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1. What's Happening in the Mathematical Sciences, 1993-1994.

Author

American Mathematical Society, Providence, RI. and Cipra, Barry

Abstract

This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous year or so. Mathematics is constantly growing and changing, reaching out to other areas of science and helping to solve some of the major problems facing society. Volumes 1 and 2 survey some of the important developments in the mathematical sciences over the past year or so. The contents of volume 1 are: (1) "Equations Come to Life in Mathematical Biology"; (2) "New Computer Insights from 'Transparent' Proofs"; (3) "You Can't Always Hear the Shape of a Drum"; (4) "Environmentally Sound Mathematics"; (5) "Disproving the Obvious in Higher Dimensions"; (6) "Collaboration Closes in on Closed Geodesics"; (7)"Crystal Clear Computations"; (8) "Camp Geometry"; (9) "Number Theorists Uncover a Slew of Prime Impostors"; and (10) "Map-Coloring Theorists Look at New Worlds." The contents of volume 2 are: (1) "A Truly Remarkable Proof" (Fermat's Last Theorem); (2) "From Knot to Unknot"; (3) "New Wave Mathematics"; (4) "Mathematical Insights for Medical Imaging"; (5) "Parlez-vous Wavelets?" (6) "Random Algorithms Leave Little to Chance"; (7) "Soap Solution"; (8) "Straightening Out Nonlinear Codes"; (9) "Quite Easily Done"; and (10) "(Vector) Field of Dreams." (MKR)

Published
1993

3. 27% Probable: Estimating Whether or Not Large Numbers Are Prime.

Author

Bosse, Michael J.

Abstract

This brief investigation exemplifies such considerations by relating concepts from number theory, set theory, probability, logic, and calculus. Satisfying the call for students to acquire skills in estimation, the following technique allows one to "immediately estimate" whether or not a number is prime. (MM)

Published
2001

4. Theory-Based Interactive Mathematics Instruction: Development and Validation of Computer-Video Modules.

Author

California Univ., Santa Cruz. and Henderson, Ronald W.

Abstract

Theory-based prototype computer-video instructional modules were developed to serve as an instructional supplement for students experiencing difficulty in learning mathematics, with special consideration given to students underrepresented in mathematics (particularly women and minorities). Modules focused on concepts and operations for factors, prime numbers, and fractions. Task analysis and demand specification procedures were used to sequence instructional objectives within and across topics. Cognitive social theory provided a framework for the incorporation of attentional, retentional, and motivational variables into the video sequences. Results of field trials show that the modules were effective in teaching/reteaching mathematical skills/concepts to secondary school students who had not made normal progress in mathematical learning. In the first trial, students who used materials gained a significant advantage over control subjects in skills/concepts involving factors and prime numbers. The pattern of gains attributable to these modules was replicated in a second trial, but without a control group. Comparable effects were also found to be associated with use of fractions modules, but these results should be interpreted with caution because of lack of a control group. Additional results indicate that the interactive computer-video modules had a beneficial effect on affective as well as cognitive outcomes. (JN)

Published
1983

5. Prime Numbers. Topical Module for Use in a Mathematics Laboratory Setting.

Author

Regional Center for Pre-Coll. Mathematics, Denver, CO. and Snyder, Pat

Abstract

The purpose of this module is to acquaint students with the terms prime, composite, and factor. This is done by offering a definition of each term, then reinforcing its meaning through activities. (Author/MK)

Published
1974

6. NCTM Student Math Notes.

Author

National Council of Teachers of Mathematics, Inc., Reston, VA., Maletsky, Evan, and Yunker, Lee E.

Abstract

Five sets of activities for students are included in this document. Each is designed for use in junior high and secondary school mathematics instruction. The first Note concerns mathematics on postage stamps. Historical procedures and mathematicians, metric conversion, geometric ideas, and formulas are among the topics considered. Successful simulation is the focus of the second Note, with activities on planning a supermarket, bowling and random digits, and other suggestions for using a random digit table. The third set of activities concerns proof; geometric, algebraic, and numerical formulas are each considered. Golden rectangles and ratios are included in the fourth topic, with a physical model for generating golden rectangles, directions for constructing a golden rectangle and generating golden ratios via Logo, and comments on the divine proportion. Finally, the fifth Note concerns primes, and includes work with the Sieve of Eratosthenes, twin primes, and other problems. (MNS)

Published
1986

7. A Specific Calculating Ability.

Author

Anderson, Mike, O'Connor, Neil, and Hermelin, Beate

Abstract

Studied the calculating ability used by a low IQ savant to identify prime numbers in two experiments comparing him to control subjects, one involving reaction time and the other involving inspection time. Concludes that this individual uses a complex computational algorithm to identify primes and discusses the apparent contradiction of his low IQ. (SLD)

Published
1998

8. The Art of Questions and Discovery.

Author

Sandel, Daniel H.

