bluuebunny/crossref_metadata_2025 huggingface dataset:
Experimental Programs: NSF-FSU math campers: evaluations of and by campers
Authors: Nelson Williard H. , Smith Marion F. , Nichols Eugene D. , Kennedy Wallace A.
Published: January 2021

Thirty of the highest-scoring applicants from over the country were selected for the Third Summer Mathematics Camp which met in 1960 at FloridaState University. The six-week 1958 and 1959 institutes sponsored by the university and the National Science Foundation have been described by their director, Dr. Eugene Nichols.
Hobladic
Authors: Horton George W.
Published: January 2021

Here is a computer that you and your class can build at no cost.
A Pascal pyramid for trinomial coefficients
Authors: Rosenthal Evelyn B.
Published: January 2021

Some students enjoy the Pascal triangle. Do they know about a Pascal pyramid?
A solution for certain types of partitioning problems
Authors: Greenblatt M. H.
Published: January 2021

How can one use a 7-quart jug and an 11-quart jug to measure 2 quarts?
The co-ordinate system of Descartes
Authors: Read Cecil B.
Published: January 2021

It is becoming an increasingly common practice to introduce, at an early stage in mathematics education, a co-ordinate system and some elementary work in graphing.
Convention and revolt in mathematics
Authors: Taylor Angus E.
Published: January 2021

“In teaching mathematics and in choosing what mathematics to teach, there is something analogous to the play of opposing tendencies in literature and art.”
Application of the Pythagorean Theorem in the figure-cutting problem
Authors: Piwnicki Frank
Published: January 2021

A follow-up of an article on cutting figures appearing earlier in this journal
Group theory for school mathematics
Authors: Dean Richard A.
Published: January 2021

Some examples of groups found in our everyday mathematics and some theorems.
Regular polygons
Authors: Yates Robert C.
Published: January 2021

Complex numbers and regular polygons.
Historically Speaking,—: Understanding through number systems
Authors: Alien Harold Don
Published: January 2021

Ancient numerals, like dead languages, have lessons to teach, and a unit on the number systems of other times and places may provide the kind of enrichment which enhances understanding and appreciation of the simple, effective decimal system we employ. Roman numerals are introduced to all pupils, normally in the modified form in which they appear on clock faces, chapter headings, and engraved dates.
The equation
Authors: Swain Robert L.
Published: January 2021

A detailed treatment of the logic of a basic topic in secondary-school mathematics
Curves with corners
Authors: Perisho Clarence R.
Published: January 2021

The graphs of functions usually studied in algebra and analytical geometry are smooth, continuous curves, with no sharp corners or discontinuities. There is, however, a certain fascination about equations that represent curves with unusual characteristics. The absolute-value notation can be used to write equations for many common geometric figures1 and to simplify equations which involve the step function.2 Absolute-value notation can also be used to write the equations of graphs involving straight-line segments with any number of corners or vertices.
The changes taking place in mathematics
Authors: Adler Irving
Published: January 2021

Those who would improve mathematics teaching in the schools must keep turning their heads, now to look at mathematics, and now at the schools.
Topology: its nature and significance
Authors: Wilder R. L.
Published: January 2021

Modern mathematics emphasizes the study of patterns and structures, and one of the best examples of this emphasis is topology.
Joseph Moxon, mathematical practitioner
Authors: Hallerberg Arthur E.
Published: January 2021

The recent description [1]* of Joseph Moxon's Mathematicks Made Easie, the first mathematical dictionary (published in London in 1679), included a large number of interesting “definitions” of mathematical terms. The form and style of these statements have both historical and pedagogical value when examined by students who are interested in the role of definitions in mathematical structure.
Tips for Beginners: Using the overhead projector in teaching geometry
Authors: Unkrich Hannon
Published: January 2021

During the school year 1960-61, an experiment using an overhead projector in teaching geometry was conducted at Carl Hayden High School, Phoenix, Arizona.
The golden rectangle and Fibonacci sequence, as related to the Pascal triangle
Authors: Raab Joseph A.
Published: January 2021

Some enrichment ideas suitable for the advanced algebra class or the mathematics club
A problem in seventh-grade mathematics
Authors: Harner William A.
Published: January 2021

A reaction from a seventh-grade class to what seems to be a difficult problem for most junior high school pupils. The discussion is reproduced here as it happened.
The three faces of (—)
Authors: Williams Kenneth C.
Published: January 2021

Being able to present concepts clearly is of prime importance in good mathematics teaching. To this end, precise terminology plays a significant role. Whenever the terminology becomes ambiguous, there is the danger of misinterpretation. This is true especially for students of elementary algebra, where many important mathematical concepts are introduced.
Pascal's Triangle and Powers of 11
Authors: Morton Robert L.
Published: January 2021

A novel use of double digits in single places
Pierced Polygons
Authors: Moore Charles G.
Published: January 2021

