bluuebunny/crossref_metadata_2025 huggingface dataset:
Summer In-Service Experiences in Teaching Noncollege Preparatory Mathematics
Authors: Foley Jack , Smith Leroy B.
Published: January 2021

Does it warm your heart to know that you will be assigned one or more basic, general, or remedial mathematics classes this year? It did for twenty-five teachers who participated in a unique in-service summer program this past summer. Most of these teachers were eager to return to their counties to make certain they had at least one noncollege preparatory mathematics class and to start their instructional plans for the year.
The Two-by-Two Transportation Problem
Authors: Shudde Rex H.
Published: January 2021

Linear programming is one of the tools of operations research which has been developed in the past two decades. It is a natural extension of linear algebra.
A Topological Problem for the Ninth-Grade Mathematics Laboratory
Authors: Auclair Jerome A. , Hillman Thomas P.
Published: January 2021

It is often difficult to maintain an exciting and interesting atmosphere in a ninth-grade general mathematics class. Emphasis on computational skills that students have studied many times but not yet mastered can become routine and ineffective. Lagging student interest and enthusiasm can discourage a teacher from continuing the proper time-consuming preparations necessary to make stimulating and academically satisfying classes. New approaches to old ideas are not always embraced by the class. Good ideas are not easy to find.
Mr. Harmon O. Graph
Authors: Shipley Lois Q.
Published: January 2021

A listing of PACE (Tille III ESEA) projects that are believed to be of special interest to mathematics teachers has been prepared by Edwina Deans and Dexter Magers of the U.S. Office of Education. Single copies only of this listing may be obtained from Dexter Magers, Division of Plans and Supplementary Centers, U.S. Office of Education, 400 Maryland Avenue, S.W., Washington, D.C. 20202.
Functions: Dependent Variables to Fickle Pickers
Authors: Hight Donald W.
Published: January 2021

IN THE last century much has been said about functions, and the concept has become a central theme in secondary school curricula. Magazine articles, convention speeehes, and some of the newer text materials have devoted considerable effort to present, clearly, this important, unifying mathematical topic.
Points and Viewpoints: Welcome to a New Editor
Authors: Brune Irvin H.
Published: January 2021

OUR new editor of “Reviews and Evaluations” is Richard R. Eakin. It pleases us to welcome him to this post. He brings to THE MATHEMATICS TEACHER. excellent ability, genuine dedication, and a keen interest in this kind of work. We greatly appreciate his willingness to assume this weighty responsibility and step into the breach caused last March by the untimely death of Harold Tinnappel.
Mathematical Education for a Scientific, Technological, and Industrial Society
Authors: Fehr Howard F.
Published: January 2021

Foreword: In proposing a radical departure from an existing program in mathematical education, one is always open to justifiable criticism from those who would maintain the status quo or those who would proceed otherwise in reform. One who seeks a change also has to some extent a bias for his point of view, which may prejudice the proposal. The following thesis, supported in part by experiments now under way, although presented strongly, is not advocated as THE program but is presented for consideration and dialogue aiming toward educational development.
Experimental Programs: Factors Relating to a Teacher's Knowledge of Contemporary Mathematics
Authors: Lyng Merwin J.
Published: January 2021

Some of the teaching materials that have evolved as a result of national and local curriculum developments are often referred to as modern or contemporary mathematics. The mathematics that is included in some of the programs of the secondary schools today is, in many ways, different from that of a decade ago. Corresponding changes in the curricula for the education of mathematics teachers have only recently been introduced. Because of the nature of their preparation and experience, many mathematics teachers have discovered that they do not have the knowledge of contemporary mathematics that is needed to function adequately with the contemporary materials.
Historically Speaking— Giuseppe Peano at the University of Turin
Authors: Kennedy Hubert C.
Published: January 2021

Giuseppe Peano visited America only once, as a delegate to the International Mathematical Congress of 1924 in Toronto. A group photograph was made and published in the Proceedings. Peano is near the center of the last row, a balding man with gray hair and beard. His vest is buttoned, but his coat is not, and his tie is skewed to his left. He was the official delegate of the University of Turin, the Academy of Sciences of Turin, and the Academia pro Interlingua. At the Congress Peano gave a paper entitled “De Aequalitate,” which appear as two pages of the Proceedings in the section containing abstracts. However, it is probably the complete paper. One wonders what impression Peano made on the younger delegates at the congress. Here was a man who had emerged in the last decades of the nineteenth century as an acute mathematician and logician, now reading a distressingly simple paper in a strange language (his own invention!), speaking with a gruff voice that must have contrasted sharply with his childish-sounding pronunciation. (He was unable to say the letter “r” and said “I” in its place.)
Finger Reckoning in an Arabic Poem
Authors: Saidan A. S.
Published: January 2021

Among the arithmetical systems of the Middle Ages was the so-called finger reckoning. It received its name from the fact that it involved the peculiar way of indicating numbers by placing the fingers of the two hands in distinguishing positions.
A New Approach to the Teaching of Constructions
Authors: Usiskin Zalman
Published: January 2021

