CSMP programs in their "Mathematics Enrichment" program. For instance, Minicomputers and "Eli
945-453: Is lacking') is the name used familiarly for the character ^ provided on most QWERTY keyboards by typing ⇧ Shift + 6 . The symbol has a variety of uses in programming and mathematics. The name "caret" arose from its visual similarity to the original proofreader's caret , ‸ , a mark used in proofreading to indicate where a punctuation mark, word, or phrase should be inserted into a document. The ASCII standard (X3.64.1977) calls it
1008-469: Is the method return statement. In C++/CLI , .NET reference types are accessed through a handle using the ClassName^ syntax. In Apple's C extensions for Mac OS X and iOS, carets are used to create blocks and to denote block types. Go uses it as a bitwise NOT operator. Node.js uses the caret in package.json files to signify dependency resolution behavior being used for each particular dependency. In
1071-428: Is typically called a caret. It can signify exponentiation , the bitwise XOR operator, string concatenation , and control characters in caret notation , among other uses. In regular expressions , the caret is used to match the beginning of a string or line; if it begins a character class, then the inverse of the class is to be matched. ANSI C can transcribe the caret in the form of the trigraph ??' , as
1134-445: 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
1197-602: The Bourbaki group 's work in France in the 1930s and the Synopses for Modern Secondary School Mathematics published in Paris in 1961. Indeed, most European secondary schools were teaching a more integrated approach. Also, this was one of several American efforts to address a particularly controversial issue, the teaching of a full year of Euclidean geometry in secondary school. Like many of
1260-542: The Mathematics Level II Achievement Test as traditional students taking college preparatory courses or, indeed, as college freshmen taking introductory calculus courses. Another study found SSMCIS students well prepared for the mathematics portion of the regular Scholastic Aptitude Test . However, SSMCIS developed slowly. Funding became an issue, and indeed it was never funded as well as some other mathematics curriculum efforts had been. Despite
1323-401: The U.S. Congress . As one of the participants in creating SSMCIS, James T. Fey of Teachers College, later wrote, "Schools and societal expectations of schools appear to change very slowly." In the end, SSMCIS never became widely adopted. One SSMCIS student, Toomas Hendrik Ilves of Leonia High School , decades later became Foreign Minister and then President of Estonia . He credited
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#17330861961541386-677: 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, some staff of the Elements of Mathematics were also involved with the Secondary School Mathematics Curriculum Improvement Study program being. What follows
1449-628: 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. Including online courses, IMACS currently serves over 4,000 students across the U.S. and in over ten countries. CSMP is also used by some homeschooling families either as a core math program or for enrichment exercises. Secondary School Mathematics Curriculum Improvement Study The Secondary School Mathematics Curriculum Improvement Study (SSMCIS)
1512-461: The New Math . Many reform efforts had underestimated the difficulty of getting the public and the mathematics educational community to believe that major changes were really necessary, especially for secondary school programs where college entrance performance was always the key concern of administrators. Federal funding for curriculum development also came under attack from American conservatives in
1575-572: The SSMCIS course, the early exposure it gave him to computer programming, and the teacher of the course, Christine Cummings, with his subsequent interest in computer infrastructure, which in part resulted in the country leaping over its Soviet -era technological backwardness; computer-accessible education became pervasive in Estonian schools , and the Internet in Estonia has one of the highest penetration rates in
1638-473: The SSMCIS program began in 1965 and took place mainly at Teachers College. Fehr was the director of the project from 1965 to 1973. The principal consultants in the initial stages and subsequent yearly planning sessions were Marshall H. Stone of the University of Chicago , Albert W. Tucker of Princeton University , Edgar Lorch of Columbia University , and Meyer Jordan of Brooklyn College . The program
1701-407: The arrow usage, it can also mean that the user who posted the ^ agrees with the above post. Multiple carets may be used to indicate that the comment is replying to, or relating to, the post above that correlates with the number of carets used, or to "underscore" the correct portion of the previous post, or simply for emphasis. A similar use has been adopted by programming language compilers , such as
1764-403: The caret to escape reserved characters (most other shells use the backslash ). For example, to pass a 'less-than' sign as an argument to a program, one would type ^< . In internet forums , on social networking sites such as Facebook, or in online chats , one or more carets may be used beneath the text of another post, representing an upward-pointing arrow to that post; in addition to
1827-492: The case of Node.js, a caret allows any kind of update, unless it is seen as a "major" update as defined by semver . In mathematics , the caret can signify exponentiation (e.g. 3^5 for 3 ) where the usual superscript is not readily usable (as on some graphing calculators ). It is also used to indicate a superscript in TeX typesetting. The use of the caret for exponentiation can be traced back to ALGOL 60 , which expressed
1890-404: The character was originally not available in all character sets and keyboards. C++ additionally supports tokens like xor (for ^ ) and xor_eq (for ^= ) to avoid the character altogether. RFC 1345 recommends that the character be transcribed as digraph '> when required. Pascal uses the caret for declaring and dereferencing pointers . In Smalltalk , the caret
1953-399: The course material for each year included some material related to algebra, some to geometry, and so forth. Even when abstract concepts were being introduced, they were introduced in concrete, intuitive forms, especially at the younger levels. Logical proofs were introduced early on and built in importance as the years developed. At least one year of university-level mathematics education