THE material to be presented here can provide an interesting extension of the work on polygons usually presented in a high school course in geometry. It has the advantage of being new, and consequently the teaching of the material lends itself readily to the discovery method of teaching. The order in which ideas are presented in this article is intended to suggest a sequence in which ideas may unfold, and theorems be discovered, in the classroom. It will also illustrate one of the types of pitfalls into which one may blunder. But, of course, no one is guaranteed a smooth road with no rocks or detours when pursuing an investigation of the unfamiliar.
The Affinity of Mathematics to Music
Authors: Rice Jack A.
Published: January 2021

Neither have I heard of any team teaching projects involving mathematics and music nor do I expect to hear of any. However, the close relationship of the two subjects has long been known.
Congruence Geometry for Junior High School
Authors: Sanders Walter J. , Dennis J. Richard
Published: January 2021

Because Euclid did such a superb job in organizing the geometry of the plane, the practice has been to follow his example almost exclusively in preparing elementary and high school materials. The results at the elementary and junior high levels have been limited to a presentation of point-set definitions, with at best a minimal exploration of the geometric properties of the figures defined. This reluctance to include the study of relationships between figures may be a consequence of difficulties inherent in the standard organization.
Mathematics by Analogy
Authors: Moser James M.
Published: January 2021

Among other things, the newer approaches to mathematics teaching attempt to have students gain an appreciation of the subject by means of seeing patterns and generalizations which emerge from a study of certain mathematical instances. Hopefully, the students get a feeling for the beauty and power of mathematics from their realization of the existence of the structure, regularity, and order which permeate every branch of the subject. Yet there is another way in which students can sense the strength of mathematics. This is in the recognition of the fact that, at times, seemingly different situations actually have elements in common which, when seen from a certain point of view, produce strikingly analogous results. It is the purpose of this article to give an example of such an analogue. It has to do with the graphs of equations of two variables involving absolute values.
Einstein and the Ice-Cream Cone
Authors: O'Brien Katharine
Published: January 2021

His first day at Princeton, the legend goes, he went for a stroll (in his rumpled clothes). He entered a coffee-shop-moment of doubt-then climbed on a stool and looked about. Beside him a frosh, likewise strange and alone, consoling himself with an ice-cream cone.
Historically Speaking— Mathematics as an Art—The Higher Arithmetic
Authors: Barnett I. A.
Published: January 2021

Mathematics possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, sublimely pure, and capable of a stern perfection, such as only the greatest art can show.—BERTRAND RUSSELL.
What Does a Proof Really Prove?
Authors: Smith Stanley A.
Published: January 2021

An important goal of contemporary school mathemetics is the development of an understanding of the nature of proof. Some new programs and texts have incorporated discussion of proof and proof-writing into the work on algebra. However, the bulk of such work still falls within the standard course in Euclidean geometry.
Can Space Be Overtwisted?
Authors: Engel Douglas A.
Published: January 2021

AT FIRST sight the question “Can space be overtwisted?” seems absurd, if not ridiculous. In this article it will be shown that, given the right tools, space ran be overtwisted under the meaning that these tools allow. All mathematical systems fit into a set of rules, and their meaning, consequently, does not go beyond certain boundaries unless the rule are expanded indefinitely. So if space can be overtwisted, it is with the restriction that you do it within a specifie mathematical system.
Experimental Programs: Large-Group Instruction in Mathematics Under Flexible Scheduling
Authors: Bhushan Vidya , Jeffryes James , Nakamura lrene
Published: January 2021

We chose the words “large-group instruction” in lieu of “team teaching,” since the goals of this innovation are somewhat different from those commonly associated with team teaching. The most commonly offered goal of team teaching is that of providing students with a richer educational experience by combining the specialties of the teachers in a given school. While this idea could be incorporated into the structure of our large-group instruction in mathematics, this was not our primary concern. Flexible scheduling offers many possibilities for a variety of combinations of large-group leeture and small-group discussion labs. Our question with regard to this freedom was simply this: Can a teacher's load, in terms of classroom contact hours with students, be substantially reduced under large-group instruction while maintaining a high degree of learning within the group?
The Crossnumber Puzzle Solves a Teaching Problem
Authors: Moskowitz Sheila
Published: January 2021

OFTEN teachers complain that review lessons are dull and sometimes boring for them and their students. Then they ask how they could make these lessons more interesting and more exciting.
International Mathematical Education: Mathematics in the Schools of the U.S.S.R.
Authors: Masloya G. G. , Markushevitz A. I.
Published: January 2021

MUCH work has been done in the Soviet Union over the past years in improving school programs. A commission on the content of education, convened by the Academy of Sciences and Academy of Pedagogical Sciences of the U.S.S.R., prepared a new academic plan for the high school and programs for all subjects, includiug mathematics. The chairman of the program commission in mathematics was academician A. N. Kolmogorov.
On The Positive Square Root of Two
Authors: Beckenbach Edwin F.
Published: January 2021

This article discusses two geometric proofs of the irrationality of . It is based on an article that appeared in The Arithmetic Teacher1 and relate to another article2 and an editorial note3 in that journal; it is presented here for teachers; at the secondary-school level.
Letter to the Editor
Authors: Pollman William
Published: January 2021