“Constructions are different!” “Constructions are interesting!”
Classics in Mathematics Education: A New Approach to Elementary Geometry
Authors: Birkhoff George D. , Beatley Ralph
Published: January 2021

Purpose of Demonstrative Geometry.— In demonstrative geometry the emphasis is on reasoning. This is all the more important because it deepens geometric insight. To the extent that the subject fails to develop the power to reason and to yield an appreciation of scientific method in reasoning, its fundamental value for purposes of instruction is lessened.
Exploring Geometric Maxima and Minima
Authors: Garfunkel J.
Published: January 2021

In an Article that appeared in The Mathematics Teacher, * many interesting geometric as well as trigonometric inequalities were developed by starting with the theorem that the arithmetic mean of n positive quantities is not less than their geometric mean. The author also developed a few geometric maxima and minima properties in this manner.
Research in Programmed Instruction in Mathematics
Authors: Zoll Edward J.
Published: January 2021

Now that programmed instruction has gained some acceptance in the schools, various questions concerning its format, applicability, etc., are being investigated in doctoral research studies. Not only are some earlier questions being answered by the growing body of research, but additional areas have been indicated as necessary and fruitful for study. The purpose of this paper is to examine recent research in the use of programmed instruction in mathematics.
Historically Speaking— Anomalous Mathematical Nomenclature
Authors: Read Cecil B.
Published: January 2021

One often finds that a theorem, a process, a curve, etc. has attached to it the name of the mathematician who was its discoverer. In many cases, however, a mathematician who made the same discovery earlier has been completely overlooked. Sometimes both names are now associated—again, tradition or custom leaves a single name, not always that of the first developer.
The Dilemma in Geometry
Authors: Allendoerfer Carl B.
Published: January 2021

THE mathematical curriculum in our elementary and secondary schools faces a serious dilemma when it comes to geometry. It is easy to find fault with the traditional course in geometry, but sound advice on how to remedy these difficulties is hard to come by. The Commission on Mathematics of the CEEB, the School Mathematics Study Group, the Illinois Project, and many other curricular reform groups at home and abroad have tackled the problem, but with singular lack of success or agreement. On the other hand, the “new math” has made great strides in arithmetic and algebra that seem to be acceptable to all except the congenital standpatters who resist change of any kind. We are, therefore, under pressure to “do something” about geometry; but what shall we do? In this article I shall discuss the reasons for the present state of confusion and make suggestions for modest first steps toward clearing it up.
Teaching the Low Achiever in Mathematics
Authors: Beckmann Milton W.
Published: January 2021

THE crisis in education for the low achiever in mathematics can be expressed in many ways— in personal terms: eyes filled with fear or boredom, families frustrated or completely uninterested, a collapse of self-respect;
International Mathematical Education: Elitism and Excellence
Authors: Fehr Howard F. , Snow Lord C. P.
Published: January 2021

I thought of speaking about Science, Mathematics and the Imagination, but I have changed my mind. I fancy enough has been said on this kind of subject to last us for some time. I don't believe that many sentient educated people nowadays doubt that creative mathematics and science call for as high qualities of imagination as any human activity: if they do, they have no excuse. And I believe people are beginning to realise that creative science doesn't work as scientists used to pretend it did. Medawar's writings1 and James Watson's recent book2 have taught the simple lesson that, as a rule, scientists know the answer before they prove it. This is called the hypothetico-deductive method. All this is very interesting, but it is becoming part of the intellectual climate. So I have decided to say something on a more practical topic, where there are some decisions we may have to make—some of them quite soon. I am calling this topic Elitism and Excellence.
Graphing True-False Statements
Authors: Wiscamb Margaret
Published: January 2021

In elementary logic the construction of truth tables, while not difficult, can be a long and tedious process. In this article I would like to present a simple graphic representation of the truth values of compound statements involving two or three components. The graph gives all the information found in a truth table and pictures the statement as an easily recognizable pattern. By using this graphing procedure, the simplifying of statements is shortened considerably. In fact, for statements involving only two components, with a little practice it can usually be done by inspection. Proving that a statement is a tautology becomes almost trivial.
Computer-Oriented Mathematics: A Case Study in Mathematics—the Cone Problem
Authors: Koetke Walter , Damaskos Nickander J.
Published: January 2021

An INNOVATIVE program, Preview of Modern Concepts in Engineering,* is under development for all senior or junior level college-bound students. Now in its third year, the program is built around case studies of large-scale engineering systems several of which illustrate the applications of computer technology in the realistic or natural setting provided by the cases. The program emphasizes the hands-on approach to computer instruction.
Experimental Programs: A Study of Placement Methods for Entering College Freshmen in the Proper Mathematics Sequence at Michigan Technological University
Authors: Nichols Eugene D. , Howlett John L.
Published: January 2021