Abstract

The discovery method, according to the author, promotes logical thinking, is motivational in nature, makes learning more permanent, produces more usable knowledge, and gets students actively involved. A discovery lesson is characterized by the following: (1) the concept to be learned is not announced, (2) experiences and activities are developed which involve the concepts to be learned, (3) the ideas are given names, (4) definitions are generated, (5) pupils are actively involved, (6) practice experiences are provided and disguised to some extent, and (7) questions are raised to provoke additional thought. These points are illustrated with an example discovery lesson on prime numbers. (JG)

Published
1971

9. Mathematical Structures 1, Mathematics (Experimental): 5211.21

Author

Dade County Public Schools, Miami, FL., Gordon, Marjorie, and Wilson, Pamela

Abstract

This is the first of two guidebooks for Grade 7 recommended to build fundamental concepts necessary for success in algebra. Topics covered include numeration systems, operations in non-decimal bases, whole numbers, factors and primes, and fractions. Goals for the course are stated, then, for each topic, performance objectives, a course outline, references, and suggested teaching strategies are provided. Posttest items are included, along with a list of twelve references. For the second guidebook in this series, see ED 067 293. (DT)

Published
1972

10. Basic Math I, Package 01-04, Factoring, Prime Numbers and Divisibility.

Author

Arnold Public Schools, NE., Thompson, Russ, and Fuller, Albert

Abstract

This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for each topic area and guided to materials written for a given topic. Three short criterion tests are included for each topic covered. The work for this package covers prime numbers, prime factorization, number multiples, least common multiple, and tests for divisibility. This work was prepared under an ESEA Title III contract. (JP)

Published
1972

11. Mathematics, Grade 8, De Soto Parish Curriculum Guide.

Author

DeSoto Parish School Board, Mansfield, LA. and Sanders, Marguerite

Abstract

This guide is designed to aid the teacher in planning and teaching an eighth-grade mathematics course which should strengthen the student's understanding of the basic structure of mathematics through experience with and appreciation of abstract concepts. Thirteen units outlined are entitled: Numeration Systems; Natural Numbers and Zero; Integers; Equations; Writing and Solving Equations; Factoring and Prime Numbers; Rational Numbers; Ratio-Proportion-Percent; Points, Lines and Planes; Measurement; Construction; Perimeter-Area-Volume; and Linear Metric Measure. Behavioral objectives are listed for each unit. Aims, suggested materials and methods, and teaching techniques are written for each lesson. (JP)

Published
1971

12. An Introduction to the Theory of Numbers for Elementary School Teachers.

Author

Michigan Univ., Ann Arbor. and Beougher, Elton D.

Abstract

This is one of a series of units intended for both preservice and inservice elementary school teachers to satisfy a need for materials on "new mathematics" programs which (1) are readable on a self basis or with minimal instruction, (2) show the pedagogical objectives and uses of such mathematical structural ideas as the field axioms, sets, and logic, and (3) relate mathematics to the "real world," its applications, and other areas of the curriculum. This unit explores with teachers fundamental concepts involving number theory. Chapter 1 answers questions concerning the meaning of theory of numbers and why it should be studied in elementary school mathematics. Chapter 2 deals with various subsets of the whole numbers such as even numbers, odd numbers, prime numbers, composite numbers, and factorization. Chapter 3 presents elementary notions on the greatest common divisor and least common multiple. Chapter 4 introduces to the elementary teacher some enrichment topics from number theory. (RP)

Published
1966

13. Junior High School Mathematics Units, Volume I, Number Systems. Commentary for Teachers.

Author

Stanford Univ., CA. School Mathematics Study Group.

