bluuebunny/crossref_metadata_2025 huggingface dataset:
Functions Give Three Points of View on the New Income Tax Law
Authors: Nievergelt Yves
Published: December 2020

The new federal income tax, signed into law on 22 October 1986, spurred extensive analysis in the daily newspapers, an analysis similar to the study of a function in a beginning mathematics course. This similarity with the familiar income tax may help students understand three aspects of the abstract concept of “function”: formulas, graphs, and ordered pairs. Defined by several formulas—not just one—the tax function also prepares beginners for such functions as the a bsolute value, which also involves both a lgebraic formulas and logical tests, a combination that poses difficulties to many students (see Johnson [1986]).
Estimating Pi by Microcomputer
Authors: Donahue Richard J.
Published: December 2020

Students are typically introduced to the concept of pi while studying the circumference and area of a circle. Usually the class· is then instructed to approximate pi as 22/7 or 3.14 with little explanation. With the availability of microcomputers, techniques for estimating pi can be demonstrated. Four BASIC programs, coded from several pi-generating formulas, will be compared for efficiency. The approximation algorithms are easily adaptable to microcomputers, use infinite sums and products, and yield interesting results. Such programming activities also introduce the concept of a converging series. Students familiar with BASIC can code the algorithms themselves. whereas others should be given the programs.
Patterns in Powers of Digits
Authors: Shoemaker Richard W.
Published: December 2020

We sometimes find it useful, when considering a natural number, to form some function of the digits of the number.
Invertible Points of Time
Authors: Stensholt Boonchai Kuekiatngam , Stensholt Eiuind
Published: December 2020

Look at a clock with hands. Will it happen during the next twelve hours that the hands interchange their positions?
Summary of the Report of the NCTM-MAA Task Force on the Mathematics Curriculum for Grades 11-13
Authors: Lichtenberg Donovan R.
Published: December 2020

Early in 1986, the National Council of Teachers of Mathematics and the Mathematical Association of America established a joint Task Force on the Mathematics Curriculum for Grades 11- 13. The task force consisted of a five-person executive committee and a sixteen-member corresponding committee. The members of the executive committee were Joan Leitzel, chair, of Ohio State University; Philip Curtis of the University of California, Los Angeles; Charles Hamberg of the Illinois Mathematics and Science Academy; Donovan Lichtenberg of the University of South Florida: and Ann Watkins of Los Angeles Pierce College.
Difference Equations
Authors: Olson Alton T.
Published: December 2020

Much talk is heard these days about the importance of including topics from discrete mathematics in our secondary mathematics curriculum. They are characterized by their treatment of discrete quantities rather than continuous quantities and limit processes. The mathematics of continuity and limit processes leading into calculus will continue to be a major part of our mathematics curriculum. At the same time topics from discrete mathematics will take on more importance because of the presence of inexpensive computing power that is fundamentally finite and discrete.
Applications: An Application of Linear Equations to the VCR
Authors: Fiore Gregory N.
Published: December 2020

The VCR has invaded the American home. Video rental stores are everywhere, and many homes have a shelf set aside for videotaped shows. How can a viewer get the highest quality recording from the VCR? This article uses the theory of linear equations to solve this problem.
Solving Extreme—Value Problems without Calculus
Authors: Spanagel David I. , Wildenberg Gerald
Published: December 2020

Too frequently students who are veterans of high school calculus arrive at the college campus only to fail even to place into first-semester calculus courses or to have difficulties with subsequent courses should they succeed in “placing out” of first-semester calculus.
Thinking the Unthinkable: The Story of Complex Numbers (with a Moral)
Authors: Kleiner Israel
Published: December 2020

The usual definition of complex numbers, either as ordered pairs (a, b) of real numbers or as “numbers” of the form a + bi, does not give any indication of their long and tortuous evolution, which lasted about three hundred years. I want to describe this evolution very briefly because I think some lessons can be learned from this story, just as from many other such stories concerning the evolution of a concept, result, or theory. These lessons have to do with the impact of the history of mathematics on our understanding of mathematics and on our effectiveness in teaching it. But more about the moral of this story later.
Problem Solving Also Raises Questions
Authors: Wiener Joseph , Watkins Will
Published: December 2020

Students sometimes confuse problem solving with getting an answer. Indeed, correctly stating and justifying an answer to a well-posed problem is an elementary example of problem solving. However, the student who poses problems and identifies increasingly general methods for solving those problems is gaining problem-solving maturity.
Imagination, Intuition, and Computing in School Algebra
Authors: Kieren Thomas E. , Olson Alton T.
Published: December 2020