Producing a capable and well rounded engineer and scientist is a pri mary goal at Michigan Technological University. A necessary ingredient of that engineer is a firm understanding by the individual of basic mathematical concepts. In the expanding technology of today there is a need for a strong background in the mathematics field at an early date. Because of this need a lag or gap has de veloped between the educational require ments of a student entering an engineering program and that of the actual degree of preparation of the student. Some high schools have begun to comply with the recommendations of such authorities as the Committee for the Undergraduate Program in Mathematics (CUPM); others have not.1 This problem has presented much difficulty to Michigan Technological University as well as to other schools across the nation. In order to be able to produce the qualified engineer, Michigan Technological University has had to assume the very recommendations of the CUPM group; that is, the engineering stu-dent must at least begin with analytic geometry if the student hopes to complete his degree work in a normal four-year course. But this certainly brings about a difficult problem; what do we do with the young man who wants to be an engineer and is not prepared? Much more, how can we properly decide which student is ready and which is not?
Points and Viewpoints: Holiday Gratitude
Authors: Brune Irwin H.
Published: January 2021

The GOOD work of numerous contributors continues. Indeed, as the National Council of Teachers of Mathematics grows, the number and kinds of volunteer services grow. This, the fifth card of thanks in a series begun in 1965, attempts to convey appreciation to numerous people who have helped to maintain and extend the Mathematics Teacher.
Nominations for the 1976 Election
Authors: Hlavaty Julius H. , Begnaud Lurnice , Brydegaard Marguerite , Edwards E. L. , Hardgrove Clarence E. , Howitz Thomas , Schaaf Oscar , Taylor B. Ross , Thomason Gladys M.
Published: January 2021

The Nominations Committee needs your help in selecting nominees for the 1976 election. At that time four new members for the Board of Directors will be elected.
Polynomial Prime Producers: A Computer Problem for Secondary Students
Authors: Bidwell James K. , Fallon Ann
Published: January 2021

An unsolved problem in mathematics is the existence of a formula (function) that produces nothing but prime numbers. Many mathematicians have thought that they had discovered such a function, only to have composite numbers eventually pop up for some integer substitutions. In particular, it is known that no polynomial function over the integers can produce only primes. In fact, the proof of this theorem is not difficult and is found in many elementary number theory texts.
Models for Rational Number Bases
Authors: Pedersen Jean J. , Armbruster Frank O.
Published: January 2021

We think it’s important that you have some background on how this article came to be written. One of the authors sometimes plays a game he invented, called “hats,” in which he puts on a funny hat and converts base-ten numerals into another base representation. For example, he puts on a beanie and calls for anyone to say a favorite number. Someone says “six.” He goes to the chalkboard and writes “110,” The object of the game is for the students to figure out what he is doing, Someone who figures it out says, “Gotcha!” And then that person gets to wear the hat until someone else says, “Gotcha!” (In case you haven’t “got it” yet, the beanie hat converts numbers to the binary representation.) Several hats are used in the course of play, and each represents a different number base, but it’s always a natural number base greater than one. Recently we began to wonder if perhaps you can have a negative number base system in which the base is not an integer. And if you can, what will the numerals look like?
Adam Smith in the Mathematics Classroom
Authors: Lipsey Sally I.
Published: January 2021

Economists are constantly in the news. We think of their pronouncements as we shop, write laws, elect officials, declare war or peace, negotiate (personally or as a nation) with our friends and rivals all over the world. Can we use these deep concerns to enrich the teaching of mathematics? The purpose of this paper is to indicate how the standard curriculum can be motivated, illuminated, and reviewed by ideas from economics without overburdening either student or teacher.
Getting Bounds on π Using Trigonometric Tables
Authors: Hollist J. Taylor
Published: January 2021

The first known scientific attempt to calculate the ratio of the circumference of a circle to its diameter was made by Archimedes about the year 240 B.C. Proposition 3 of his “Measurement of a Circle” states that this ratio is between 223/71 and 22/7, or 3.14, an accuracy of two decimal places. This ratio of the circumference to the diameter has been called pi (π) since the days of Euler (1737). Archimedes inscribed and circumscribed regular polygons, beginning with hexagons, until he had polygons of 96 sides. He then calculated the perimeters of the inscribed and circumscribed polygons in terms of the diameter of the circle.
Cross-Polynomial Puzzle
Authors: Hoerbelt Bernard G.
Published: January 2021

A cross-polynomial puzzle provides enjoyment as well as a review of addition, subtraction, multiplication, division, and simplification of algebraic expressions.
Instant Insanity—a Significant Puzzle for the Classroom
Authors: Troccolo Joseph A.
Published: January 2021

Puzzles are made of the things that the mathematician, no less than the child, plays with, and dreams and wonders about, for they are made of the things and the circumstances of the world he lives in (Kasner 1940, p. 188).
A Non-Simply Connected Geoboard—Based on The “What if Not” Idea
Authors: Schmidt Philip A.
Published: January 2021