Abstract

This is volume one of a three-volume set for teachers using SMSG junior high school text materials. Each unit contains a commentary on the text, answers to all the exercises, a copy of the questionnaire used for evaluating the material, and a summary of comments by the teachers using the text. Unit topics include: (1) numeration; (2) natural numbers and zero; (3) factoring and primes; (4) supplementary tests for divisibility and repeating decimals; (5) non-negative rational numbers; and (6) mathematical systems. (MP)

Published
1959

14. Mathematics for the Elementary School, Grade 5, Student's Text, Part I, Unit No. 29. Revised Edition.

Author

Stanford Univ., CA. School Mathematics Study Group. and Beatty, Leslie

Abstract

This is part one of a two-part SMSG elementary school text for fifth-grade students. The content is aimed at the development of some of the fundamental concepts of mathematics such as number, numeration, the operations of arithmetic, and intuitive geometry. Chapter topics include extending systems of numeration, factors and primes, extending multiplication and division, and congruence of common geometric figures. (MP)

Published
1962

15. Junior High School Mathematics Units, Volume I, Number Systems.

Author

Stanford Univ., CA. School Mathematics Study Group.

Abstract

This is volume one of a three-volume SMSG junior high school mathematics text. This volume contains units concerned with the structure of the number systems of arithmetic. Unit topics include: (1) numeration; (2) natural numbers and zero; (3) factoring and primes; (4) supplementary tests for divisibility and repeating decimals; (5) the non-negative rational numbers; and (6) mathematical systems. (MP)

Published
1959

16. Reprint Series: Prime Numbers and Perfect Numbers. RS-2.

Author

Stanford Univ., CA. School Mathematics Study Group. and Schaaf, William L.

Abstract

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the prime numbers; (2) mathematical sieves; (3) the factorgram; and (4) perfect numbers. (MP)

Published
1966

17. Supplementary and Enrichment Series: Factors and Primes. SP-17.

Author

Stanford Univ., CA. School Mathematics Study Group. and Syer, Henry W.

Abstract

This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series is designed to make material for the study of topics of special interest to students readily accessible in classroom quantity. Topics covered include primes, factors, divisibility, greatest common factor, least common multiple, Robinson's Results, and Proth's Theorem. (MP)

Published
1965

18. Supplementary and Enrichment Series: Factors and Primes. Teachers' Commentary. SP-18.

Author

Stanford Univ., CA. School Mathematics Study Group. and Syer, Henry W.

Abstract

This is one in a series of manuals for teachers using SMSG high school supplementary materials. The pamphlet includes commentaries on the sections of the student's booklet, answers to the exercises, and sample test questions. Topics covered include factors and primes, perfect numbers, divisibility, expanded notation, repeating decimals, number systems in other bases, common factors, and common multiples. (MP)

Published
1965

19. Mathematics, Book S. Teacher Guide.

Author

Southwest Educational Development Corp., Austin, TX.

Abstract

This book is the teacher's manual to a text designed to meet the particular needs of those children who have "accumulated discouragements" in learning mathematics. It is a manual of suggested teaching strategies and additional materials aimed at compensating for past student failures to understand mathematical concepts. This book, S, is designed for the common seventh-grade mathematics program. Individual chapter titles are: The Basic Operations: A Different Look; Geometry; and Factors and Primes. (MP)

Published
1970

20. Mathematics, Book S. Student Edition.

Author

Southwest Educational Development Corp., Austin, TX.

Abstract

This book is intended to make common seventh-grade mathematical concepts both interesting and easy to understand. The text is designed to meet the particular needs of those children who have "accumulated discouragements" in learning mathematics. The reading level required of pupils has been reduced. Individual chapter titles are: The Basic Operations: A Different Look; Geometry; and Factors and Primes. (MP)

Published
1970

21. A Brief Course in Mathematics for Junior High School Teachers, Part 2. Revised Edition.

Author

Stanford Univ., CA. School Mathematics Study Group. and Maletsky, Evan M.

Abstract

This is part two of a two-part School Mathematics Study Group (SMSG) textbook. The text serves as a means to prepare teachers to teach the SMSG text "Mathematics for Junior High School." The eight chapters found in part two are: (1) Primes and Factors; (2) Decimals, Ratios, and Percents; (3) The Real Number System; (4) Non-Metric Geometry, I; (5) Non-Metric Geometry, II; (6) Measurement; (7) Perimeters, Areas, Volumes; and (8) Descriptive Statistics and Probability. (MK)

Published
1965

22. The Arithmetic Project Course for Teachers - 7. Topic: Lower Brackets. Supplement: Using Centimeter Blocks to Introduce Prime Numbers to a Third Grade.