I read with interest Lee Boyer's article in the March issue of the journal, “The Five-pointed Star.”
Have You Read …?
Authors: Peak Philip
Published: January 2021

Computers are the “in thing” at present. This article gives some information about computers in Kansas. Seven school districts are using computers: six use them for bookkeeping duties in administration, seven offer data processing courses to business education students, and two have computer-oriented mathematics for advanced students.
International Mathematical Education: Mathematics In British Secondary Schools: Curriculum Projects
Authors: Fehr Howard F. , Campbell Lawrence G.
Published: January 2021

Not long after American teachers began the current reconstruction of the secondary mathematics curriculum, British mathematicians and educators, also recognizing the need for rejuvenation, instituted several projects for reform of an out-of-date curriculum. Among these, the programs of the School Mathematics Project and the Midlands Mathematical Experiment are most frequently cited.
Classics in Mathematics Education: Buddha's Advice to Students and Teachers of Mathematics
Authors: Crosswhite F. Joe , Bell E. T.
Published: January 2021

Some explanation for the existence of this article is in order. First, the Editor must be disposed of. My kindest advice to him is that he turn this over to the compositor, or file it in the nearest wastebasket, and take a long walk. For on a previous occasion, which he doubtless has forgotten, he turned a requested article of mine over to one of the most dignified pedagogues in the teaching profession for bowdlerization. The outcome may be imagined. The present case differs from the former in one crucial technicality, which leaves the Editor ethically free to file this article as suggested. The article was indeed requested, but it was not the Editor who asked for it. Under the circumstances, he has my sympathy.
An Intuitive Leap or an Unscholarly Lapse?
Authors: Farrell Margaret A.
Published: January 2021

How much guessing do you encourage in your classroom? What value do you place on intuitive hunches? The history of mathematics repeatedly illustrates the necessity of intuition in the continuing generation of mathematics. Moreover, present-day researchers of the psychology of learning emphasize the importance of facilitating intuitive ventures in our students. Yet many teachers of mathematics avoid “hunching” for fear of error; and a few, as disastrously, play with intuition without the essential companion study of mathematics.
Using Symmetry Arguments to Solve Problems
Authors: Ram Budh
Published: January 2021

The use of symmetry principles to solve problems at the graduate level is quite prevalent. The use of such arguments often makes a difficult problem simple enough for its solution to be quite apparent.
From the Geoboard to Number Theory to Complex Numbers
Authors: Lichtenberg Donovan R.
Published: January 2021

Patterns on a geoboard lead to interesting insights into prime and complex numbers.
Elementary Linear Algebra and Geometry via Linear Equations
Authors: Brieske Thomas J.
Published: January 2021

The unifying power of vector space concepts can be developed with rich geometric intuition and practical payoff following this guided tour through linear equations.
Enrichment Motivation Using General Fibonacci Sequences
Authors: Hosford Philip L.
Published: January 2021

A classroom trick can be the beginning of a mathematical investigation.
An Application of Functions and Graphs to Inequalities
Authors: Smith Arthur F.
Published: January 2021

The language of functions and graphs is applied in yet another context to unify a commonly fragmented set of rules around one intuitively simple principle.
An Indirect Method for Calculating Ages
Authors: Wang Carl , Woo Norman
Published: January 2021

This ancient trick of Chinese prognostication supplies an intriguing situation for the exploration of factors, multiples, and equations.
N-Gami, a Variation of Origami
Authors: Pedersen Jean J.
Published: January 2021

Origami is the ancient Japanese art of folding objects from a single sheet of paper without cutting or pasting. A variation, N-gami, can be studied as a follow-up project after a study of the Platonic solids. Admittedly, the Platonic solids are easier to construct, appear more frequently in mathematics, and have much greater cultural significance. The investigation of other solids, however, gives students a chance to participate in solving a new geometric problem in its natural mathematical development. First, they play with the concepts; then they formulate and prove or disprove their conjectures. Thus the students are participating mathematicians rather than spectators.
A Relevant Calculus Problem: Estimation of U.S. Oil Reserves
Authors: Weyland Jack A , Ballew David W.
Published: January 2021

Relevant? You bet! And, although most of the conclusions here involve calculus, the approximation used to compute the peak oil production year involves a simple triangle.
Benjamin Banneker, Pioneer Negro Mathematician
Authors: Mulcrone T. F.
Published: January 2021

In almost every history of the Negro in the United States one can find an account of the incidental contributions of Benjamin Banneker (1731-1806) to the social history of Ms race. But no chronicle is readily available of the scientific life of Banneker as a student of mathematics, almanac compiler, surveyor, and astronomer. The object of this article is to provide such an account of the scientific activity of Benjamin Banneker, whom W. Douglas Brown called “the first American Negro to challenge the world by the independent power of his intellect,” and to indicate how close Banneker comes to approximating the composite picture of the mathematician in the United States at the end of the eighteenth century.
Sam Loyd, America's Greatest Puzzlist
Authors: Spaulding Raymond E.
Published: January 2021