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2016-408: The curriculum was developed by eighteen mathematicians from the U.S. and Europe in 1966 and subsequently refined in experimental course material by mathematical educators with high school level teaching experience. By 1971, some thirty-eight contributors to course materials were identified, eight from Teachers College, four from Europe, one from Canada, and the rest from various other universities (and
2079-618: The early 1960s and by the Cambridge Conference on School Mathematics (1963), which also inspired the Comprehensive School Mathematics Program . There were some interactions among these initiatives in the early stages, and the development of SSMCIS was part of a general wave of cooperation in the mathematics education reform movement between Europe and the U.S. "The construction is to be free of any restrictions of traditional content or sequence." Work on
2142-454: The exponentiation operator as an upward-pointing arrow, intended to evoke the superscript notation common in mathematics. The upward-pointing arrow is now used to signify hyperoperations in Knuth's up-arrow notation . It is often seen in caret notation to show control characters: for instance, ^A means the control character with value 1. The Windows command-line interpreter ( cmd.exe ) uses
2205-433: The federal funding source, there was no centralized, national focal point in the U.S. for curriculum changes – such as some European countries had – and that made adoption of SSMCIS innovations a harder task. By the mid-1970s there was a growing backlash against the "New Math" movement, spurred in part by a perceived decline in standardized test scores and by Morris Kline 's critical book Why Johnny Can't Add: The Failure of
2268-433: The fundamental concepts of sets , relations , operations , and mappings , and fundamental structures such as groups , rings , fields , and vector spaces . Other terms used for this approach included "global" or "integrated"; Fehr himself spoke of a "spiral" or "helical" development, and wrote of "the spirit of global organization that is at the heart of the SSMCIS curriculum – important mathematical systems unified by
2331-465: 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 Minicomputer 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
2394-501: The late 1960s and early 1970s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College who was internationally known and had published numerous mathematics textbooks and hundreds of articles about mathematics teaching. In 1961 he had been the principal author of the 246-page report "New Thinking in School Mathematics", which held that traditional teaching of mathematics approaches did not meet
2457-555: 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 4s with an 8. 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 students were assessed according to The Mathematics Applied to Novel Situations (MANS) tests, introduced to measure students' ability to problem solve in novel situations. Copyright
2520-463: 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
2583-420: The mathematics education literature would cite it in subsequent years, including references to it as a distinct, and the most radical, approach to teaching geometry; as using functions as a unifying element of teaching mathematics; and as its course materials having value when used as the vehicle for further research in mathematics education. Caret Caret (from Latin caret 'there
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2646-493: The more radical of the reform efforts lumped under the "New Math" label. Moreover, Fehr believed that the SSMCIS could not just improve students' thinking in mathematics, but in all subjects, by "develop[ing] the capacity of the human mind for the observation, selection, generalization, abstraction, and construction of models for use in the other disciplines." The course books put out by SSMCIS were titled Unified Modern Mathematics , and labeled as Course I through Course VI, with
2709-447: The national educational laboratories funded at that time by the U.S. Office of Education. In 1984, the project moved to Mid-continental Research for Learning (McREL) Institute's Comprehensive School Reform program, who supported the program until 2003. Heidema remained director to its conclusion. In 1984, it was implemented in 150 school districts in 42 states and about 55,000 students. The CSMP project employs four non-verbal languages for
2772-479: The needs of the new technical society being entered into or of the current language of mathematicians and scientists. Fehr considered the separation of mathematical study into separate years of distinct subjects to be an American failing that followed an educational model two hundred years old. The new curriculum was inspired by the seminar reports from the Organisation for Economic Co-operation and Development in
2835-831: The next with their students, and so it was typical for students to have one of the same two teachers, or even the same teacher, for five or six years in a row. More teachers were added in 1968 and 1969 and the University of Maryland and University of Arizona were added as teaching sites. Eighteen schools in Los Angeles adopted SSMCIS in what was called the Accelerated Mathematics Instruction program; some 2,500 gifted students took part. By 1971, teacher education programs were being conducted in places like Austin Peay State University in Tennessee , which
2898-399: The others, it did this by teaching geometric transformations as a unifying approach between algebra and geometry. Regardless of all these influences and other projects, the SSMCIS study group considered its work unique in scope and breadth, and Fehr wrote that "nowhere [else] had a total 7–12 unified mathematics program been designed, produced, and tested." It was thus considered one of
2961-409: The public domain for any organization to use. The pages of the books were formatted by typewriter, augmented by some mathematical symbols and inserted graphs, bound in paper, and published by Teachers College itself. A more polished hardcover version of Courses I through IV was put out in subsequent years by Addison-Wesley ; these were adaptations made by Fehr and others and targeted to students with
3024-545: 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
3087-610: The standard Regents Examinations due to a mismatch in curriculum. However, SSMCIS was one of the direct inspirations for the New York State Education Department , in the late 1970s and 1980s, adopting an integrated, three-year mathematics curriculum for all its students, combining algebra, geometry, and trigonometry with an increased emphasis in probability and statistics. Given the differences in subject matter and approach, how SSMCIS-taught students would perform on College Entrance Examination Board tests became