Author

Education Development Center, Inc., Newton, MA. and Illinois Univ., Urbana.

Abstract

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being taught to classes of children, extensive discussion notes, and detailed guides for correcting written lessons. This booklet contains exercises on the use of lower brackets, a summery of the problems in the film "Lower and Upper Brackets," and the supplement. (MK)

Published
1973

23. Media Clips.

Author

Lancaster, Ron and Marion, Charlie

Abstract

Contains 10 miscellaneous mathematics questions and their answers that teachers can use in their lessons. Topics include estimation, prime numbers, line equations, and investment strategies. (ASK)

Published
1996

24. Prime Number Identification in Idiots Savants: Can They Calculate Them?

Author

Welling, Hans

Abstract

The ability of some individuals with mental retardation to identify prime numbers despite their lack of necessary arithmetical skills is discussed. The article suggests that a distinction between prime and nonprime numbers can be made by utilizing the tendency of visual perception to be symmetrically organized. (Author/DB)

Published
1994

25. Old Glory: A Practical Investigation into Pattern.

Author

Selkirk, Keith

Abstract

Suggests that there is sufficient interest in the changing arrangements of stars in the flag of the United States over the years to introduce a mathematical investigation into the various possible patterns of stars. (Author/JJK)

Published
1992

26. The Bursting of the Dam (Infinite Sets, Countable and Otherwise).

Author

Francis, Richard L.

Abstract

Examines infinite sets and cardinality classifications of empty, finite but not empty, and infinite through discussions of numbers that fall into particular categories. Categories discussed include perfect numbers, Mersenne primes, pseudoprimes, and transcendental numbers. Discusses the Null Or Infinite Set Effect (NOISE) and infinitude resulting from generation patterns. (MDH)

Published
1992

28. It All Depends What You Mean by 'Able.'

Author

Gardiner, Tony

Abstract

Proposed is a way for teachers to distinguish between rich, challenging material that encourages mathematical thinking and material that is unsuitable. Included are multistep problems that encourage a broader understanding of mathematics. (KR)

Published
1990

29. On the Distribution of Primes.

Author

Johnson, John M.

Abstract

Discusses the distribution of primes and focuses directly on one particular recurring pattern among them. (Author/NB)

Published
2003

31. Privacy for the Twenty-First Century: Cryptography.

Author

Petras, Richard T.

Abstract

Introduces RSA, one of the most popular public-key cryptosystems that is used to protect the privacy of computer users. Describes the mathematical foundation of public key cryptography. (KHR)

Published
2001

32. The Dating Game.

Author

Zerger, Monte J.

Abstract

Presents activities to cultivate the tendency to see special qualities in numbers that can be played on certain calendar days. Includes games on the constant of the day, Fibonacci and golden ratio dates, primes, powers, December 25, and the day of the year. (ASK)

Published
1998

33. Ryan's Primes.

Author

Juraschek, Bill and Evans, Amy S.

Abstract

Presents a teacher's journal that describes a third-grader's investigation of prime numbers including his communications with a university faculty member. (JRH)

Published
1997

34. Extending the Number Line to Make Connections with Number Theory.

Author

Graviss, Tom and Greaver, Joanne

Abstract

Shares a coded version of the number line to provide concrete experiences for learning abstract concepts. Using the fundamental theorem of arithmetic, appropriate coded symbols are determined for the prime factorization of each natural number and used to study the concepts of greatest common divisor, least common multiple, square roots, and exponents. (MDH)

Published
1992

35. Playway Mathematics: Theory, Practice and Some Results.

Author

Rogers, P. J. and Miller, J. Valarie

Abstract

The use of play as a means of teaching elementary mathematics is discussed. Earlier work is summarized and fresh results offered, particularly those concerned with the retention and transfer of play-acquired learning. The mathematical content chosen (factor, multiple, prime number, common factor, prime factor, and factorizing) is discussed. (CT)

Published
1984

37. Ideas.

Abstract

Activities are presented that focus on attributes of numbers. The activities highlight such attributes as more than, equal to, greater than, less than, LCM, prime and factor. The activities provide practice in motivational game-oriented situations. (RH)

Published
1987

38. Building Understanding with Blocks.

Author

Beattie, Ian D.

