The author argues that the idea of canonical elements provides a coherent relationship between equivalence relations, the basis of modern approaches to too many mathematical topics, and the traditional aspect of computation. Examples of equivalent relations, canonical elements, and their calculations are given. (MK)

There are two main claims in this article. First, that the classic pillars of engineering education, namely, traditional mathematics and differential equations, are merely a particular, if not old-fashioned, representation of a broader mathematical vision, which spans from Turing machine programming and symbolic productions sets to sub-symbolic…

Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less…

The transition to modern mathematics in the schools is described, and future changes are predicted. Problems which could develop with the current trends toward use of computers, calculators, multiple choice examinations, and new teaching materials are noted. (SD)

THE CURRICULUM CONSISTS OF FOUR MAJOR TOPICS--EQUATIONS, FUNCTIONS, GRAPHING, AND SIGNED NUMBERS. EACH TOPIC CAN BE INITIATED INDEPENDENTLY AND BUILT CUMULATIVELY THROUGHOUT THE ELEMENTARY SCHOOL GRADES. THE TOPICS ARE DEVELOPED LARGELY THROUGH GAMES AND/OR LESSONS DESIGNED TO HELP PUPILS DISCOVER "SECRET" PATTERNS OR DEVELOP TENTATIVE…

Described is the development of an approach to the algebra of real numbers which includes three areas of mathematics not commonly found in grade 9--the theory of limits of infinite sequences, a frequent use of Cartesian co-ordinates, and algebra of matrices. Seventy per cent of the course is abstract axiomatic algebra and the remaining portion…

The first part of Course III focuses on matrix algebra, graphs and functions, and combinatorics. Topics studied include: matrices and transformations, the solution of systems of linear equations, matrix multiplication, matrix inversion and a field of 2 x 2 matrices. The section on graphs and functions considers regions of the plane and…

The author describes the concept of Randolph diagrams (R-diagrams) which is a scheme for simplifying set-theoretic and/or logical expressions. Several applications of R-diagrams are presented. [Not available in hardcopy due to marginal legibility of original document.] (FL)

This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…

Assessed was the performance of subjects who had been exposed to transformational geometry treatment. The performance test consisted of geometry achievement and spacial ability measures. Second and third grade subjects were randomly assigned to experimental and control groups. The experimentals received a twelve lesson treatment and the controls a…

In this paper, the point of view is taken that matters of logic which are of principal concern in mathematics are those which deal with the validity of inferences rather than with the truth-values of the sentences being dealt with. Consequently, the author presents and exemplifies some of the most basic inference schemes. He states that knowledge…

This curriculum bulletin is the second part of "Mathematics--Pre-Kindergarten, Kindergarten, and Grade One." This is a developing curriculum program that incorporates the pre-kindergarten into the educational system and reorganizes mathematics materials in the early childhood years. The materials in this bulletin deal with numbers and operations…

Written to provide some basic information for parents about the New York State Elementary School Mathematics Program, this pamphlet briefly discusses techniques of number operations on the whole numbers, number systems, sets, and geometric concepts. (DT)