bluuebunny/crossref_metadata_2025 huggingface dataset:
The Educational Debate Over Darwinism
Authors: Campbell John A. ,   Institute for Interdisciplinary Research
Published: January 2021

The debate over teaching Darwin's theory in public schools has been a feature of American public life since at least the Scopes trial of 1925. Drawing on the liberal arts tradition centered in rhetoric and civic argument, this essay argues that science education should not merely prepare tomorrow's scientists, but also educate scientifically articulate citzens. It offers the Origin of Species as a model for educational strategies that would protect the integrity of science, while addressing the objections of students and their parents to Darwin's ideas. Darwin's work belongs in the great tradition of two-sided humanistic argument central to Western education since antiquity, and exemplified in John Milton and John Stuart Mitt. Debate between Darwin's theory and its alternatives, whether young earth creationism or Intelligent Design, is recommended as a means to teach Darwin's theory and train students in the central role of critique and argument in scientific reasoning.
Virtue and Markets
Authors: Gruenwald Oskar ,   Institute for Interdisciplinary Research
Published: January 2021

This essay proposes an interdisciplinary framework for teaching markets and morals by exploring the linkages between political economy, civil society, and culture. Free markets in capitalist mixed economies shape, and are shaped by, political institutions of representative democracy, the vibrancy of civil society, and the values, norms, and beliefs embedded in culture. The major challenge for liberal society and free markets is to reconcile individual and group interests with the common good. The cultural contradictions of capitalism reflect the inadequacy of commercial virtues to sustain a liberal society. External constraints of law and institutional checks and balances in all spheres need to be conjoined with internalized moral constraints of a well-ordered individual conscience. This, in turn, requires a normative order which transcends radically the selfishness of individual and group interests, thus preserving liberty and democracy while enhancing economic efficiency and the social beneficence of free markets. The essay thus confirms Alexis de Tocqueville's notion of the interdependence of liberty, morality, and faith.
Friedrich Hayek and Reinhold Niebuhr on the Moral Persistence of Liberal Society
Authors: McDaniel Charles ,   Institute for Interdisciplinary Research
Published: January 2021

Attempts by Christian social theorists to harmonize Austrian liberalism and Christian tradition ignore serious contradictions in their respective moral systems. Friedrich Hayek's conception of the "spontaneous order" portends potentially harmful consequences for corporate religion by elevating the subjective individual as the singular source of value in human culture. Thus, Hayek's ideas on cultural evolution may provide insight into the perceived loss of moral voice among American religious institutions, Reinhold Niebuhr's economic realism is more conducive to exploring the moral persistence of liberal society recognizing the need for balance between subjective and collective expressions of the good. Key concepts in Niebuhr's economic thought are a unique value theory, a holistic conception of the individual and society, an understanding of the moral ambiguities associated with technological innovation, and recognition that balances of power are necessary to preserve social organicism and the Christian conception of personality.
A mathematics record card
Authors: Olander Clarence
Published: January 2021

An adequate system for keeping records forms the basis of good counseling programs, research studies, and curriculum studies. This paper describes the efforts of one group of teachers to develop a good system for keeping a record of the students’ achievements.
The functional approach to elementary and secondary mathematics
Authors: Gager William A.
Published: January 2021

There are those who feel that adolescents will like mathematics if it is meaningful to them. Many feel that “making mathematics functional” is the best way to make mathematics meaningful.
Let's stop hoarding our talent
Authors: Du Bridge Lee A.
Published: January 2021

This article appeared in The Saturday Review, August 4, 1956 and is reprinted with the permission of The Saturday Review and the author.1 This penetrating analysis of our “shortage” of engineers and scientists should provide educators with food for thought.
Mathematics in the Junior High School: Removing the “dis” from dislike for mathematics
Authors: Hach Alice
Published: January 2021

Ralph Pringle once wrote that “The junior high school age is the most unloved age but when we come to know it, it is the most lovable age.” In view of this statement it seems important that we examine together this important three-year block in our educational training.
Points And Viewpoints: How are we doing?
Authors: Price H. Vernon
Published: January 2021

A column of unofficial comment.
More new exercises in plane geometry
Authors: _ _
Published: January 2021

The stock of geometrical exercises of the new type introduced in the February 1957 issue of The Mathematics Teacher is here increased so that a wide range of suggested problems is opened to the teacher of geometry.