SAM Loyd (1841-1911) has been called by Martin Gardner “America's greatest puzzlist.” Two volumes of his mathematical puzzles, selected and edited by Martin Gardner, were published by Do-ver Publications in 1959. These puzzles originally appeared in the Brooklyn Daily Eagle and the Woman's Home Companion.
Coordinates for Lines: An Enrichment Activity
Authors: Osborne Alan R.
Published: January 2021

Using the two-point form of the equation of a line, excluding lines containing the origin. the author describes a way of naming a line by defining an ordered pair.
The Citardauq Formula
Authors: Goff Gerald K.
Published: January 2021

A new and revealing perspective on the quadratic formula.
The Barber Queue
Authors: Mathers Jolly
Published: January 2021

Have you ever waited in line for something? Mathematics can help students analyze this problem.
Your Council at Work
Authors: Zweng Marilyn J.
Published: January 2021

The Editorial Panel of the Arithmetic Teacher sets standards for the content of the journal and specifies the procedure for the refereeing and acceptance of manuscripts. The Panel determines the general format of the journal and defines the content and balance of materials in individual issues. They decide on the departments of the journal and appoint the appropriate editors for specified terms.
It's in the Bag
Authors: Heintz Ruth E.
Published: January 2021

Simulation of a probability experiment adds meaning to some anti-intuitive results.
Mathematics Examinations in the Soviet Union
Authors: Goldberg Julius , Swetz Frank
Published: January 2021

Could your seniors solve the mathematics problems posed to Soviet candidates for admission to institutes of higher education?
A Least Squares Approximate Solution to Polynomial Equations Over the Real Numbers
Authors: Poole George
Published: January 2021

Solutions to x2 + bx + c = 0 give insight to those of y = x2 + bx + c.
Maps: Geometry in Geography
Authors: Shilgalis Thomas W.
Published: January 2021

Your geometry students will be particularly curious about the shapes of figures as they are projected from a sphere to a plane.
A Remarkable Trigonometric Identity
Authors: Maor Eli
Published: January 2021

An unusual trigonometric identity and its physical interpretation.
An Application From the History of Mathematics
Authors: Campbell William L.
Published: January 2021

Computing areas is possible for anyone who can “sum” an infinite geometric series.
Discovery in One, Two, and Three Dimensions
Authors: Smith Lyle R.
Published: January 2021

You and your students should find these exercises a refreshing way to explore mathematics.
A Unit Factor Method for Solving Proportion Problems
Authors: Herron J. Dudley , Wheatley Grayson H.
Published: January 2021

Here is an alternative for enabling your students to solve proportions.
Survival Skills in Mathematics Program
Authors: Fulkerson Russell D. , Gilmer Thomas A.
Published: January 2021

A workable plan for assuring minimum competency.
A Recursive Approach to the Construction of the Deltahedra
Authors: Mcgowan William E.
Published: January 2021

A helpful guide for constructing polyhedra.
Can Computers Really Improve School Mathematics?
Authors: Bell Frederick H.
Published: January 2021

When We've been and where we ought to be going with computer-enhanced mathematics (plus a computer-assisted update to Polya's “How to Solve It”.
Aiding the Seriously Deficient Learner in Computation
Authors: Doggett Maran
Published: January 2021

Everyone teaches students who don't know their number facts. Here is an exciting alternative for you to try.
National Council of Teachers of Mathematics
Authors: Egsgard John C.
Published: January 2021

One of the greatest joys in doing mathematics is finding the solution to a problem. The problem does not need to be difficult. Even discovering the answer to a simple problem can bring happiness. All of us know the excitement that comes with suddenly finding the key to the solution of a problem on which we have been working for a long time.
The Give-and-Take-Away Strategy
Authors: Staib John
Published: January 2021

A single problem-solving strategy can be the key to a wide variety of problems.
Basic Skills: What are They?
Authors: Hiatt Arthur A.
Published: January 2021

While examining basic skills in mathematics, why not take a look at process?
The Tenth Step—Metric Time and Angles
Authors: Frasier E. Lewis
Published: January 2021

A proposal that metric time and angles would be convenient for conducting business, doing mathematics, navigating, and scheduling our daily lives.
Discovery of A Property of Consecutive Integers
Authors: DiDomenico Angelo S.
Published: January 2021

An arithmetic exercise yields a surprising result.
Square Roots From Anywhere
Authors: Goodman Terry A. , Bernard John
Published: January 2021

A novel approach to roots, building algebra, fraction, and intuitive limit skills.
The Fifteen Puzzle
Authors: Hollist J. Taylor
Published: January 2021

Save time—determine if the solution to a puzzle exists before you start.
Activities from “Activities”: an Annotated Bibliography
Authors: Hirsch Christian R.
Published: January 2021

The “Activities” section of each issue of the Mathematics Teacher provides an excellent source of discovery lessons, laboratory experiences, mathematical games and puzzles, and model constructions for pupils in grades 7-12. These activities are designed for reproduction in worksheet and/ or transparency form for immediate classroom use. Whereas the activities may be used to provide supplementary/enrichment experiences for individual or small groups of students, many of the activities can often be used to motivate, enhance, or extend the learning of particular topics that appear in standard mathematics programs. This bibliography was compiled to expedite the classroom teacher's search for content-specific activities that have appeared in the journal during the seventies.
Some Uses of the Exchange Key on a Calculator
Authors: Maor Eli
Published: January 2021