3150-512: The symbol is encoded as U+005E ^ CIRCUMFLEX ACCENT ; in HTML it may be used directly or inserted with ^ . The combining character for use as a diacritic is U+0302 ◌̂ COMBINING CIRCUMFLEX ACCENT , although precomposed characters (like U+00E2 â LATIN SMALL LETTER A WITH CIRCUMFLEX ) are available for most European languages. The symbol ^ has many uses in programming languages , where it
3213-444: The two volumes in each year labeled as Part I and Part II. Materials for the next year's course were prepared each year, thus keeping up with the early adoption programs underway. Using largely formative evaluation methods for gaining teacher feedback, revised versions were put out after the first year's teaching experience. By 1973, the revised version of all six courses had been completed. The first three volumes were put into
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#17330861961543276-427: 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
3339-421: The world. As his tenure as president came to a close in 2016, Ilves visited his old school building with Cummings and said, "I owe everything to her. Because of what she taught us, my country now uses it." Cummings said that SSMCIS not only introduced beginning computer programming but also taught students "how to think". SSMCIS did represent a productive exercise in thinking about mathematics curriculum, and
3402-459: Was Eli the Elephant, a 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 . One device used throughout the program was the Papy Minicomputer , named after Frédérique Papy-Lenger – the most influential figure to the project – and her husband Georges Papy. A Minicomputer
3465-714: Was attended by junior high school teachers from seventeen states and one foreign country. By 1974, Fehr stated that 25,000 students were taking SSMCIS courses across the U.S. The Secondary School Mathematics Curriculum Improvement Study program did show some success in its educational purpose. A study of the Los Angeles program found that SSMCIS-taught students had a better attitude toward their program than did students using School Mathematics Study Group courses (another "New Math" initiative) or traditional courses. In New York State schools, special examinations were given to tenth and eleventh grade SSMCIS students in lieu of
3528-673: Was incorporated into the later courses. Solving traditional applications problems was de-emphasized, especially in the earlier courses, but the intent of the project was to make up for that with its focus on real numbers in measurements, computer programming, and probability and statistics. In particular, the last of these was a pronounced element of the SSMCIS, with substantial material on it present in all six courses, from measures of statistical dispersion to combinatorics to Bayes' theorem and more. The curriculum that SSMCIS devised had influences from earlier reform work in Europe, going back to
3591-467: Was no decline in performance due to the unusual organization of material. Some 400 students were involved in this initial phase. Because the program was so different from standard U.S. mathematics curricula, it was quite difficult to students to enter after the first year; students did, however, sometimes drop out of it and return to standard courses. As teaching the program was a specialized activity, teachers tended to move along from each grade to
3654-468: Was no middle school then), called the program "Math X" for experimental, with individual courses called Math 8X, Math 9X, etc. Hunter College High School used it as the basis for its Extended Honors Program; the school's description stated that the program "includes many advanced topics and requires extensive preparation and a considerable commitment of time to the study of mathematics." Students were periodically given standardized tests to make sure there
3717-527: Was not always supported well by printers, and was almost never possible on video terminals. Instead, precomposed characters were eventually created to show the accented letters. The freestanding circumflex (which had come to be called a caret) quickly became reused for many other purposes, such as in computer languages and mathematical notation. As the mark did not need to fit above a letter any more, it became larger in appearance such that it can no longer be used to overprint an accent in most fonts. In Unicode
3780-484: Was targeted at the junior high and high school level and the 15–20 percent best students in a grade. Funding for the initiative began with the U.S. Office of Education and covered the development of the first three courses produced; the last three courses produced, as well as teacher training, were funded by the National Science Foundation and by Teachers College itself. The scope and sequence of
3843-418: Was the name of an American mathematics education program that stood for both the name of a curriculum and the name of the project that was responsible for developing curriculum materials. It is considered part of the second round of initiatives in the " New Math " movement of the 1960s. The program was led by Howard F. Fehr, a professor at Columbia University Teachers College . The program's signature goal
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#17330861961543906-583: Was the typical physical environment. Starting in 1966, teachers from nine junior high and high schools, mostly in the New York metropolitan area , began getting training in the study program at Teachers College. Such training was crucial since few junior high or high school teachers knew all the material that would be introduced. They then returned to their schools and began teaching the experimental courses, two teachers per grade. For instance, Leonia High School , which incorporated grades 8–12 (since there
3969-649: Was to create a unified treatment of mathematics and eliminate the traditional separate per-year studies of algebra , geometry , trigonometry , and so forth, that was typical of American secondary schools. Instead, the treatment unified those branches by studying fundamental concepts such as sets , relations , operations , and mappings , and fundamental structures such as groups , rings , fields , and vector spaces . The SSMCIS program produced six courses' worth of class material, intended for grades 7 through 12, in textbooks called Unified Modern Mathematics . Some 25,000 students took SSMCIS courses nationwide during
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