This paper, the last in a series of five devoted to the cutting of squares, also supplements similar material in

The Mathematics Student Journal for April1957.
Mathematics in the Junior High School: Trigonometry in Grade Eight
Authors: Steinen Ramon
Published: January 2021

Few would deny that an important conrem of the mathematics theacher in grades seven and eight is the further development of computational techniques introduced in the first six grade. That it is the most imporLant objective is questionable. Hather than just “tying up loose ends” for two years, teachers should be doing a more efficient job of sowing new ideas and helping students build up a large, accurate vocabulary of maLhematical terms.
Some drill techniques for arithmetic
Authors: Vaughn William D.
Published: January 2021

Teachers will enjoy using the interest-catching drill devices presented in this article.
On teaching angle and angle measure
Authors: Fehr Howard F.
Published: January 2021

An algebraic approach to some problems untouched by classical Euclidean geometry.
Elementary school and high school mathematics for the colleges?
Authors: Smiley M. F.
Published: January 2021

Today's pressure on college enrollments has forced many colleges to adjust courses much as high schools have done in the past. Can This He Justified?
Some implications of twentieth century mathematics for high schools
Authors: Rourke Robert E. K.
Published: January 2021

Recent developments in mathematics have a bearing on the mathematics taught in the secondary schools. This article shows how these developments should affect elementary algebra.
Finding out about “modern mathematics”
Authors: May Kenneth O.
Published: January 2021

What is this “modern mathematics” about which we hear so much? In this article some easily accessible and readable sources of information arc briefly described.
A note on number creation
Authors: Brumfiel Charles
Published: January 2021

The author explores some common misconceptions about number and creates a new number system.
Degree of accuracy of square roots
Authors: Ogilvy C. Stanley
Published: January 2021

An odd misconception has crept into some textbooks and thence into the classroom, namely, that the process of extracting arithmetic square root yields a result which has only half as many significant figures as the original number. A specific example from a current book will perhaps recall for the reader similar statements made by his instructors in years gone by.
Points and Viewpoints: It's up to us!
Authors: Immerzeel George , Nielsen Ross A.
Published: January 2021

A column of unofficial comment
The changing concept of trigonometry as a school subject
Authors: Rosenberg Herman
Published: January 2021

A résumé of the status of trigonometry and some comments on desirable changes are presented.
Creative teaching in mathematics
Authors: Christofferson H. C.
Published: January 2021

Three levels of teaching mathematics are explored, and it is asserted that the product of creative teaching is insight.
Historically Speaking,— Pappus's extension of the Pythagorean Theorem
Authors: Eves Howard
Published: January 2021

Every student of high school geometry sooner or later becomes familiar with the famous Pythagorean Theorem, which states that in a right triangle the area of the square described on the hypotenuse is equal to the sum of the areas of the squares described on the two legs. This theorem appears as Proposition 47 in Book I of Euclid's Elements, written about 300 B.C.
New Ideas for the Classroom: Bridget, an Algebra Card Game
Authors: Johnson Donovan A.
Published: January 2021

Bridget is a card game that can develop in your algebra class a climate which is favorable to learning. By adding variety and competition, it will provide practice that builds accuracy and efficiency in evaluating algebraic expressions. A deck can easily be made up with 3″ by 5″ cards.
The fundamental theorem on linear programming
Authors: Avital Shmuel
Published: January 2021

An expression ax+by defined over a closed convex polygon assumes its maximum and minimum value at one (or more) of the vertices of the polygon.
A report of a National Science Foundation summer institute in mathematics for high school students at Columbia
Authors: Grossman George
Published: January 2021

Study of the programming of an automatic digital computer stimulates study of advanced topics in mathematics.
Digital computer programming in high school classes
Authors: Van Tassel Lowell T.
Published: January 2021

A student can obtain programming experience without an electronic computer.
Analysis of a spider nomograph
Authors: Jeffery Jay M.
Published: January 2021

An additional analysis of the spider nomograph published in a previous issue of this journal.
Probability and statistics in the twelfth year?
Authors: Grossman George
Published: January 2021

For the mathematically talented, this writer prefers other courses to the one in probability and statistics.
A bibliography for careers in mathematics
Authors: Turner Nura D.
Published: January 2021

Sources of information concerning careers in mathematics.
Experimental Programs: A study of pupil age and achievement in eighth-grade algebra
Authors: Messler Dorothy L.
Published: January 2021

More and more, educators are evaluating curriculum programs to ascertain what can be done to meet the academic needs of pupils whose differences vary according to abilities and interests. One of the greatest problems has been in the field of mathematics, because it is one of the fastest growing and the most rapidly changing of the sciences. Many changes are taking place in the various school systems throughout the country to enrich and extend the mathematical program for the benefit of exceptional students.
Abstracting, generalizing, and explaining – processes or relations?
Authors: Hendekson Kenneth B.
Published: January 2021

Perhaps psychologists have learned so little about “processes” like those considered herein because they are trying to study the elements of the null set.
Probability and the radioactive disintegration process
Authors: Mucci Joseph F.
Published: January 2021

An application using the mathematical topics of probability, the binomial theorem, and the number e
A unit of original mathematics investigation in grade 9
Authors: Degraaff Homer R.
Published: January 2021

Sometimes students like to be creative mathematicians rather than learners.
Locus proofs
Authors: Ash Carol
Published: January 2021

The advantage of considering every locus theorem as a statement of equality of two sets.
The nature of mathematics
Authors: Rees Mina
Published: January 2021