One of the least frequently used keys available on many calculators is the exchange key. This key usually comes in one of two versions. Some calculators such as the Texas Instruments TI-25, TI-30, and SR-40, have an exchange-memory key. denoted EXC or X-M, which swaps the current content of the display with that of the memory.
One Step Further
Authors: Roberti Joseph V.
Published: January 2021

Sketching functions and finding slopes and roots all without calculus.
An “Almost” Diophantine Equation
Authors: Gaughan Edward D.
Published: January 2021

Equations and inequalities can he combined to solve an intriguing problem.
Probability Simulation in Middle School
Authors: Lappan Glenda , Winter M. J.
Published: January 2021

By middle-school age many students have formed notions about the likelihood of an event happening. These notions are often incorrect, and yet firmly fixed in the minds of students. Studying probability as a set of theoretical rules, in our expenence, is very unlikely to change any of these preconceived notions. Teaching probability through concrete experiments holds much more promise.
An Introduction to Calculator Logic Systems
Authors: Mitchell Charles E. , Blume Glendon W.
Published: January 2021

The nature of the work you do will determine the logic system you should buy.
Clubs: e = mc2 (Enthusiasm = Mathematics Club Competition)
Authors: Steege Kenneth L.
Published: January 2021

Cheers are coming from eighteen different classrooms as students congratulate their fellow team members for answering a mathematics question within the 1.5-minute time limit. Then at the conclusion of an exciting match, 160 students and advisors crowd around the master score chart to check the latest standings before hurrying off to their next 20-minute match.
Clubs: Some Math Club Icebreakers
Authors: Ecker Michael W.
Published: January 2021

As a mathematics club advisor and organizer, I have found it essential to compile a list of good challenging problems. These can be used at the start of each meeting as icebreakers, or even an entire meeting can be devoted to them.
Mathematics For The Average College-Bound Student
Authors: Whitesitt John
Published: January 2021

Mathematics educators continue to be concerned with developing the best cur- riculum for the college-bound student in secondary school. This is certainly an important concern, but too often we become so involved in this problem that we overlook a related and equally important problem. Far too many students who eventually go on to college are not in the “college bound” group while they are in secondary school. This article deals with the curriculum for these students.
Angles of Elevation of the Pyramids of Egypt
Authors: Smith Arthur F.
Published: January 2021

Only an unfortunately blasé person could stand at the foot of the Great Pyra- mid of Giza without experiencing waves of wonder at its very existence. Everything about it is astonishing-its beauty, its bulk, its history, its mystery. By day it is awesome-a man-made mountain that originally towered 147 meters above its base; a square, 230 meters on a side: and covering some 5 Ά hectares of desert. By night, a looming mass under a starry sky, it seems what its builders might very well have intended it to be-a stairway to heaven.
Another Look at the Quadratic Formula
Authors: Obermeyer Dean D.
Published: January 2021

In a particularly interesting article from the Mathematics Teacher (May 1975), Larry Hoehn gave an alternate method of deriving the quadratic formula. Hoehn’s step-by-step comparison of the standard method and the alternate method is found in table I.
Central-Point Problems
Authors: Krause Eugene F.
Published: January 2021

A nice mathematical approach for finding the best place for a meeting when dix lance is a consideration.
Using the Monochord: a Classroom Demonstration on the Mathematics of Musical Scales
Authors: Haak Sheila
Published: January 2021

Many students have been told that mathematics and music are strongly related. But have they heard or seen this wonderful relationship? Those who know the musical scale (do-re-mi-fa-sol-la-ti-do) and can handle ratios will be fascinated as they apply mathematics to music. More advanced students will have the opportunity to apply their work with algebra and logarithms to musical scales. A single-stringed instrument, the monochord, demonstrates the mathematics of musical scales.
Hawaiian Number Systems
Authors: Hughes Barnabas
Published: January 2021

English-speaking visitors to the Hawaiian Islands delight in interspersing Hawaiian words with their own language. The is-lands are perhaps the only place in the United States where the English-speaking haole (Caucasian) can mix a different language with one’s own and be understood. The tourist easily learns many Hawaiian words and phrases from pamphlets available in stores and hotels. For instance, in Honolulu, directions are mauka (“toward the mountain”), makai (“toward the sea”), ewa (“toward the west”) or Diamond Head (“toward the east”) rather than compass oriented. Everywhere in the islands, aloha means “love,” “greetings,” “welcome,” or “farewell,” depending on circumstances of time, place, and persons.
Making Mathematical Notation More Meaningful
Authors: Perlman Gary
Published: January 2021