An interesting topic for use in the mathematics classroom with varying degrees of sophistication for students in grades 7-12.
The Meaning of Euclidean Geometry in School Mathematics
Authors: Moise Edwin E.
Published: January 2021

Geometry is an important vehicle for helping students understand that mathematical procedures are methods of acquiring mathematical knowledge.
What Do Mathematics Teachers Think about the High School Geometry Controversy?
Authors: Gearhart George
Published: January 2021

A survey of the attitudes of secondary school mathematics teachers toward geometry.
Applications of Transformations to Topics in Elementary Geometry: Part I
Authors: Jackson Stanley B.
Published: January 2021

Some simple, intuitively appealing transformations form the basis for applications that may be presented at different levels of sophistication.
Derivatives of Trigonometric Functions-Revisited
Authors: Luthar R. S.
Published: January 2021

Here's a classic topic from analysis treated in an interesting new way with skillful application of identities and differentiation techniques.
Your Council at Work
Authors: Gibb E. Glenodine
Published: January 2021

We know that the NCTM exists to improve mathematics education from kinderga rten th rough the two-year colleges, but we don't always know just how. What exactly is the NCTM? How does it operate? What does an NCTM committee do all year?
Checkerboard Mathematics
Authors: Billstein Richard
Published: January 2021

Here are activities that fascinate students and motivate problem solving.
Comments on Euclid's Proof of the Infinitude of Primes
Authors: Schatz Mary Christine
Published: January 2021

The concept of the infinitude of primes is interesting if we exhibit a sequence of consecutive composite integers.
Your Council at Work: Meetings Committee
Authors: Cohen Louis S.
Published: January 2021

The Meetings Committee is responsible for all NCTM conventions and conferences not specifically designated as charges of other committees. Their duties include site and time selection, local arrangements, coordination with other major NCTM committees, and program planning, implementation, and evaluation.
Electronic Calculators—Friend or Foe of Instruction?
Authors: Machlowitz Eleanore
Published: January 2021

Bombarded with questions on pocket calculators? Here are some thoughts and references on their purchase. and on their use in the classroom.
1976—A Nice Number for the Bicentennial
Authors: Richbart Lynn A.
Published: January 2021

The year 1976 will be an interesting one, Since its last two digits (76) are divisible by 4, we know that the whole number (1976) is divisible by 4. That makes it a leap year (watch out, fellows!) and a presidential election year (watch out, everybody!).
A Strategy for Using Lsd!
Authors: Hancock Robert R.
Published: January 2021

Es1ablishing relationships in the process of solving problems.
The Pocket Calculator as a Teaching Aid
Authors: Maor Eli
Published: January 2021

Encourage your students to use their minicalculators to discover pallerns and verify mathematical statements.
A Mathematics Intramurals Contest
Authors: Elgarten Gerald H.
Published: January 2021

Did your general students ever win a mathematics trophy? Read this article and find out how it can be done.
Polya’S Triangular Array Problems
Authors: Palagi George H.
Published: January 2021

Dialogue between a bright student and a teacher that will have you thumbing through Polyas “How to Solve It” again.
A Mathematical Finish for 1976
Authors: Cunningham Helen
Published: January 2021

Mathematical decoding to celebrate the nation s 200th birthday.
Using Writing About Mathematics as a Teaching Technique
Authors: Geeslin William E.
Published: January 2021

Have we emphasized getting the answer to the point where our students cannot talk or write about mathematical concepts?
The Relationship Between ∫abf(x) dx and ∫kakbf(x) dx
Authors: Ahuja Mangho
Published: January 2021

A class discussion of the log function leads to an interesting generalization.
The Ladies' Diary … Circa 1700
Authors: Perl Teri
Published: January 2021

A documentation of women's interest in mathematics more than two hundred years ago.
Difference and Sum of Squares of Whole Numbers
Authors: Didomenico Angelo S.
Published: January 2021

Induction followed by deduction. An example from the world of whole numbers that you might like to try with your students.
Notes on the Partial Converses of a Familiar Theorem
Authors: Waters William M.
Published: January 2021

An example of getting more for your money from a given theorem.
Divisor Lattices and the Teaching of GCD and LCM
Authors: Miller Ann
Published: January 2021

Diagrams are used to record divisibility facts.
Sixteenth-Century Astronomers Had Prosthaphaeresis
Authors: Pierce R. C.
Published: January 2021

Did you ever wonder what numerical methods were used prior to logarithms? Werner's formulas provide the answer.
Graphical Properties of Sequences and Equations
Authors: Alexander Robert D. , Gatlin Andrew L. , Meehan Gregory , Williams David O.
Published: January 2021

An exploration of intriguing relationships between elementary analytic geometry and several familiar types of number sequences.
Word Problems: Abundant and Deficient Data
Authors: Francis Richard L.
Published: January 2021

A penetrating and intriguing analysis of the nays problems can be formulated.
Basic Skills Program in Phoenix
Authors: Mccully Ron
Published: January 2021