Abstract

A series of nine activities that illustrate prime factorization and other elementary number theory ideas in concrete, representative, and symbolic form are described. (MNS)

Published
1986

39. The Number Phoenix: A Summer Awakening.

Author

Kuhn, Stephen W.

Abstract

Describes a three-week summer course for academically talented high school students which explored the integers and some classical topics from number theory. (PK)

Published
1988

40. Stimulating Presentation of Theorems Followed by Responsive Proofs.

Author

Movshovitz-Hadar, Nitsa

Abstract

Several ways to present two theorems (concerning a square matrix and a property of prime numbers) are demonstrated. One way for each theorem is more stimulating, better setting the stage for the proofs. Several methods of presenting proofs are illustrated, with the outcomes considered from the learner's viewpoint. (MNS)

Published
1988

41. Divisor Lattices and the Teaching of GCD and LCM

Author

Miller, Ann

Abstract

Divisibility facts, greatest common divisors, least common multiples, and relative primes are explored through the use of lattice diagrams. (JT)

Published
1977

42. IDEAS

Author

Bright, George W.

Abstract

Two ideas to use as a bulletin board display as an activity center, or as worksheets emphasizing whole number concepts are described. (JT)

Published
1978

43. Mathematical Games

Author

Gardner, Martin

Abstract

A sequence of numbers from combinatorial theory called the Bell numbers is discussed, along with several problems and examples that demonstrate their usefulness. (MN)

Published
1978

44. Las Matematicas: Lenguaje Universal. Nivel 2c: Factores y Multiplos (Mathematics: A Universql Language. Level 2c: Factors and Multiples).

Author

Dissemination and Assessment Center for Bilingual Education, Austin, TX. and Fort Worth Independent School District, TX. Bilingual Education Program.

Abstract

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include factors, prime and composite numbers, divisibility, and exponents. (MK)

Published
1979

45. Some 'Prime' Comparisons.

Author

National Council of Teachers of Mathematics, Inc., Reston, VA., Brown, Stephen I., Brown, Stephen I., and National Council of Teachers of Mathematics, Inc., Reston, VA.

Abstract

Topics that deal with prime numbers are presented with the intent of allowing the student to re-create the excitement of the original investigation. Suitable for advanced high school students as an introduction to number theory at the college level or as a text for courses in teacher education, the book covers the following topics: (1) the number and generation of primes, (2) the determination and distribution of primes, (3) unique factorization, and (4) odd and even numbers. (MP)

Published
1978

46. A Pattern: Pascal's Triangle and Prime Numbers

Author

Duncan, David R. and Litwiller, Bonnie H.

Abstract

Illustrated are the discovery and verification of new patterns in Pascal's Triangle. Discovery activities appropriate for students when they are learning to expand binomials are provided. (JP)

Published
1975

48. Patterns From a Birthdate Chart

Author

Bernstein, Robert and Barson, Alan

Abstract

A chart is described which gives children an opportunity to discover prime and composite numbers and which leads to discussions of the associative and commutative laws, multiplication by 1, and powers and exponents. (DT)

Published
1974

50. Effects of Interactive Video/Computer Instruction on the Performance of Underachieving Students in Mathematics.

Author

Henderson, Ronald W.

Abstract

Two field trials were conducted to test the effectiveness of instructional materials, which were presented on an Apple II Plus microcomputer interfaced with a videocassette recorder, in teaching mathematical skills to students who had not made normal progress in mathematics learning. In the first field trial, 58 experimental students from a high school with a high proportion of Hispanic students participated in modules covering instruction in factors and prime numbers. A criterion-referenced pre- and posttest and a School Learning Questionnaire (SLQ) were administered to both the experimental students and to 43 control students. A second field trial retested the factors and prime numbers modules and provided a pilot test of a fractions module. The subjects were 11 volunteers from an alternative school remedial program for students who had failed to pass the basic skills competency test required for high school graduation. Pre- and posttests were again administered. The results of the field trials showed that the computer-video instructional modules were effective in teaching or reteaching mathematical skills to secondary school students. However, the hypothesis that exposure to the instructional materials would be reflected in an increase in effort attributions specific to mathematics was not supported. A 38-item bibliography accompanies this report. (ESR)

Published
1983

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