Consider the formula for the arithmetic average, which states that the average of a set with n members, X1, X2, X3,…, Xn, is the sum of all its members divided by n. If we assume students can add and divide, then the ability of students to learn how to compute an average depends largely on their ability to decipher the meanings of all the symbols in (I). I believe there are some rules that can simplify the task of communicating mathematical ideas with symbols. For example, to simplify (I), two appropriate rules are the following: symbols should be familiar (out with sig- ma), and symbols should be mnemonics (in with SUM). Another notational rule is the following: a notation should promote generalization. This suggests the follow- ing scheme appropriate for the computer age.
Clubs: Rivers Computer Club: Space Invaders, Or What?
Authors: Teukolsky Roselyn
Published: January 2021

Several articles have appeared in recent issues of the Mathematics Teacher describing computer clubs. At Rivers Country Day School we have had much success with a rather different approach.
Sylvester And Scott
Authors: Kenschaft Patricia C. , KATZ KAILA
Published: January 2021

Two British mathematicians, both the victims of discrimination in their native country, were instrumental in stimulating the mathematical research community in the United States. James Joseph Sylvester (1814-1897) and Charlotte Angas Scott (1858-1931) inspired and trained many younger mathematicians here, served as editors of the first continuing mathematical research journal in this country, and contributed substantial research to the early American journals. Both overcame obstacles in their careers and promoted the study of mathematics by young women at a time when it was unpopular to do so.
Applications: Getting The Big Picture
Authors: Ecker Michael W.
Published: January 2021

A painting on a wall is 5 feet in height, and an observer notes that the bottom of the painting is 2 feet above eye level.
Sum Squares On A Geoboard Revisited
Authors: L’Heureux James E.
Published: January 2021

Some reasonable Conjectures for counting squares don't seem to hold. Less able students can count the squares, whereas more talented studems can develop a general approach.
Geometrical Probability— A Source Of Interesting And Significant Applications Of High School Mathematics
Authors: Dahlke Richard , Fakler Robert
Published: January 2021

What is geometrical probability? Why is it interesting and profitable to study? In answer to the first of these questions, geometrical probability deals with probability on infinite sample spaces where each outcome of the experiment in question is equally likely to occur. It allows us to calculate the probability of an event occurring at random in a single trial of an experiment by identifying the sample space with a geometric region R and the event with a subregion r of R. We can then proceed to use geometry to find the desired probability.
Shipboard Weather Observation
Authors: Palmaccio Richard J.
Published: January 2021

On many ships there can be found an anemometer (ăń-ə-mŏḿ-ət-ər) for measuring wind speed, and a wind vane for indicating direction, both mounted together near the bridge area. These two instruments thus indicate the wind velocity, a vector quantity. Even though there are a number of orbiting weather satellites transmitting cloud pictures, meteorologists still depend heavily on surface observations in preparing forecasts.
Alternative Educational Programs For Gifted Students In Mathematics
Authors: House Peggy A.
Published: January 2021

If one were to select a metaphor for education in the United States, perhaps nothing would be more apt than the pendulum. And few aspects of education have experienced more pronounced oscillations of that pendulum than the education of the gifted.
Contests and Competitions
Authors: Badoian Martin J.
Published: January 2021

In 1968 the National Council of Teachers of Mathematics published a booklet by Howell L. Gruver entitled School Mathematics Contests: A Report. Although this report was an extensive survey of competitions in mathematics at that time, it did not cover the even wider range of competitive activities that were taking place in each state to challenge the brightest of mathematics students.
Personal Glimpses from Two Gifted Students
Authors: Primer Jeremy , Staples Susan
Published: January 2021

By the time I completed seventh grade, I had received a good foundation in mathematics. I had been tutored in algebra by older students and had taken Mary Dell Morrison's excellent honors geometry and precalculus courses at the local high school. Socially I was not a high school student, but I accepted my situation and had a fine time learning mathematics.
Mathematical Research in the Honors Classroom
Authors: Borenson Henry
Published: January 2021

Whereas a research unit in an honors class is appropriate, regular classes can benefit from some of the same strategies.
Activities: More Calculator Capers
Authors: Schmalz Rosemary
Published: January 2021

This section is designed to provide mathematical activities suitable for reproduction in worksheet and transparency form for classroom use. This material may be photoreproduced by classroom teachers for use in their own classes without requesting permission from the National Council of Teachers of Mathematics. Laboratory experiences, discovery activities, and model constructions drawn from the topics of seventh, eighth, and ninth grades are most welcome for review.
Microcomputer-assisted Discoveries: Number Bases
Authors: Kimberling Clark
Published: January 2021

Students who discover something mathematical themselves usually remember it especially well, and the resulting sense of ownership will often motivate them to learn and discover even more. The study of various number bases, greatly facilitated by BASIC programming on a microcomputer, provides fertile ground for such discoveries.
Great Expectations— Challenging the Interests of the Gifted and Talented Junior High Student
Authors: Lerner Bao-Ting , Crawford Carol G.
Published: January 2021

Group theory, transfinite numbers, and Eulerian circuits can these college-level topics be taught in a junior high school curriculum? Surprisingly, they are just some of the topics and courses that comprise the advanced study program sponsored by the U.S. Naval Academy for the Anne Arundel Public School System in Maryland.
Microcomputer-assisted discoveries: Probability Machine
Authors: Kimberling Clark
Published: January 2021