Some of the most noted mathematicians and philosophers have addressed themselves to a discussion of the nature of mathematics, and I can hope to add very little to the ideas they have expressed and the insights they have given; but I shall attempt to draw together some of their ideas and to view the issues in the perspective that seems to me appropriate to the present state of mathematical scholarship, taking account of the great increases that have been taking place in the body of mathematical learning and of the changes in viewpoint toward the old and basic knowledge that grow out of deeper understandings brought about by generations of mathematical research.
A discussion of powers of whole numbers
Authors: Smith Shelby D.
Published: January 2021

Developing creativity in mathematics students
The Saccheri quadrilateral
Authors: Kattsoff Louis O.
Published: January 2021

The Saccheri Quadrilateral, (hereafter refened to as S.Q.) shows quile dearly the possibility of non-Euclidean geometries and, in addi t ion, the relation of the Euclidean to certain non-Euclidean geometries.
Experimental Programs: Mathematics Via Radio in Wisconsin
Authors: Henderson George L.
Published: January 2021

AN OLD Chinese proverb states, “I hear-and I forget.” This implies, and rightly so, that speaking-listening is our least effective means of communication.
A Tiny Treasury of Tessellations
Authors: Ranucci Ernest R.
Published: January 2021

If a series of points on some region of a plane is connected by segments in groups of three, the portion of the plane selected may be considered to be completely covered by the triangular regions formed. The same portion could, of course, be covered by a different set of triangular regions (Figs. 1 and 2).
Letters to the Editor
Authors: Murray Peter J.
Published: January 2021

I have generally had some difficulty convincing high school students that the empty set is a subset of every set by a direct use of the definition: “A is a subset of B if every element of A is an element of B.”
Pythagorean Triples Grouped into Families
Authors: Archambeau Sister Mary Leona
Published: January 2021

Relating some new equations to some classical equations.
A Project in Mathematics
Authors: Garfunkel J.
Published: January 2021

A student of yours wants to do a project in mathematics. What advice and guidance can you give him”? How can you help him to get started? Answers to these questions are being sought now more than ever before. No longer is a high school project in mathematics the rare event that it was twenty years ago. Mathematics has become a living subject; we can now boast that almost one project out of ten is in mathematics and, hopefully, this ratio will be increased in the near future.
The Ubiquitous Number Five
Authors: Barnett I. A.
Published: January 2021

It is of interest to observe how the number five occurs in different parts of mathematics. Below is a list of such occurrences. No doubt others can he added.
International Mathematical Education: Reforms in Mathematical Education in Central and South America
Authors: Garcia Mariano
Published: January 2021

For all practical purposes, mathematical reform in Latin America began with the First Inter-American Conference on Mathematical Education, held in Bogota, Colombia, December 4 to 9, 1961.
Classics in Mathematics Education: Mathematics and Liberal Education
Authors: Whitehead A. N.
Published: January 2021

The subject of my address today is the consideration of the part which the elements of mathematics should play in a liberal education for the generality of boys up to the age of nineteen. The boys I mean are, of course, those who are capable of a liberal education. Wealth can do much, but it cannot give brain, and it cannot give character; nor can it give the intellectual interests which come from the union of brain with character. Accordingly, I exclude the residuum of boys and am thinking of those only with fair brain and decent interests. Happily for England, these constitute the great majority of the ordinary students who pass on to our universities.
In-Service Education in Mathematics: Continual In-Service Education
Authors: Smith Lehi
Published: January 2021

Most teachers, when they consider in-service education, begin looking to colleges and universities for opportunities. This is not surprising, in view of the nature of their previous educational experiences. The purpose of this article will be to suggest some other opportunities and possibilities for in-service education, opportunities and possibilities that are frequently overlooked.
Classics in Mathematics Education: Reorientation in Math Education
Authors: Fehr Howard F.
Published: January 2021

IN MATHEMATICS, as in other areas of knowledge, shifts of emphasis and of content take place in instruction from one generation to the next. This is as it should be. Discoveries are being made in subject matter and in the way human learning takes place. During the last quarter of a century sufficient changes in mathematics knowledge, in mathematical procedures and applications, and in the explanation of human behavior have occurred to warrant a reappraisal of our program in mathematics education. This evaluation can serve as a guide to reorientation of mathematics instruction in the schools.
Points and Viewpoints: The Season's Thanks
Authors: Brune Irvin H.
Published: January 2021

As The Council grows, The Mathematics Teacher requires more and more volunteer workers. It therefore seems appropriate to express thanks occasionally to the numerous people who help to keep the journal in print. Some of our helpers have joined us relatively recently; others have contributed through the years. We need them, every one, and we hope that our list for 1968 lacks no rightful entry and misspells no name.
Simplified Procedures for Computing the Federal Income Tax
Authors: Morton Robert L.
Published: January 2021

The procedure outlined by the Internal Revenue, service (IRS) for computing the amount of tax due, after the taxable income has been determined (line lld, Form 1040), requires five computational steps: (1) subtract the lower limit or the top bracket from the taxable income, (2) multiply the difference by the applicable rate, (3) add the product to a stated amount, (4) multiply the amount obtained in Step 3 by .075, and (5) add the product to the amount obtained in Step 3.
He That Has Eyes, Let Him See!
Authors: Schulz Raymond H.
Published: January 2021