A school system tackles the challenge of minimum competency.
The Mathematics Usage Test of The Act Assessment Program: An Overview of its Purpose, Content, and Use
Authors: Ferguson Richard L. , Schmeiser Cynthia B.
Published: January 2021

The assessment of students during the transition from high school to college serves to collect and disseminate relevant information essential for decision making by the concerned parties: students and their parents, high schools, colleges, and—to a certain extent—the public, which helps to finance postsecondary education.
The Pascal Pyramid
Authors: Staib John , Staib Larry
Published: January 2021

Have you considered the patterns of the coefficients in the expansion of (x + y + z)n?
If You Can Count, You Can Add, Subtract, Multiply, and Divide Any Amount
Authors: Roseman Louis
Published: January 2021

Many students in my remedial classes claim they can count, but they still have difficulty with the basic operations on whole numbers. I have developed a “periodic table” of whole numbers so that they can accurately add. subtract, multiply, and divide (see fig. 1). The table has a “period” of ten, and every element in the first period generates an infinite family of multiples.
The World of Buckminster Fuller
Authors: Ranucci Ernest R.
Published: January 2021

“To me no experience of childhood so reinforced self-confidence in one's own exploratory faculties as did geometry. Its inspiring effectiveness in winnowing out and evaluating a plurality of previously unknowns from a few given knowns, and its elegance of proof lead to further discovery and comprehension of a grand strategy for all problem solving.”
Geodesic Domes by Euclidean Construction
Authors: Wenninger Magnus J.
Published: January 2021

In the February 1977 issue of the Mathematics Teacher, Fred Blaisdell and Art Indelicato coauthored an article entitled “Finding Chord Factors of Geodesic Domes.” Their approach involved threedimensional coordinate geometry and vector analysis, and the opinion was expressed that “the mathematics of geodesic domes is well within the capability of most senior high school mathematics analysis classes.”
Educational Quality Assessment in Pennsylvania
Authors: Guerriero Carl A.
Published: January 2021

The “what” and “for whom” of minimum competencies.
A Duplation Method of Long Division
Authors: Simpson Peter A.
Published: January 2021

Of the four basic arithmetic operations, division is perhaps the most poorly learned and the first forgotten. There is no denying that the compactness of the standard division algorithm makes it a desirable method to be learned. However, we are seeing a whole generation of people who learned it but forgot it as quickly as they could. I have developed a “duplation division” (so-called because of a doubling process) that is a viable alternative for many students who have difficulties with the traditional method of long division.
Rounding As A Binary Operation
Authors: Ross Joan
Published: January 2021

From this new perspective, rounding combines elementary number theory, number system properties, and fascinating Junction graphs.
Using Tables to Teach Mathematics
Authors: Keller Clifton
Published: January 2021

To generate a table is one thing—the search for patterns in the numbers generated is another.
The Even Triangle: A Heuristic Approach
Authors: Ouellette Hugh
Published: January 2021

A simple number-pattern setting for exploring, conjecturing, and, ultimately, proving.
Binomial Coefficients and The Partitioning of N-Dimensional Space
Authors: Crouse Richard
Published: January 2021

An example of extending Pascal's triangle to “higher” dimensional applications.
Curve-Stitching The Cardioid and Related Curves
Authors: Catranides Peter
Published: January 2021

Some mathematics behind some popular laboratory activities.
The Role of Programmable Calculators and Computers in Mathematical Proofs
Authors: Snover Stephen L. , Spikell Mark A.
Published: January 2021

Data generated by computing devices may he used as an essential part of a mathematical proof.
Magic Square Matrices
Authors: Lancaster Ronald J.
Published: January 2021

What happens when we think of magic squares as matrices?
An Application of An Algebraic Proof
Authors: Knaus Ronald M. , Knaus Christopher G.
Published: January 2021

Which do you prefer? Sales tax, then discount, or discount, then sales tax?
Two Sides to Zero: An Arithmetic Game with Integers
Authors: Taizi Naomi
Published: January 2021

In the Mathematics Teacher, Miller and Jeffrey (1977) describe an addition game with integers. They begin by remarking on the importance of making available to junior and senior high school students games providing skill practice whose rules are sufficiently simple. However, they claim that many of the available games for these students are so complicated that only those students not needing skill practice can learn them.
Sketching The Curve y=x sin1x
Authors: Baker Thomas B.
Published: January 2021

The graph of this function in most texts is misleading. Here are the facts!
Pascal's Triangle and Computer Art
Authors: Lund Charles
Published: January 2021

The famous triangle lives again with new and unexpected patterns in this delightful open-ended investigation.
Why I Teach Mathematics
Authors: Fujii John N.
Published: January 2021

Some reflections by a teacher … like you.
One Answer to “What is Calculus?”
Authors: Shilgalis Thomas W.
Published: January 2021