Two incidents involving novice teachers with junior high and senior high school classes form a background for this article. In the first, a seventh-grade class was involved in a variety of problem-solving activities. They had just engaged in a very active exchange of questions involving complex pricing of pizza orders. Then the lesson turned to representing problems and situations with equations.
Probability and Intuition
Authors: Shultz Harris S. , Leonard Bill
Published: December 2020

In recent years we have seen numerous recommendations that statistics and probability should be integrated into the mathematics curriculum at all levels. A major rationale for this new emphasis is the acknowledgment that in everyday life we repeatedly encounter data and information from which we must make intelligent ceonomic and political decisions.
Piano Tuners and Problem Solving
Authors: Philipp Randolph A.
Published: December 2020

The draft of the NCTM Standards document states that problem solving should be the central focus of the mathematics curriculum (Commission on Standards for School Mathematics of the NCTM 1987). Now, more than ever, problem solving is being defined as a process. Akers (1984, 34) defined problem solving as “what you do when you don't know what to do,” and Schoenfeld (1988) wrote, “Indeed, ‘figuring it out’ is what mathematics is all about” (p. 8). Mathematics teachers, left with the task of determining how problemsolving skills should be taught, have the potential to play a key role in developing and sharing problems that interest students. I will share a certain type of problem that I think might be of some interest at the secondary and college levels.
Pythagoras Meets Fibonacci
Authors: Boulger William
Published: December 2020

One of the key aspects of the study of I mathematics is the search for patterns. New patterns are developed regularly in each mathematical discipline, but some are so significant that they become an integral part of mathematical lore and understanding. More significant still are patterns that relate important mathematical ideas to one another, sometimes in unexpected ways. Euler's discovery of the principle that leads to the relationship among the five most important mathematical constants.
Infinity: The Twilight Zone of Mathematics
Authors: Love William P.
Published: December 2020

The concept of infinity has fascinated the human race for thousands of years. Who among us has never been awed by the mysterious and often paradoxical nature of the infinite? The ancient Greeks were fascinated by infinity, and they struggled with its nature. They left for us many unanswered questions including Zeno's famous paradoxes. The concept of infinity is with us today, and many ideas in modern mathematics are dependent on the infinitely large or the infinitely small. But most people's ideas about infinity are very vague and unclear, existing in that fuzzy realm of the twilight zone
A Computer-graphing-based Approach to Solving Inequalities
Authors: Waits Bert K. , Demana Franklin
Published: December 2020

Virtually every algebra or precalculus high school textbook uses either a “case by case” analysis or a “sign chart” method to solve inequalities. Both methods are very limited because they require that the expressions involved be easily factored or given in factored form. Developing noncontrived applications is difficult because of the limitations of these traditional methods. Furthermore, some students do not understand the logic involved in using these traditional methods, nor do they understand the meaning of a solution to an inequality. This lack of understanding about the method and the context of the problem often leads to an ineffective learning experience. Establishing a geometric representation for solving an inequality leads to two major results. First, it serves as a foundation from which the algebraic techniques can be understood. Second, it offers a more general method of solution than the signchart method because it is applicable to expressions that do not factor.
Simple Constructions for the Regular Pentagon and Heptadecagon
Authors: Detemple Duane W.
Published: December 2020

This article discusses two new Euclidean constructions to inscribe regular polygons of five and seventeen sides in a circle. The pentagon's construction shares many common elements with the familiar Ptolemaic method (see, e.g., Jacobs [1982, 254 55]), but an interesting variation occurs in the final steps. The explanation given for why the construction works is unusual in that it does not make use of the distance formula of the Pythagorean theorem.
Essential Mathematics for the Twenty-first Century: The Position of the National Council of Supervisors of Mathematics
Authors: Carl Iris M.
Published: December 2020

Since A Nation at Risk was released five years ago, we have experienced a most serious and sustained national effort to improve education. That attention has been welcomed, and it requires our continued support.
Implementing The Standards: Beginning To Implement The Standards In Grades 7–12
Authors: Schoen Harold L.
Published: December 2020

Now is an exciting time to be a mathematics teacher! One major reason is that technology has developed to the point that we must reconsider what mathematics should be taught and in what way. The position of the NCTM concerning this and other curricular issues can be found in Curriculum and Evaluation Standards for School Mathematics (Standards) (NCTM 1989). The Standards document is a fairly specific set of curricular recommendations (standards) with examples of content and teaching scenarios that illustrate concretely the meaning of each standard, but it is not a set of course descriptions or a list of behavioral objectives. No attempt is made in the document to describe exactly how to implement the standards in a given school setting, so not surprisingly, many mathematics teachers are seeking more specific ideas for implementation
The Role of the Teacher in Implementing the Standards
Authors: Mumme Judith , Weissglass Julian , Schoen Harold L.
Published: December 2020