A rhapsody without words the algorithm for square root gives way to methods that accommodate machine calculations. This one also sets bounds
Computer-Oriented Mathematics: Quadratic Equations—Computer Style
Authors: Koetke Walter , Kieren Thomas E.
Published: January 2021

ONE of the “old” topics that has been approached in a “new” way in modern mathematics is quadratic equations. No longer do students simply memorize the quadratic formula and do hundreds of exercises using it.
Experimental Programs: Achievement in Senior Advanced Mathematics and First-Year College Mathematics
Authors: Nichols Eugene D. , Shimizu Mildred T.
Published: January 2021

There has been increased attention throughout the nation to the problem of improving mathematics curricula. Changes in approach and content are being made at all levels of education. Senior high schools are also offering advanced courses for college credits. Only a few studies (Howell, 1964; Peters and Miller, 1958; Wick, 1964) have been done to examine the value of accelerated courses.
The Uniqueness of the Field of Complex Numbers
Authors: Willson William Wynne
Published: January 2021

IN A recent paper in this journal Dorman, Tollefson, and Stein1 considered under what binary operations of addition and multiplication the set S of ordered pairs of real numbers becomes a field. In particular they showed that the three following assumptions lead to infinitely many possible fields, which they classified into three types. The assumptions are these:
The Last Word on Solving Inequalities
Authors: Frandsen Henry
Published: January 2021

When we are teaching methods for solving problems, it is often good pedagogical practice to present several methods, including those which we may regard as difficult or inefficient, and to work some problems by these various methods. The final technique to be emphasized should be the most efficient one that can be made available to the students at their particular level. The following technique is the one that I have found to be “the last word” for solving inequalities. Although it does appear in several college textbooks (some of which are listed in the bibliography), I believe it deserves more widespread use at the secondary level.
Experimental Programs: Academic Stimulation of Mathematics Pupils from Their Classroom Association with Brighter Pupils
Authors: Nichols Eugene D. , Schrank Wilburn R.
Published: January 2021

One of the most frequent reasons given for grouping pupils according to ability in mathematics is that this procedure provides for the maximum development of each pupil's potential. It is frequently argued that the academic stimulation a bright pupil receives by association with other bright pupils motivates him to greater achievement. If this is true, then the slow student should also benefit by associating with the brighter students; and this is one of the arguments of those who advocate heterogeneous grouping. The results of the experiment described in this paper indicate that academic stimulation is not a factor in the learning situation as far as academic achievement is concerned. This implies that ability grouping for the purpose of increasing achievement is worth less unless provision is also made for curriculum differentiation to the extent that each homogeneous group has the opportunity to learn at its optimum level.
Historically Speaking— The Teaching of Arithmetic in England from 1550 until 1800 as Influenced by Social Change
Authors: Bidwell James King
Published: January 2021

In 1542 there appeared in London a book by Robert Recorde entitled “The Grounde of artes: Teaching the worke and practice of Arithmetike, both in whole numbers and Fractions, after a more easyer and exacter form than any like hath hitherto been sette forthe.” This publication was the first significant arithmetic book printed in English. Its printing marked the beginning of the dissemination in England of arithmetic techniques that we today would consider typical in our elementary schools. In the middle of the sixteenth century, however, these techniques were not widely known and were not taught in the vernacular English in the formal grammar schools.
In-Service Education in Mathematics: Patterns for Professional Progress
Authors: Whitmore Edward H.
Published: January 2021

These guidelines were developed by the 1967/68 MCTM Professional Standards Committee to provide a statement of preservice and in-service conditions for mathematics teaching. While attempting to be comprehensive, the document certainly does not exhaust the domain of professional concerns. In particular, the preservice training programs for mathematics teachers deserve much more attention and monitoring than these guidelines offer.
Computer-Oriented Mathematics: Computers in Mathematics Education
Authors: Koetke Walter , Zoet Charles J.
Published: January 2021

The advent of the computer has served as a catalyst to the turmoil in mathematics and mathematics education during the past decade. Mathematicians have run the gamut from 1950 when only a few innovative souls ventured to use computers to explore solutions of mathematical relationships to the present time when a majority of those who make extensive use of mathematics do so by means of a computer. Debates over whether the computer influences the essence of mathematics would not be difficult to locate, but there is no debating that the use of mathematics, now and in the future, is directly related to computer technology.
Experimental Programs: What Mathematics Shall We Teach the Low Achiever?
Authors: Nichols Eugene D. , Weiss Sol
Published: January 2021

It DOES not require an intensive reading of the literature to discover that wide and deep disagreement exists among teachers of mathematics as to what mathematics should be taught to the low achiever.
A Medieval Proof of Heron's Formula
Authors: Id Yusuf , Kennedy E. S.
Published: January 2021

