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Ross, Joan – Mathematics Teacher, 1978
The operation of rounding is shown to lead into an investigation of an abstract mathematical system. Properties of the system are discussed and graphs of the rounding function are drawn. Some questions for discussion are given. (MP)
Descriptors: Algebra, Discovery Learning, Graphs, Instruction

Minne, Nels; Johnson, Herbert N. – Mathematics Teacher, 1972
A theorem on divisibility in decimal and non-decimal numeration systems is developed; its use in a series of discovery-centered lessons is suggested. (DT)
Descriptors: Division, Induction, Instruction, Mathematics

Dubisch, Roy – Arithmetic Teacher, 1971
Descriptors: Elementary School Mathematics, Mathematical Concepts, Mathematics, Number Concepts
Henkin, Leon; Kessner, Arthur – 1969
Reports on the development of a course in modern mathematics for elementary school teachers. The subject matter for the course is concentrated on whole numbers, integers, and rational numbers. Ideas of logic and set theory are brought into the discussion incidently as needed for developing the number systems. Part 1 of the course is a brief essay…
Descriptors: Curriculum Development, Elementary School Teachers, Instructional Materials, Mathematics
Rosenfeld, Bob – MATYC Journal, 1978
An approach close to the original Greek geometric point of view regarding the question and proof of the irrationality of the square root of two is given. (MN)
Descriptors: College Mathematics, Geometry, Higher Education, History

English, Richard – Mathematics in School, 1985
Tests for divisibility in bases 2 through 10 are presented. Two strategies used by a group of fourth-year students are described. (MNS)
Descriptors: Elementary Education, Elementary School Mathematics, Learning Activities, Mathematics

Wyvill, Ron – Mathematics in School, 1973
Modular arithmetic is used to find the frequency of Friday 13th's in any year. (MM)
Descriptors: Arithmetic, Elementary School Mathematics, Mathematical Applications, Mathematics

Johnston, J. H. – Mathematics in School, 1972
After briefly presenting possible origins for the use of the decimal system for counting and the duodecimal (base twelve) system for many measures, a notational scheme using six positive'' digits and six negative'' digits is presented. Examples and algorithms using this set of digits for operations with whole numbers, fractions, and in…
Descriptors: Algorithms, Arithmetic, Mathematical Concepts, Mathematics

Dence, Thomas P. – Mathematics and Computer Education, 1983
Representation of integers in various bases is explored, with a proof. (MNS)
Descriptors: College Mathematics, Higher Education, Integers, Mathematics

Buck, R. Creighton – American Mathematical Monthly, 1980
The archaeology of mathematics is discussed by tracing a portion of the research of Otto Neugebauer and Abraham Sacks. Patterns found on an ancient cuneiform tablet are explored. (MK)
Descriptors: Archaeology, Higher Education, Mathematics, Mathematics Education
Len, Amy; Scott, Paul – Australian Mathematics Teacher, 2004
Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…
Descriptors: Foreign Countries, Number Concepts, Biographies, Algebra
Allen, Charles; And Others – 1970
Developed by a committee of the National Council of Teachers of Mathematics, this publication is designed to help teachers provide interesting and worthwhile learning opportunities for slow learners in grades five through eight. It employs a variety of teaching strategies, many not commonly known or practiced, which are particularly helpful with…
Descriptors: Arithmetic, Elementary School Mathematics, Instruction, Instructional Materials
Topics in Mathematics for Elementary School Teachers, Booklet Number 11, The System of Real Numbers.
Beckenbach, Edwin F.; And Others – 1968
This booklet has been written for elementary school teachers as an introductory survey of the real number system. The topics which are developed include the number line, infinite decimals, density, rational numbers, repeating decimals, irrational numbers, approximation, and operations on the real numbers. (RS)
Descriptors: Elementary School Mathematics, Elementary School Teachers, Mathematical Concepts, Mathematics

Johnson, R. W.; Waterman, M. S. – International Journal of Mathematical Education in Science and Technology, 1976
In a thesis written for the Doctor of Arts in Mathematics, the connection between Euclid's algorithm and continued fractions is developed and extended to n dimensions. Applications to computer sciences are noted. (SD)
Descriptors: Algorithms, College Mathematics, Computers, Doctoral Dissertations

Picard, Anthony J. – Mathematics Teacher, 1971
Descriptors: Congruence, Geometry, Graphs, Mathematical Concepts