NCTM's Standards document sets forth a new vision for mathematics education. The changes envisioned will require teachers both to develop a deeper understanding of mathematics and to construct new understandings of the teaching and learning of mathematics. In the previous article in this series, a prototype was suggested for beginning to implement the Standards at the district level. For individual teachers to fulfill the goals of the Standards—improving the mathematical learning experiences for all students and enabling them to gain mathematical power—teachers must themselves be empowered. Empowerment implies that teachers cannot simply be handed a curriculum package and be told to “go teach.” Teachers will need to be empowered to make decisions not only about the curriculum but also about the nature of their own professional-development experiences.
Representing, Solving, and Using Algebraic Equations
Authors: Austin Joe Dan , Vollrath H. J.
Published: December 2020

Students of beginning algebra are quickly expected to solve linear equations. The solution procedures are generally abstract, involving the manipulation of numbers and algebraic symbols. Many students, even after completing a year of algebra, do not understand variables, equations, and solving equations (cf. Carpenter et al. [1982]). One way to help students learn to solve equations is to use physical objects, diagrams, and then symbols to represent equations. (Bruner [1964, 1967] calls such representations enactive (concrete), iconic (pictorial), and symbolic.) Although solving equations symbolically is essential, many students can benefit from working with physical problems that can also be symbolized mathematically. This article describes one way for students to learn to solve certain linear equations using pan balances, diagrams, and then symbols.
Implementing the Standards: Transition to High School Mathematics
Authors: Hirsch Christian R. , Lappan Glenda , Schoen Harold L.
Published: December 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) proposes a common core of mainstream mathematical topics that all high school students should have the opportunity to learn. The need for such a reconceptualization of the curriculum is dramatically documented in the NRC report Everybody Counts (MSEB and National Research Council 1989). But the success of the proposal hinges to a large degree on the nature of mathematical experiences in the transition years, grades 7-8.
Napoleon's Waterloo Wasn't Mathematics
Authors: Maynard Jacquelyn
Published: December 2020

When students think of Napoleon Bonaparte, they probably think of a famous military leader who met his defeat at Waterloo, or maybe they remember the portraits of the general with his hand in his jacket. But it's almost certain that students don't think of Napoleon in connection with mathematics. This article will acquaint you with Napoleon's interest and involvement in mathematics and education.
Sharing Teaching Ideas: Practical Practice
Authors: Hastings William R.
Published: December 2020

Unimaginative and repetitive drills of elementary number facts can be boring to both students and teachers. Yet computational facility is very important and must be developed and strengthened. The following exercise helps students practice computational skills, discover patterns, and check their own answers.
Which Mean Do You Mean?
Authors: Lubecke Andre Michelle
Published: December 2020

This article can be viewed as a script for a classroom presentation introducing weighted means and geometric means to students who are already familiar with arithmetic means. It is written in the style and language I actually use in the classroom, illustrating a method of teaching I have found to be effective with students in elementary statistics courses. The frequent questioning is designed to keep the students mentally active and involved in the development of a new idea, and typical student or class responses have been indicated in parenthetical statements throughout the text.
Number Theory and Public-Key Cryptography
Authors: Lefton Phyllis
Published: December 2020

Secret ciphers fascinate students and are an ideal subject with which to motivate them to study mathematics. Recent articles in the Mathematics Teacher, for example, have described how various types of ciphers can be taught to high school students to enhance their learning of statistics (Feltman 1979), matrices (Camp 1985), functions and their inverses (Reagan 1986), and remainder arithmetic (Meneeley 1981). Ciphering also offers interesting examples of how so-called “pure” mathematics can be applied to real-world problems (Hilton 1984).
Implementing the Standards: Trigonometry Today
Authors: Hirsch Christian R. , Weinhold Marcia , Nichols Cameron
Published: December 2020

Trigonometry, either as a separate course or as part of an advanced algebra-and-precalculus course, has traditionally been an integral part of college-preparatory mathematics. As college programs evolve to encompass the full range of the mathematical sciences (Ralston and Young 1983, Ralston 1985, National Research Council 1989), preparation for college can no longer be synonymous with preparation for calculus-or at least calculus as it is often taught with the emphasis on recipes and procedural skills. This realization opens the question of the place and nature of trigonometry in contemporary high school mathematics.
Fractals and Transformations
Authors: Bannon Thomas J.
Published: December 2020