THE expresion for the area of a triangle where a, b, and c are the sides and s is the semiperimeter, is associated with the name of Heron1 of Alexandria, although it may be due to Archimedes.
Notes on an Extension of Pythagorean Triplets in Arithmetic Progression
Authors: Waters William M.
Published: January 2021

IF ONE considers the equation x2 + y2 = z2, where x, y, and z are positive integers in arithmetic progression, it is obvious that the primitive solution of this equation is {3, 4, 5} and that all solutions are of the form {3d, 4d, 5d}, where d represents the common difference of the arithmetic progression.
Crisscross Multiplication
Authors: Smith Douglas D.
Published: January 2021

We present here an activity involving an unusual “multiplication” of natural numbers that has been enthusiastically received by junior high school students. Student enjoy computing a special product (called the crisscross product) of numbers geometrically and filling out the multiplication table for larger and larger numbers. The table has some surprising patterns and properties, including commutativity. If your students have learned about the greatest common divisor (g.c.d.) of two numbers, the activity reveals a connection between the crisscross product and the g.c.d.
Serendipitous Discovery of Pascal’s Triangle
Authors: Stanley Francis W.
Published: January 2021

Teachers often welcome questions from students—especially if the questions were anticipated in preparing the lesson. But unanticipated questions may not be so eagerly received. Some of these are motivated by a student’s desire to divert the teacher from the subject at hand; others, by honest curiosity. Regardless of their motivation, there are those occasional questions that fit naturally into the discussion. Many of these may well be worth the price of preempting a carefully planned lesson to search out a reasonable conclusion with the students. Such a question was responsible for a serendipitous digression in our first-year algebra class.
Given a Length x, Construct the Unit Segment—an Unfinished Problem for Geometry Students
Authors: Davis Edward J. , Smith Thomas
Published: January 2021

Taking a given segment as unity, geometry teachers have frequently challenged their students to construct a segment of length , where x is a positive integer.
Pythagorean Triples: What Kind? How Many?
Authors: Watson James D. , Comella James J.
Published: January 2021

Here are some illleresting observations about the Pythagorean triples—some things you may not have known about.
Patterns: Digits, Squares, and Bases
Authors: Duncan David R. , Litwiller Bonnie H.
Published: January 2021

Using this pattern approach in the study of properties and operations of numbers will increase understanding and lead to some interesting discoveries.
Self-Paced Mathematics Instruction: How Effective Has It Been in Secondary And Postsecondary Schools?
Authors: Schoen Harold L.
Published: January 2021

The May 1972 issue of the Mathematics Teacher contained eight articles dealing with individualizing mathematics instruction. Most of the articles discussed a modular, self-paced approach to individualization. Since that time a substantial amount of research testing the effectiveness of such programs has been reported. This paper is a review of studies comparing self-paced, individualized programs with other teaching approaches at the secondary and post-secondary levels. A recent review of similar studies conducted with elementary school students showed that the results were overwhelmingly against individualized instruction as measured by mathematics achievement, with some ambiguity on attitude and other affective measures (Schoen 1975). Do these negative findings continue into secondary school and beyond? Mathematics teachers at these levels will find the results summarized here very informative, especially if they are considering adopting an individualized program.
Individualization
Authors: Willoughby Stephen S.
Published: January 2021

The teaching of mathematics has always been individualized. In its simplest and unfortunately most common form, this individualization has consisted of lectures by the instructor, which were individually “turned off” or ignored by the students whenever they got the urge. Good teachers have always attempted to do more than this to help individual students learn material that is appropriate to their background and interests.
Issues from the NACOME Report
Authors: Hill Shirley
Published: January 2021

There can be little question that following a fifteen-year period of unprecedented favor and prominence in the curricula of American schools, mathematics teaching today faces the future with less certainty of its goals and less optimism about its potential effectiveness.
Dense, Denser, Densest
Authors: Lamon Richard A.
Published: January 2021

Try to discover your own method for proving that between any two rational numbers is another rational number.
Exploring Skewsquares
Authors: Olson Alton T.
Published: January 2021

If you are into transformational geometry—this will delight you. If not, you'll enjoy exploring the structure that evolves.
Transformation Geometry and The Artwork of M. C. Escher
Authors: Haak Sheila
Published: January 2021

Students can learn to analyze the symmetries and transformations in Escher's drawings. What's more, they can he taught the techniques necessary to make their own drawings.
“Digital Sum” Divisibility Tests
Authors: MCcaffrey Kenneth J.
Published: January 2021

Modular arithmetic offers new insight into divisibility.
Problem Posing and Problem Solving: An Illustration of Their Interdependence
Authors: Walter Marion I. , Brown Stephen I.
Published: January 2021

Generating questions is as important as answering them. Mathematics offers many opportunities for teaching students to ask a wide variety of related questions on a given problem.
A Further Neglected Mean
Authors: Iles Kim , Wilson Lester J.
Published: January 2021

The root mean square will add to your repertoire of means from the Maor article.
Polar Coordinates and Computer-Linked Plotters
Authors: Allison Joe Frank
Published: January 2021

