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Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon – Clearing House: A Journal of Educational Strategies, Issues and Ideas, 2016
Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.
Descriptors: Animals, Number Concepts, Mathematics, Mathematics Education
Katz, Karin Usadi; Katz, Mikhail G. – Educational Studies in Mathematics, 2010
The view of infinity as a metaphor, a basic premise of modern cognitive theory of embodied knowledge, suggests in particular that there may be alternative ways in which one could formalize mathematical ideas about infinity. We discuss the key ideas about infinitesimals via a proceptual analysis of the meaning of the ellipsis "..." in the real…
Descriptors: Number Systems, Epistemology, Mathematics Education, Evaluation
Rich, Andrew – College Mathematics Journal, 2008
The leftist number system consists of numbers with decimal digits arranged in strings to the left, instead of to the right. This system fails to be a field only because it contains zerodivisors. The same construction with prime base yields the p-adic numbers.
Descriptors: Number Systems, Mathematics, Number Concepts
Peralta, Javier – International Journal of Mathematical Education in Science and Technology, 2009
The general purpose of this article is to shed some light on the understanding of real numbers, particularly with regard to two issues: the real number as the limit of a sequence of rational numbers and the development of irrational numbers as a continued fraction. By generalizing the expression of the golden ratio in the form of the limit of two…
Descriptors: Numbers, Mathematics, Number Concepts, Number Systems
Cunningham, Clifton – College Mathematics Journal, 2008
An interesting number system is developed in the context of an encounter with alien culture. The resulting system has intriguing parallels and contrasts with our real number system.
Descriptors: Foreign Culture, Number Systems, Mathematics, Number Concepts
Kathota, Vinay – Mathematics Teaching, 2009
"The power of two" is a Royal Institution (Ri) mathematics "master-class". It is a two-and-a half-hour interactive learning session, which, with varying degree of coverage and depth, has been run with students from Year 5 to Year 11, and for teachers. The master class focuses on an historical episode--the Josephus…
Descriptors: Number Systems, Number Concepts, Pattern Recognition, Mathematics Instruction
White, Paul – Australian Mathematics Teacher, 2004
Bases such as 5 and 12 provide the same structural place value benefits as base 10. However, when numbers less than one are concerned, base 10 provides friendly decimals for the most common fractions of half, quarter, three-quarters. Base 5 is not user friendly at all in this regard. Base 12 would provide nice dozenimals(?) for the same…
Descriptors: Number Systems, Mathematics, Computation
Yan, S. Y.; James, G. – International Journal of Mathematical Education in Science & Technology, 2006
The modular exponentiation, y[equivalent to]x[superscript k](mod n) with x,y,k,n integers and n [greater than] 1; is the most fundamental operation in RSA and ElGamal public-key cryptographic systems. Thus the efficiency of RSA and ElGamal depends entirely on the efficiency of the modular exponentiation. The same situation arises also in elliptic…
Descriptors: Mathematics, Item Response Theory, Calculus, Multivariate Analysis
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

Olson, Melfried; Olson, Judith – School Science and Mathematics, 1988
Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)
Descriptors: Algorithms, Arithmetic, Elementary Education, Elementary School Mathematics

Robold, Alice I. – School Science and Mathematics, 1989
Discusses figurate number learning activities using patterns and manipulative models. Provides examples of square numbers, triangular numbers, pentagonal numbers, hexagonal numbers, and oblong numbers. (YP)
Descriptors: Mathematical Applications, Mathematics, Mathematics Instruction, Mathematics Materials

Anderson, Oliver D. – Mathematics and Computer Education, 1990
Discusses arithmetic during long-multiplications and long-division. Provides examples in decimal reciprocals for the numbers 1 through 20; connection with divisibility tests; repeating patterns; and a common fallacy on repeating decimals. (YP)
Descriptors: Arithmetic, Computation, Decimal Fractions, Division

Jean, Roger V.; Johnson, Marjorie – School Science and Mathematics, 1989
Describes properties of Fibonacci numbers, including the law of recurrence and relationship with the Golden Ratio. Discussed are some applications of the numbers to sewage of towns on a river bank, resistances in electric circuits, and leafy stems in botany. Lists four references. (YP)
Descriptors: College Mathematics, Higher Education, Mathematical Applications, Mathematical Concepts

Herman, Eugene A., Ed. – College Mathematics Journal, 1990
Describes a number sequence made by counting the occurrence of each digit from 9 to 0, catenating this count with the digit, and joining these numeric strings to form a new term. Presents a computer-aided proof and an analytic proof of the sequence; compares these two methods of proof. (YP)
Descriptors: College Mathematics, Computer Oriented Programs, Computer Software, Mathematical Concepts

Nicholson, A. R. – Mathematics in School, 1989
Presents examples of 3-by-3 and 4-by-4 magic squares. Proves that the numbers 1 to 10 can not be fitted to the intersections of a pentagram and that the sum of the 4 numbers on each line is always 22. (YP)
Descriptors: College Mathematics, Higher Education, Mathematical Applications, Mathematical Formulas
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