In traditional geometry we model nature using the points, lines, and planes of Euclid. Very recently Mandelbrot (1983) gave us fractals to use in building new models. One of the reasons these new fractal models are successful is that a great deal of self similarity is found in nature. Weather patterns over local areas resemble large-scale weather patterns. Branches resemble trees and rocks resemble mountains. The regularities as well as the irregularities of nature repeat at different scales. Geographical features are so self-similar that cartographers must place scales on maps to keep islands from being mistaken for continents or hills for mountains. Self-similarity is a property of many fractals, so whenever nature proves to be self-similar, a fractal will usually furnish a good model of it.
Sharing Teaching Ideas: Improving Students' Understanding of Geometric Definitions
Authors: Hersberger Jim , Talsma Gary , Herrmann James P.
Published: December 2020

As middle school mathematics teachers work to restructure a mathematics curriculum that now contains little in the way of new ideas or concepts (Flanders 1987), careful attention must be paid to pedagogical ideas that enhance and facilitate the attainment of newly developed curricular goals. In particular, even as a greater amount of class time is spent considering geometric topics, care must be taken to employ activities that help students attain higher levels of geometric understanding (Crowley 1987; Talsma and Hersberger 1990).
Implementing The Standards: Evaluation: A New Vision
Authors: Lester Frank K. , Kroll Diana Lambdin
Published: December 2020

Teaching according to the vision of the NCTM's Curriculum and Evaluation Standards will involve numerous changes in the content and instruction of the school mathematics program. Moreover, this vision will also require a change in testing procedures and methods for evaluating the effectiveness of instructional practices (Clarke, Clarke, and Lovitt 1990; EQUALS and California Mathematics Council 1989; NAEP 1987; NCTM 1989). As is pointed out in NCTM's curriculum standards, an evaluation program that is properly aligned with the proposed curriculum standards can no longer use only written tests. Calculators, computers, and manipulatives must be included in the evaluation process.
No Time for Writing in Your Class?
Authors: Mcintosh Margaret E.
Published: December 2020

Many school districts are beginning to use a “writing across the curriculum” approach in the middle and secondary school. Certainly, English teachers are aware of the need to have students write. Social studies teachers are reasonably easy to convince that their students should write as a part of their class (e.g., writing reports, keeping diaries like someone from a different historical period, and so forth). Science teachers can see the reasoning behind having students write as part of the science curriculum (e.g., using writing as problem solving, writing up results of experiments, and so forth). Teachers in other content areas, such as health, foreign language, business education, and so on, are amenable to the notion that they shou1d require some writing from their students other than the typical short-answer, fill-in-the-blank-type exercises that they have been using as a means of facilitating and assessing students' learning.
Egyptian Fractions: Ahmes to Fibonacci to Today
Authors: Hurd Spencer P.
Published: December 2020

Sometime between 1850 B.C. and 1550 B.C. an Egyptian scribe named Ahmes (or Ahmose) obtained fresh papyrus for a roll about eighteen feet long and one foot high. On this papyrus he wrote, copied, or, more likely, edited his mathematical text “in likeness to writings of old.” The work consists mostly of annotated lists of fractions and about a hundred solved “word” problems.
The Sign-Chart Method for Solving Inequalities
Authors: Dobbs David E. , Peterson John C.
Published: December 2020

Many methods have been proposed for solving inequalities (Dreyfus and Eisenberg 1985; Eaves and Wilson 1964; Garfunkel and Plotkin 1966; McLaurin 1985). The sign-chart method described in this article is not fundamentally new. We became acquainted with it while using a later edition of Eaves and Wilson (Eaves and Carruth 1978). It is interesting to note that as the method evolved from the earlier edition to the later one, the roles of the rows and the columns were interchanged. The original's tabular presentation has evolved to the more graphical form presented in this article.
Soundoff: The SAT Should Be Revised
Authors: Baker Harold
Published: December 2020

In response to Harold Baker's concerns, the Editorial Panel invited representatives of the Educational Testing Sevice (ETS) and American College Testing (ACT) to prepare articles on how the SAT and ACT tests are changing. These articles follow in this issue, Reactions to all three of them are welcomed.
The ACT Assessment in the 1990s
Authors: Candace Noble A. , Mullen Kenneth B.
Published: December 2020