When plotting polar relations, don't forget to use the familiar facts R2 = X2 + Y2 and COS2θ + SIN2θ = 1.
An Overview of the Mathematics Achievement Tests Offered in the Admissions Testing Program of the College Entrance Examination Board
Authors: Jones Chancey O. , Rowen Mildred R. , Taylor Howard E.
Published: January 2021

In the 1964-65 academic year, the College Entrance Examination Board introduced two new levels of mathematics Achievement Tests in its Admissions Testing Program (ATP): Mathematics Level I and Mathematics Level II. They replaced the intermediate and advanced mathematics examinations in response to factors affecting mathematics education from the mid-1950s to the mid-1960s.
The Teaching of Percent
Authors: Schmalz Rosemary
Published: January 2021

You will find this article helpful if your students are still confused about percent.
The High School Mathematics Research Paper
Authors: Woerner Kathy
Published: January 2021

Excellent ideas on that assignment you've often considered—plus a student's remarks on the “thrill of discovery” in doing a research paper.
Only You Will Know
Authors: Cunningham Helen
Published: January 2021

Three quizzes designed to provoke the mathematics teacher to self-analysis.
Another Look at The Tower of Hanoi
Authors: Shwarger Michael
Published: January 2021

A complete analysis of an old problem, which fascinates students of all ages.
A Demonstration of Terrible Teaching Techniques
Authors: Davidson Neil
Published: January 2021

Is this anyone we know?
Constructions With Obstructions
Authors: Avital Shmuel , Sowder Larry
Published: January 2021

A challenging twist to revitalize some familiar construction problems.
Calculations You Would Never Make Without a Minicalculator
Authors: Litwiller Bonnie H. , Duncan David R.
Published: January 2021

An excellent collection of interesting problems for minicalculators.
The Greatest Integer Symbol—an Applications Approach
Authors: Usiskin Zalman
Published: January 2021

A collection of problems for classroom use.
Rated X for Mathematical Minors
Authors: Lorch Edgar R.
Published: January 2021

A challenging point of view on the appropriate preparation for the study of calculus.
Are Calculators a Crutch?
Authors: Usiskin Zalman
Published: January 2021

The “crutch premise” is essentially that if you allow students to use a calculator for arithmetic problems that can be done by hand, then the students will be unable to do arithmetic when the calculator is absent. A corollary to this premise is that calculators should not be used with young students who are still learning arithmetic. Another corollary is that calculators should not be used with older students who have not yet learned arithmetic— that is, calculators should not be used in remedial classes.
Getting to The Roots of the Problem
Authors: Aieta Joseph F.
Published: January 2021

An innocent problem on provokes provokes an investigation by algebra students which applies a lot of familiar mathematics and opens the door to some that is not so familiar.
Microcomputers in the Classroom
Authors: Price Camille C.
Published: January 2021

Do reductions in size and cost non make a classroom computer available to you?
Sharing Teaching Ideas
Authors: Aidala Gregory , Rosenfeld Peter
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 an original and four copies of your ideas to the managing editor for review.
Sharing Teaching Ideas
Authors: Turner Sally
Published: January 2021

Have you discovered that your college-bound first- and second-year algebra students, as well as your trigonometry students, cannot compute with fractions and decimals? Try using cross-number puzzles—self-checking activities that provide practice in basic computation.
Activities: Calculating Order
Authors: Smith Susan
Published: January 2021

This section is designed to provide mathematical activities suitable for reproduction in worksheet and transparency form for classroom use. Appropriate laboratory experiences, discovery activities, and model constructions of mathematical significance drawn from the topics of the seventh, eighth, and nine grades are most welcome. Send your suggestions, in a four-page format similar to the “Activities” already published, to the managing editor for review.
The Seventh U.S.A. Mathematical Olympiad
Authors: Greitzer Samuel L.
Published: January 2021

The Seventh U.S.A. Mathematical Olympiad was held on 2 May 1978. From the Honor Roll of the Annual High School Mathematics Examination, 108 students, who had scored 118 points or better, were invited to take part, and 106 did participate. The papers were graded, first by Professors Michael Aissen and John Bender, of Rutgers University, and then by Professor Murray Klamkin, of the University of Alberta, and me. The Olympiad problems appear at the end of this article.
Sharing Teaching Ideas
Authors: Sanok Gloria
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 an original and four copies of your ideas to the managing editor for review.
Secondary School Mathematics from The EPA Gas Mileage Guide
Authors: Vest Floyd
Published: January 2021

Some timely applications of algebraic ideas and skills.
The Student's Universal Distributive Law
Authors: Maron Melvin J.
Published: January 2021

An examination of an all too universal misconception.
Determining Fuel Consumption—An Exercise in Applied Mathematics
Authors: Wagner Clifford H.
Published: January 2021

A trillion miles of U.S. driving consumes gasoline in staggering amounts.
Spirolaterals: Advanced Investigations from An Elementary Standpoint
Authors: Schwandt Alice Kaseberg
Published: January 2021