The question is often asked—and seldom answered in such an intriguing manner.
Trial and Error—Adams, Bettr, Best
Authors: McCabe John , Ransom Marshall R.
Published: January 2021

Students get hooked on a problem and explore some variations.
What is There so Mathematical About Music?
Authors: Maor Eli
Published: January 2021

After twenty years of teaching, Eli Maor still finds exciting the search for new applications of mathematics. His teaching experience reflects a long standing interest in science and in music in particular. In 1968 he gave sixteen lectures on music and science on the Israeli State Radio.
Results of A Questionnaire on Secondary Mathematics Teacher-Education Programs
Authors: Aviv Cherie Adler , Cooney Thomas J.
Published: January 2021

The survey reported here was conducted for the purpose of obtaining information about the status of secondary school mathematics teacher-education programs. The dearth of information about teacher-education programs was emphasized in the NACOME report (1975). The NACOME report particularly pointed out that little evidence exists on activities oriented toward preparation of mathematics teachers. This report represents an attempt to provide such information. In reporting the results, questions will be identified that need to be asked in order to obtain a clearer picture of the dynamics of a teacher-education program. We regret that we did not ask these questions.
Involving Students in Problem Solving
Authors: Gathany Timothy A.
Published: January 2021

Having students consider variations of a familiar problem can help to involve them in problem solving and often leads to interesting new problems.
A Computer Discovery Approach for Quadratic Equations
Authors: Zabinski Michael P. , Fine Benjamin
Published: January 2021

How often can we expect the roots of a quadratic equation to be real or imaginary?
When are We Ever Gonna Have to Use This?
Authors: Saunders Hal
Published: January 2021

If you teach junior high or high school mathematics, chances are you've heard this question before. And unless you happen to be a “jack of all trades,” you probably have not always been able to answer it. It was this predicament that led me to search for the missing answers as part of a sabbatical project.
An Improvement of a Historic Construction
Authors: Iles Kim , Wilson Lester J.
Published: January 2021

Some algebra helps show how five different means can be included on one figure.
Give ‘Em A Good Clubbing
Authors: Coffield Pamela W.
Published: January 2021

Mathematics teachers have precious little time during a school day to step back and view mathematics in perspective. Because of the rush of daily activity we also tend sometimes to fail to stress the enjoyment that can come from the study of mathematics. Consequently, an attitude of mathematical stoicism is conveyed to our students.
Where do These Numbers Come From?
Authors: Stover Donald W.
Published: January 2021

Some insight into techniques for removing the mystery of how calculators evaluate functions.
“I Have…. Who Has…?”
Authors: Giambrone Tom
Published: January 2021

Give your students a chance to practice some good listening skills while refreshing their algebraic skills.
The Randomized Response Technique: Using Probability Theory to Ask Sensitive Questions
Authors: Curlette William L.
Published: January 2021

Some surprising activities and some of the mathematics behind a comparatively new survey method, the randomized response technique.
Applications: Marketing Records
Authors: Knill George
Published: January 2021

The record industry provides many interesting applications of percent. In making a record, a company (the publisher) provides a studio, background musicians, a producer, technicians, and recording equipment as well as pays the artist for recording. These initial expenses can be substantial. The record company gets a return on this investment from marketing the record.
Those Elusive Imaginary Zeros
Authors: Travers Robert , Kim David
Published: January 2021

Surprisingly, there is a method to show the complex roots on a graph.
Learning by Example
Authors: Butts Thomas
Published: January 2021

For most students, it is a quantum leap from working exercises to solving nonroutine problems. The use of ’’give an example of problems is one approach that has helped my students bridge this gap. Let’s consider a dialogue illustrating how one such problem could be used. Then we’ll explore several purposes of such problems and how they could be used in the classroom. Fifty sample problems are included for your use.
Spacing Radicals
Authors: Sconyers James M.
Published: January 2021

Students sometimes casually make state- ments or draw figures that reveal their misconception that square roots of integers are evenly spaced, just like the integers themselves. An investigation of this misconception is very well suited to student work with a calculator or computer. It is also a topic that can be approached arithmetically, graphically, and algebraically.
Because a Door has to be Open or Closed…
Authors: Cassidy Charles , Hodgson Bernard R.
Published: January 2021

An intriguing problem solved by some inductive exploration.
Backing Into a General Solution
Authors: Carlucci Joseph di
Published: January 2021

Simplify a problem, organize Jala into tables, and then generalizations will emerge.
Odd And Even Numbers-Magician’s Approach
Authors: Hadar Nitsa
Published: January 2021

Magicians somehow manage to produce a “question mark look” on the faces of their audience. Their audiences whisper, “Wow. I wonder how that happened?” “I wish I knew how it works.” They would try to understand the magic trick and to learn how to perform it if the magicians were ready to reveal the secrets.
Applications: Days Of Our Lives
Authors: Knill George , Fawcett George
Published: January 2021