This article was prepared at the invitation of the Editorial Panel to respond to the concerns addressed in Harold Baker's “Soundoff” in this issue. Reactions to this article are welcomed for consideration in “Reader Reflections.”
Applications: Squeal Those Tires!: Automobile-Accident Reconstruction
Authors: Caples Linda Griffin
Published: December 2020

The procedures used by law-enforcement officers in traffic-accident reconstruction contain a wealth of material that can be applied in teaching secondary school mathematics. Students are highly interested in the milestone of obtaining a driver's license, It is important that they recognize their responsibility of driving within the speed limits to reduce the chance of their involvement in an accident. Should they be in an accident, they may be surprised to know that methods of estimating minimum speeds are available. These methods require a basic knowledge of vectors and trigonometry, which makes their use an ideal real-life application for students in precalculus, mathematical analysis, or trigonometry.
Soundoff: A Case against Computer Symbolic Manipulation in School Mathematics Today
Authors: Waits Bert K. , Demana Franklin
Published: December 2020

The National Council of Teachers of Mathematics and leaders in mathematics education must move vigorously to build a consensus for acceptance of the Curriculum and Evaluation Standards (NCTM 1989). One important assumption of the Curriculum and Evaluation Standards is that all students should use computers and graphing calculators on a regular basis in school mathematics. The symbol-manipulating ability of such computer algebra systems (CAS) as the IBM Math Exploration Tool Kit, Mathematics™, and Derive™ can be used today in school mathematics to do algebra. However, we take exception to the use of computer symbol manipulation in school mathematics today for two important reasons.
Matching Garage-Door Openers
Authors: Litwiller Bonnie H. , Duncan David R.
Published: December 2020

Probability is an increasingly important topic in mathematics education. To teach probability effectively and meaningfully, real-world examples are needed. Consequently, probability teachers are always on the lookout for examples they can use in their classes. We shall describe a real-world probabilistic situation.
A Core Curriculum in Geometry
Authors: Tietze Martha
Published: December 2020

What do a course for mathematically talented geometry students and a course for the non-college-bound have in common? Concepts and learning activities! I teach both courses and have found that many of the same activities can be used to develop concepts. Both the depth and breadth of the activities need to be adjusted to the developmental level of the students—a good example of the core curriculum as described in NCTM's Curriculum and Evaluation Standards (1989). The focus of this article is the use of hands-on activities in the third year of an integrated sequence for the non-college-bound. Reference is made to variations and extensions for an honors geometry course.
Treating Mathematics Anxiety: The Optional Contract
Authors: Fairbanks Paul J.
Published: December 2020

Much like a novice golfer on the first tee, the mathematics student can seriously hamper her or his performance by nervousness and insecurity toward mathematics. At the college level, this anxiety is most often seen in mathematics courses required for nontechnical majors. At my college, this uneasiness is particularly evident in Selected Topics in Mathematics, most commonly used to satisfy a graduation requirement, and Elementary Statistics, which is required for a number of majors. Approximately half my students enrolled in these courses are freshmen. The upperclassmen have delayed taking them because of anxiety toward, or dislike of, mathematics; many are on a second or subsequent attempt to pass the course.
The Railroad-Track Problem
Authors: Bridger Maxine
Published: December 2020

A section of railroad track, one mile long, is firmly fixed at both ends. During the night someone cuts the track and welds in an additional foot.
Soundoff: Where are the Counselors?
Authors: Peterson Marla P.
Published: December 2020

While reading the list of people who were involved in planning the 1991 National Summit on Mathematics Education Assessment, I noticed that no school counselors were included. However, individuals who have given excellent support to school counselors were represented. These National Summit representatives, along with others who are implementing and assessing the effectiveness of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989), need to encourage the mathematics education profession to solicit assistance from school counselors.
Tips for Beginners
Authors: Ropp Carol , Stanulonis Joanne
Published: December 2020

I have tried many methods to get students to complete homework assignments. Telling them that they would learn more mathmatics did not work.
Is It True That “Blonds Have More Fun”?
Authors: Bonsangue Martin V.
Published: December 2020

Most decisions involve risk. Often a person must make a yes-no decision on the basis of past experiences or incomplete information. Whether the correct choice was made is not usually known until after it is too late for change. The statistical model of decision making is a summary of the consequences of making correct or incorrect choices. This model, implicit in every yes-no decision process, is easy to visualize and exciting to teach. Imparting a deep understanding of the statistical model of decision making is central to the teaching of inferential statistics.
Implementing the Professional Standards for Teaching Mathematics: Learn from Your Students
Authors: Farrell Margaret A.
Published: December 2020