The classical probability machine is a vertical board of obstacles through which balls fall. Each time a ball meets an obstacle, the probability that it will continue its fall on the right side of the obstacle is 1/2, and likewise for the left side. The balls fall to the bottom of the board, where they form a very interesting curve. An excellent photograph of a probability machine appears in chapter 10 of the Thirty-fourth Yearbook of the NCTM.
An Astounding Revelation on the History of π
Authors: Posamentier Alfred S. , Gordan Noam
Published: January 2021

It is generally accepted that one of the earliest approximations of the value of π can be found in the Bible. The value of π here is taken directly from its definition, that is, the ratio of the circumference of a circle to its diameter.
Using Mathematical Magic to Reinforce Problem-solving Methods
Authors: Frankenstein Marilyn
Published: January 2021

I first became enchanted with magic when an elementary school classmate did the following trick and refused to explain it. With her back turned, she told me to shuffle a deck of cards and make three piles of faceup cards.
SoundOFF: The Secondary School Curriculum— What Should It Include?
Authors: Neff John D.
Published: January 2021

Much has been said in recent months about mathematics that is needed or neglected in the secondary schools. Although certain similarities exist in the various reports, there seems to be plenty of room for variations in stress and usefulness.
Sharing teaching ideas: Checking with Magic Squares
Authors: Gilmore Hal
Published: January 2021

Sharing Teaching Ideas offers practical tips on the teaching of topics related to the secondary school curriculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the beginning and the experienced teacher. Please send five copies of your ideas to the managing editor for review.
Mathematics Assessment in Canada— an Overview
Authors: Jansson Lars C.
Published: January 2021

The material reported in this article on the assessment activities of the Canadian provinces was obtained through publicly available reports (see the Bibliography) and correspondence with ministry officials and other individuals directly involved with the mathematics assessments. An earlier draft of the article was made available to these officials and to other contact persons in each province to verify the accuracy of the reports. Their help has been most valuable. In addition. the author wishes to thank Henry Schulz of the Manitoba Department of Education, who supplied valuable information from informal internal documents and who made helpful comments as the article developed.
Applications: Applying A Linear Function to Schedule Tennis Matches
Authors: Garman Brian
Published: January 2021

Over the past six years I have helped tournament director Rolla Anderson run the Junior National USTA Tennis Championship for boys aged sixteen and eighteen in Kalamazoo, Michigan. For three years I observed that after the matches were initially assigned, they got progressively further behind their scheduled times and by late afternoon some matches would be as many as three or four hours late. There had to be a better way to schedule them.
Ethics and Computer Use
Authors: Gilliland Kay , Pollard Mattye
Published: January 2021

A computer is just a piece of equipment. The people who use it have to decide what is right and what is wrong in its use. These issues must be addressed and the controversies discussed. This discussion activity is designed to help students think about the situations and understand the various points of view. Role playing can be used if the students wish, or the vignettes can simply become starting points for conversation.
Sharing teaching ideas: Photographic Slides: A Better Way to Demonstrate Software to Large Groups
Authors: Gordon Jeffry
Published: January 2021

“Sharing Teaching Ideas” offers practical tips on the teaching of topics related to the secondary school curriculum. We hope to include classroom-tested approaches that offer new slants on familiar subjects for the beginning and the experienced teacher. See the masthead page for details on submitting manuscripts for review.
SoundOFF: My Anxieties About Math Anxiety
Authors: Greenwood Jay
Published: January 2021

The views expressed in the “Soundoff” editorials do not necessarily reflect the views of the Editorial Panel of the Mathematics Teacher or the National Council of Teachers of Mathematics. Readers are encouraged to react to these editorials by writing to the author with copies to the Mathematics Teacher for consideration in “Reader Reflections.” Please double-space all letters that are to be considered for publication. Editorials from readers are welcomed.
Activities: Teaching Problem-Solving Skills
Authors: Schaaf Oscar F.
Published: January 2021

The recommendations for school mathematics contained in the Agenda for Action stress problem solving as the focus of mathematics instruction.
In Praise of Trial and Error
Authors: Butts Thomas
Published: January 2021

“There must be a formula I can use [to solve this problem], but I just can't remember (find …) it.”
Video Mathematics
Authors: Kahanec Frank A.
Published: January 2021

I'm sure you've had a student or two who like to miss school once in a while! Unfortunately, mathematics tends to be a little difficult when “occasional” absences occur. Even worse is when a serious illness keeps one of your learners out of school for weeks or longer.
Ten Essential Concepts for Remediation in Mathematics
Authors: Roseman Louis
Published: January 2021

The most flagrant and frequent mathematical errors made by remedial students in high school stem from their failure to understand important concepts. Such misconceptions lead to discouragement, absenteeism, and behavioral problems often attributed to other causes. A clear improvement in attitudes and achievement often follows clarification of these concepts.
A Few Problems Involving Scale
Authors: McKillip William D. , Kay Cynthia Stinnette
Published: January 2021