Did you ever wonder what day of the week an important event occurred? A formula has been devised to calculate the exact day without having to look back on calendars that are hard to get.
Simulation And The Microcomputer: An Approach To Teaching Probability
Authors: Collis Betty
Published: January 2021

The May 1981 issue of this journal contained five articles focusing on the some-what neglected area of the teaching of probability. Three of the articles featured the Monte Carlo technique for classroom simulation, along with some suggestions for using a microcomputer. As a follow-up to some of the ideas expressed in these articles, I would like to describe, in general, an eighteen-lesson unit of instruction that uses classic probability situations, Monte Carlo simulation techniques, and a classroom microcomputer. These lessons have been used successfully with eighth-, ninth-, and tenth-grade classes.
Place Value And The Crime Fighter
Authors: Woods James E.
Published: January 2021

A system of linear equations can lead you to the gold.
An Interesting Probability Problem
Authors: Woodward Ernest , Ridenhour Jim R.
Published: January 2021

In An Agenda for Action: Recommendations for School Mathematics of the 1980s, NCTM (1980) recommends that “problem solving be the focus of school mathematics in the 1980s." Unfortunately, present day mathematics textbook problems can often be classified and categorized, and so they are not really problems at all but actually computational exercises. As a result, mathematics teachers need to be continually searching for interesting, challenging problems. Recently we found such a problem (Gardner 1961).
Equity in Mathematics: A Case Study
Authors: Taylor B. Ross
Published: January 2021

In recent years, underrepresentation in enrollments in mathematics courses by females and minorities has started to receive considerable attention. For example, in 1979 NCTM established a task force on “Problems in the Mathematics Education of Girls and Young Women.” NCTM also received a grant from the National Science Foundation to conduct a series of conferences on equity issues in 1982 and 1983. In view of the increasing importance of mathematics for keeping student options open for higher education and careers, this attention to equity issues is timely.
Activities: Triangles, Rectangles, and Parallelograms
Authors: Olson Melfried , Olson Judith
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.
Activities: Manipulating Numbers
Authors: Firkins John
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.
Enrichment Activities for Geometry
Authors: Usiskin Zalman
Published: January 2021

Little reason exists for engaging in enrichment for enrichment's sake or in problem solving merely for mental practice unless one wishes to waste precious time. The curriculum is too crowded to allow such luxuries even for gifted students, because we want these students to be aware of a much greater range of mathematical concepts than their less knowledgeable peers.
Challenges for Enriching the Curriculum: Statistics and Probability
Authors: Swift Jim
Published: January 2021

One of the delights of learning as rich a subject as mathematics is the never-ending scries of challenges available to the student. Some of the most interesting ones are to be found in the areas of statistics and probability.
Computers and the Mathematically Gifted
Authors: Koetke Walter
Published: January 2021

Teachers of the mathematically gifted with access to computing facilities quickly learn a very basic principle—”Never underestimate the student's ability.” Some of my most enlightening experiences have occurred as my students attempt to teach me enough to understand their computer- related work. And when they do this with a patient smile, the experience is most enjoyable.
SoundOFF: Equity Through Mathematics: Everyone's Responsibility
Authors: Jacobs Judith E.
Published: January 2021

“Women and Mathematics” and “Minority and Mathematics” have become the battle cries of those individuals who are concerned with the underrepresentation, given their proportion in the population, of females and members of minority groups (blacks, Hispanics, and Native Americans) in mathematical studies and mathematics- related careers. This concern stems from the economic impact that the lack of mathematical knowledge has on these groups.
Sharing Teaching Ideas: A Linguistic Approach to Learning Mathematics Vocabulary
Authors: Milligan Constance F. , Milligan Jerry L.
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.
Microcomputer-assisted Discoveries: Euclidean Algorithm and Continued Fractions
Authors: Kimberling Clark
Published: January 2021

Students can use microcomputers to cut through algorithms and computations to gain mathematical insights. This approach is especially true for the Euclidean algorithm, so often used to find the greatest common divisor (GCD) of two positive integers. The Euclidean algorithm also yields continued fractions, at least far enough for students to find patterns and discover truths about numbers.
Problem Solving Involving an Automobile's Instrument Panel
Authors: Woodward Ernest , Crawford Jimmy W.
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.”
Common Difficulties with Probabilistic Reasoning
Authors: Hope Jack A. , Kelly Ivan W.
Published: January 2021

In the past two decades several influential organizations, including the National Council of Supervisors of Mathematics (1978), NACOME (1975), UNESCO (1972), CEEB (1959), and the Cambridge Conference on School Mathematics (1963), have acknowledged the role that probability and statistics play in our society. Consequently, each has recommended that probability and statistics be included as part of the modern mathematics curriculum.
Mary Frances Winston Newson: The First American Woman to Receive a Ph.D. in Mathematics from a European University
Authors: Whitman Betsey S.
Published: January 2021