Generate a variety of designs, then use them for mathematical investigations.
Writing Equations for Intersecting Circles
Authors: Hopkinson Richard J.
Published: January 2021

A nice method for guaranteeing that two circles will intersect at points with integral coordinates.
Generally, How do You Solve Equations?
Authors: Snover Stephen L. , Spikell Mark A.
Published: January 2021

Students get a chance to solve difficult equations with numerical techniques that can he used easily on calculators.
Baseball Statistics
Authors: Beckenbach Edwin F.
Published: January 2021

Can you determine the better batter?
On Archimedean Solids
Authors: Boag Tom , Boberg Charles , Hughes Lyn
Published: January 2021

Some junior high school students report on their explorations in solid geometry.
Geometric Transformations and Musical Composition
Authors: O'Shea Thomas
Published: January 2021

The purpose of this article is to provide a basis for interdisciplinary activities for students studying transformation geometry. Too often the manipulations of figures that experienced geometry teachers find so attractive do not evoke the same response from their students.
A “Stencil Method” for Solving Quadratics of The Type ax2 + bx + c = 0 That Have Real Roots
Authors: Smith Brother Albertus
Published: January 2021

Less able students enjoy using parabolic shapes to solve quadratic equations.
Teaching the Absolute Value Function
Authors: Brumfiel Charles
Published: January 2021

Take time to review some different approaches to absolute value. You may be surprised to find some easier methods than what you are currently using.
A General Divisibility Test for Whole Numbers
Authors: Szetela Walter
Published: January 2021

Divisibility rules are excellent examples of principles from number theory that are easily understood, interesting to explore for new conjectures, and frequently easy to prove. At the same time, some conjectures are easy to understand, yet hard to prove or disprove.
How Fast Can You Watch?
Authors: Austin Joe Dan
Published: January 2021

An optimization problem with a different slant.
Unsolved Problems in Geometry
Authors: Steen Lynn Arthur
Published: January 2021

The difficult problems we do tomorrow; the impossible ones take a little longer.
Constructing Meaning for The Concept of Equation
Authors: Herscovics Nicolas , Kieran Carolyn
Published: January 2021

We teach equation solving all the time, but what are the students learning?
Meet the Challenge: Individualize
Authors: Ortolan Cathy , Camp Carol
Published: January 2021

Students’ standardized test scores increased—and two years of mathematics are now required for all students to graduate.
Avoiding Service Station Fraud
Authors: Burton Grace M. , Burton John R.
Published: January 2021

If there is one thing as sure as death and taxes, it is that sixteen is a magic birthday for high school students. On its eve. visions of driver’s licenses dance in their heads. Many of these young men and women will own a car before they are seventeen. Since few of them have unlimited funds, they are very interested to learn ways that automobile costs can be kept to a minimum. Teenagers also derive satisfaction from outsmarting unscrupulous service station operators. This unit is designed to alert high school students to some of the more prevalent service station frauds as they practice computational skills. Apart from this introductory section, the material presented here is addressed directly to the high school student and may be reproduced and used as class handouts. It is hoped that this unit will give some interesting practice in mathematical skills to young consumers. A set of problems for the student is also included and may be photoreproduced by teachers for use in their classes without writing for permission.
From Magic Squares To Vector Spaces
Authors: Cohen Martin P. , Bernard John
Published: January 2021

Those number squares offer an opportunity to study structure.
Merlin™ And The Magic Square
Authors: Gibbs Richard A.
Published: January 2021

A nice mathematical strategy for beating the machine.
Overbooking Airline Flights
Authors: Austin Joe Dan
Published: January 2021

A practical problem for an airline company is how many reservations should be accepted for a particular flight. If everyone who makes a reservation shows up at the airport to buy a ticket, the solution would be easy. The airline should simply take no more reservations than there are seats on the airplane. However, many people with reservations do not show up at the airport, so there are empty seats on the flight that could be filled if more reservations were accepted.
Understanding Area And Area Formulas
Authors: Battista Michael
Published: January 2021

Consider the difference between the standard procedures for measuring length and area. Length is measured directly. The length of a segment is the number of arbitrarily chosen unit lengths that fit end to end on the segment. We measure length by using a ruler-like device that has the unit lengths already marked off and counted on it. Area, in contrast, is measured indirectly. Although the area of a region is the number of arbitrarily chosen unit areas that cover the region with no overlap, almost always we measure area by taking linear measurements and inserting them into a formula.
Ahsme, Aime, Usamo: The Examinations Of The Committee On High School Contests
Authors: Maurer Stephen B. , Mientka Walter E.
Published: January 2021

The Mathematical Association of America’s (MAA) Committee on High School Contests, or CHSC, sponsors three examinations given across North America and in many countries abroad. The oldest, the American (formerly Annual) High School Mathematics Examination (AHSME), is a thirty-question, one-and-one-half-hour, multiple-choice examination, now beginning its thirtyfourth year. In 1982 it was taken by over 418 000 students in 6623 schools in North America alone. It is known to many people as the “MAA Contest,” the “High School Contest,” or the “Annual High School Contest.” The USA Mathematical Olympiad (USAMO). now in its eleventh year, is a five-question, three-and-onehalf-hour. complete-answer examination, heretofore offered by invitation to the top 100 to 150 participants in the AHSME.
President Garfield’S Configuration
Authors: Weiner Allan
Published: January 2021