Many mathematics textbooks contain material on scale drawing as applications of ratio and proportion involving geometric figures. This article suggests some applications that students may find interesting. The material might be most useful in seventh- or eighth-grade mathematics or in general mathematics in secondary school. Algebra and deductive geometry are avoided.
Microcomputer-Assisted Mathematics: Lagrange Polynomials
Authors: Kimberling Clark
Published: January 2021

All around the world, teachers are discovering topics recently made accessible to their students by microcomputers. Such topics that have appeared in “Microcomputer-assisted Mathematics” include the graphing of intricate curves and the fundamental theorem of algebra. These two topics lead to a third discovery: Lagrange polynomials.
Logo in the Mathematics Curriculum
Authors: Addicks Tom
Published: January 2021

Most applications of Logo in grades 5-10 have dealt with geometric concepts. New uses of Logo are just beginning to reach the classroom. One new use that I have found is in the study of simple descriptive statistics.
Problem-solving Techniques with Microcomputers
Authors: Haigh William E.
Published: January 2021

The first recommendation in An Agenda for Action (NCTM 1980) is that problem solving “be the focus of school mathematics in the 1980s.” Too often, high school mathematics courses avoid interesting and challenging problems because students lack the necessary background to solve the problems in a conventional manner. Many of these problems are interesting to students; but, because these students cannot find limits or derivatives of functions or use “advanced” mathematical techniques they are unable to pursue such problems. For example, maximum-minimum problems are usually introduced after students have experienced some work in calculus involving first and second derivatives. Most high school students are capable of understanding problems involving maximum and minimum values and, with the exception of understanding differentiation and application of differentiation techniques, are capable of handling the necessary mathematical skills that are involved in the solution of such problems.
Flip and Twist, Shuffle, Snap, and Compose
Authors: Lovell Robert
Published: January 2021

Having been exposed to the concepts of closure, commutativity, associativity. identities, and inverses in a beginning algebra course, most students in an advanced algebra course feel that they understand these ideas. However, true understanding cannot be exhibited until the students are confronted with these ideas in unfamiliar situations.
A Property of Right Triangles and Some Classical Relations
Authors: Didomenico Angelo S.
Published: January 2021

Mathematics is an ever-growing subject. Included in this growth is a process of simplification in which formulas and relations often arrived at inductively or derived by long and difficult methods are later found to follow easily and directly from other findings. Advanced mathematics abounds with fascinating results of this kind. Similar ones also exist in elementary mathematics. I have found a property of right triangles, given by the following theorem, from which students can deduce, in a surprising and straightforward manner, some of the most significant relations encountered in high school mathematics.
Pythagorean Triples
Authors: Tirman Alvin
Published: January 2021

If a class of students completing a course in plane geometry is asked to cite a few examples of primitive Pythagorean triples (those whose greatest common divisor is 1), their answers can be assumed to be 3, 4, 5; 5, 12, 13; 8. 15, 17: and 7, 24, 25.
A New Solution to an Old Problem—Solving Word Problems in Algebra
Authors: Thaeler John S.
Published: January 2021

Many high school and college students dislike word or story problems because they have not been very successful in solving them. Teachers have had a difficult time going beyond teaching students specific approaches to certain types of problems. Students tend to memorize a certain way to work each type of problem and then are ill equipped to deal with new situations.
Do Mathematics with Interactive Geometry Software
Authors: Zheng Tingyao
Published: January 2021

Many people agree that the main objective of mathematics education is to teach students to think critically and to do mathematics as mathematicians do. The National Council of Teachers of Mathematics (2000) points out that for school mathematics programs to create autonomous learners, students should be challenged with appropriately chosen tasks. Students will then become confident in their ability to tackle difficult problems and become reflective in their thinking and learning.
Using a Model Rocket-Engine Test Stand in a Calculus Course
Authors: Weiss Mike , Dodge Brian , Harden Kate , Hempstead Amy , Lloyd Jeff , Pott Brian
Published: January 2021

Advanced Placement calculus students from Yarmouth High School, located in Yarmouth, Maine, built a model rocket-engine test stand in May 2000. This project was used to reinforce calculus concepts. In addition, it furnished data for a future freshman-science rocketry project. Students used the concepts of the average value of a function, along with Riemann-sum approximation techniques and spreadsheet skills to determine the average thrust of a model rocket engine.
The Galactic Spaceship Tour Challenge
Authors: Engel Bill , Schmidt Diane
Published: January 2021

Many students believe that the solution to most mathematics problems is fairly direct, involves only one step, and provides one final answer. In most real-life situations, however, mathematical problem solving involves several steps to obtain a complete solution. One cannot design a bridge with a simple mathematical computation. In addition, most problem-solving situations in the real world require teams of people. The National Council of Teachers of Mathematics (NCTM 2000) has promoted the use of complex problems that involve multistep solutions. Many standardized tests present problems that require expanded or extended responses. Because a simple solution with one answer might not be sufficient, rubrics are often developed to address the extent to which a problem has been solved. The mathematics assessment section of the Florida Comprehensive Achievement Test (FCAT) is one such example (Florida Department of Education 2002).