One hundred outstanding women were honored in 1940 in New York City at the Women's Centennial Congress because they held positions that were not open to women one hundred years earlier. One of them was Mary Frances Winston Newson, the first American woman to receive a Ph.D. in mathematics from a European university.
Sharing Teaching Ideas: An Approach to Teaching Mental Computation
Authors: Moore Theodore F.
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.
Results of the Third NAEP Mathematics Assessment: Secondary School
Authors: Carpenter Thomas P. , Lindquist Mary M. , Matthews Westina , Silver Edward A.
Published: January 2021

The recent publication of the Report of the National Commission on Excellence in Education (1983) has focused national attention on the state of education in the United States and the academic achievement of students. The results of the third mathematics assessment of the National Assessment of Educational Progress (NAEP) provide a basis for examining students’ performance in mathematics and how it has changed over the last decade.
Using Magic Borders to Generate Magic Squares
Authors: Lyon Betty Clayton
Published: January 2021

Magic squares and their properties have fascinated people for centuries. Those who are challenged by magic squares are always searching for new ways to generate them. A novel approach to their creation is to take an existing magic square and surround it with a magic border. For example, one can change a 3 × 3 magic square into a 5 × 5 magic square by surrounding the smaller square with a magic border.
New Settings for Regular Polyhedral Dice Games: The Probability of Winning
Authors: Litwiller Bonnie H. , Duncan David R.
Published: January 2021

Apopular dice game is Craps. The rules for one version of the game are described; many variations on the betting details are also used.
Program Your Microcomputer to Do Arithmetic
Authors: Spence Lawrence E. , Eynden Charles Vanden
Published: January 2021

Mathematics teachers frequently face the problem of teaching about computers to students who are already sophisticated in their use, for example, to students who have access to a home computer. For such students, it is desirable to suggest projects that will enhance their programming skills and reinforce their understanding of mathematics. Unfortunately, most computer programs that use mathematical knowledge require familiarity with high school mathematics. The purpose of this article is to suggest an interesting programming project that requires familiarity with only basic arithmetic skills. Thus, this project is especially suitable for secondary students with a knowledge of computers.
A Square Share: Problem Solving with Squares
Authors: Kenney Margaret J. , Bezuszka Stanley J.
Published: January 2021

Why not try this approach to problem solving with your junior high school students? As part of a unit on problem solving or in a problem-of-the-week setting, present for student exploration a wide variety of activities that are joined by a common theme.
Using Computers to Reinforce and Enrich the Mathematics Curriculum
Authors: Elgarten Gerald H.
Published: January 2021

To help us function effectively in a society that relies more and more on computers, a new basic skill is emerging: knowledge of computers. This article presents a structured approach to teaching computer programming in the secondary schools. This approach can be used in an introductory computer programming (literacy) course or as a method to teach computer programming in traditional mathematics courses.
The Importance of Three Years of High School Mathematics
Authors: Mitchell Charles E.
Published: January 2021

One of the major problems faced by high school counselors and teachers of mathematics is convincing students with college potential to remain in a mathematics program until they have completed at least two years of algebra and one year of geometry.
Mathematics in the Real World, Really
Authors: Kennedy Dan
Published: January 2021

Just in case the title of this article is not a sufficient warning to the reader that the contents fall short of being profound, let me assure all who have read this far that you are not likely to learn much mathematics in these pages. Indeed, it is the very triviality of these applications that prompted me to write this paper.
Soundoff: Some Cautions on Short-Term Solutions
Authors: Paul Clyde A.
Published: January 2021

The views expressed in the “Roundoff” 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.
A Unified Way to Teach the Solution of Inequalities
Authors: McLaurin Sandra C.
Published: January 2021

We teach students how to solve inequalities involving absolute values, quadratic expressions, and rational expressions. Each problem is usually taught from a different approach.
Microcomputer-assisted mathematics: Roots: Half-Interval Search
Authors: Kimberling Clark
Published: January 2021

According to the fundamental theorem of algebra, the roots of a polynomial all lie in the set of complex numbers. Some of the roots may be real numbers, and in many applications, only these need be found.
Dynamic Programming for Secondary School Students
Authors: Sloyer Clifford W. , Crouse Richard , Sacco William J. , Copes Wayne S.
Published: January 2021

“It is always fun to learn something entirely new.”
Two Solutions to a Problem of Huygens
Authors: Kost Franklin C.
Published: January 2021

In 1657 (Todhunter 1949), Christian Huygens (1629 1695) published a treatise, the fourteenth proposition of which contained a probability problem. This article presents two solutions to that problem, one by Huygens and the other by James Bernoulli (1654-1705), whose Art of Conjective was published in four parts in 1713.
Critical Problems in Mathematics Education Identified by the 1983-84 Presidential Awardees
Authors: Henderson Annalee
Published: January 2021

The first Presidential Awards for Excellence in Science and Mathematics Teaching were given in October 1983. One science teacher and one mathematics teacher were selected from every state, Puerto Rico, and the District of Columbia, and were brought together for four grand and glorious days of receptions, workshops, and an award ceremony at the White House.