President Garfield used a configuration consisting of a trapezoid divided into three right triangles to prove the Pythagorean theorem (fig. I). He proved that c2 = a2 + b2 by equating the sum of the areas of the triangles to the area of the trapezoid BCDE. This same configuration can be used to prove trigonometric as well as algebraic theorems in a nonstandard way.
Strategies In Yahtzee: An Exercise In Elementary Probability
Authors: Milton J. Susan , Corbet James J.
Published: January 2021

The game of Yahtzee. though fairly complex in nature, can be analyzed to some extent using the methods of elementary probability. The reader is referred to the article "Probabilities in Yahtzee” (Litwiller and Duncan, this issue) for a complete explanation of the rules of the game.
When Does A Subtraction Algorithm Involve Borrowing?
Authors: Kolb John R.
Published: January 2021

In the February 1982 issue of The Mathematics Teacher, Irvin Vance wrote an interesting article describing two algorithms for the subtraction of whole numbers. He describes an algorithm presented by Colton (1980) and concludes that it involves borrowing. Vance calls the second algorithm he discusses the residue method, and he claims that it does not involve borrowing. One of Vance's colleagues claims that both algorithms do involve borrowing. Vance ends the article by asking "What do you think—is borrowing involved?”
Eureka! Pythagorean Triples from the Multiplication Table
Authors: Didomenico Angelo S.
Published: January 2021

It is important that teachers of mathematics encourage open, imaginative investigations that give students an opportunity to probe, find patterns and relations, and derive new patterns and relations from others. Activities of this kind foster analytic and creative thinking, and so they involve students in problem solving of the highest order. They also generate enthusiasm. stimulate interest, and can give considerable insight into the nature and the underlying unity and beauty of mathematics.
Teaching Descriptive and Inferential Statistics Using a Classroom Microcomputer
Authors: Collis Betty
Published: January 2021

There is no doubt that statistics should be an important part of the secondary mathematics curriculum. A single classroom microcomputer can be valuable for work in both descriptive and inferential statistics. This article presents a framework for integrating a microcomputer into a statistics unit and includes descriptions of some programs suitable for the Apple microcomputer and ideas for lessons.
MATHCOUNTS: A New Junior High School Mathematics Competition
Authors: Jones Mary Harley
Published: January 2021

MATHCOUNTS is the first nationwide effort of industry, education, and government to promote excellence in mathematics through a junior high school mathematics competition.
Pascal's Triangle— a Serendipitous Source for Programming Activities
Authors: Eng Marita , Casey John
Published: January 2021

Pascal's triangle is an elegant array of numbers that has fascinated mathematicians since its invention. Its applications in algebra, number theory, and probability are well known. The use of Pascal's triangle in the classroom need not be restricted to these conventionally accepted applications. Explorations of Pascal's triangle through the use of computer programming create situations that are incredibly rich in their mathematical yield.
Seeking Relevance? Try the History of Mathematics
Authors: Swetz Frank J.
Published: January 2021

What is mathematics? This seems like a curious question to pose to a reading audience of mathematics educators, but I would wager that, on reflection, it is a difficult one to answer. Of course, a variety of quips and clichés can supply the answer: “It's an art,” “A science—in fact, it's the queen and the servant of science,” “It's what I use when I balance my checkbook,” “A game that we play with rules we're not quite sure of,” and the apologetic favorite, “Something I was never good at”; and so the list can go on and on.
Approximation of Area under a Curve
Authors: Sconyers James M.
Published: January 2021

High school students occasionally find themselves needing to determine the area under a curve. This problem may arise when motion or work is studied in a science course; the curve is plotted from experimental data, and no equation of the curve is known. In a mathematics course, a function may be given and the area under it may be of interest. If the equation of the curve is known, then the problem of finding the area can be a formidable one unless the student has studied calculus. If the equation of the curve is not known, even calculus wouldn't help to obtain an exact solution to the problem.
Systematic Experimentation— A Frequently Used Problem-Solving Strategy
Authors: Clemens Stanley R.
Published: January 2021

Ever since NCTM published An Agenda for Action (1980), problem solving has been a frequent topic of discussion in the literature of mathematics education and at professional meetings.
Female Mathematics Educators Recommend Books
Authors: Lazarnick Sylvia , Frantz Marny
Published: January 2021

A recent issue of the Mathematics Teacher reported the results of an interesting question posed to mathematics educators, “What are the ten most important books for a secondary school (grades 7–12) mathematics teacher to read?” (Leake 1983). As secondary mathematics teachers, we eagerly read the article and at once realized that we needed and wanted to know what books female mathematics educators might recommend. We set out to ask them.