The next four articles in this department address issues related to four of the six standards in the section of the Professional Teaching Standards (NCTM 1991) titled “Standards for the Professional Development of Teachers of Mathematics.” The series will pay particular attention to the ways in which these standards affect the in-service teacher of mathematics, whose ongoing professional development depends. to a large extent, on individual commitment, reflection, and action. We hope that these articles will furnish a basis from which teachers can begin to examine and improve their own classroom instruction.
Evaluating Problem-solving Processes
Authors: Meier Sherry L.
Published: December 2020

During the years since NCTM first published An Agenda for Action (1980), our school district has incorporated more problem-solving instruction into mathematics classes. Although we have administered monthly problem-solving tests since the early 1980s, the emphasis of scoring has been strictly on the answer. Meanwhile, instruction regarding problem solving began to emphasize techniques and strategies. In short, instruction focused on process, but assessment still focused on the end product. My own research showed that this situation was not unique. When studying problem-solving instruction, I found that teachers who used cooperative-learning groups in problem-solving instruction often did not evaluate the problem-solving process in a formal manner. This lack of formal evaluation happened most frequently when teachers viewed this type of activity as for extra credit or enrichment. When teachers treated small-group problem-solving activities as a regular portion of the mathematics class, they were more likely to assess the results (Meier 1989). Even so, the focus of the instruction was process and the focus of the assessment was often results.
The Loss of Accuracy: Pitfalls and Implications for Mathematics Instruction
Authors: Lochiel Glidden Peter
Published: December 2020

Under certain conditions, any digital computing device experiences loss of accuracy, a problem that has long been a concern to specialists in mathematics and computer science. Now, however, as more classroom teachers use calculators and computers in mathematics instruction, they should know what causes accuracy to be lost and how to prevent it.
Tips for Beginners: Algebraic A_ _ _ _ _ _ _ _S
Authors: Margulies Susan
Published: December 2020

After the initial introductions are over, classroom procedures and requirements have been explained, and a brief overview of the course has been given, I find the following activity a nice way to begin the year's work with my Advanced Placement calculus classes. I give each student a copy of the statements listed in sheet 1 and ask students to determine the truth value of the stated relationships. A relationship is true if it is true for all possible values of a and b. Students are also asked to correct those statements that they consider false.
Problem Solving on Geoboards
Authors: Kennedy Joe
Published: December 2020

See how many different triangles you can find on the geoboard. A teacher who presents this problem will get different responses, depending on the size of the given geoboard. For example, a 2 × 2 geoboard yields just one triangle; the 3 × 3 geoboard is much more productive. Students will have a good time finding its eight triangles. Without much guidance they will settle questions about which ones should be counted as different. They will rule out duplications resulting from reflections, rotations, and translations, and probably will come up with a soHd idea of congruence.
Two Egyptian Construction Tools
Authors: Lamb John F.
Published: December 2020

Among the objects in the Ramses II exhibition at Fair Park in Dallas in 1989 were two tools from the tomb of Sen-nedjem, one of Ramses II's workmen. One was a level for determining the horizontal plane, the other was a plumb level for determining the vertical plane.
Tips For Beginners: Steps To Better Homework
Authors: McLean Elizabeth
Published: December 2020

Homework can often be an exercise in frustration for both teacher and students. The students do not know what the teacher really wants and do not agree with the grades they receive. The teacher cannot understand why the students communicate so little in their work. But with a little care, home- work can enrich our students' understanding and can help us teach better.
Implementing the “Professional Standards for Teaching Mathematics”: The Excitement of Learning with Our Students—an Escalator of Mathematical Knowledge
Authors: Hoffer Alan R.
Published: December 2020

A teachers of mathematics, we represent mathematics in the schools. It is an honor to have the responsibility to represent the ancient discipline of mathematics. We are also learners, and it is likely that we know and understand only a small percent of the vast universe of mathematical knowledge. The same statement applies, of course, to professional mathematicians. Throughout our lives, certainly our teaching lives, we will continue to learn more mathematics. The authors of the Professional Standards for Teaching Mathematics (NCTM 1991) use the section “Standards for the Professional Development of Teachers of Mathematics” to address the depth of our understanding of mathematics and the ways in which that understanding affects our teaching. I happened to learn more about mathematics because of a question that a student asked in class. This experience taught me that school-level mathematics has the potential for being a source of exploration and discovery for a professional mathematician. I found that there are many new things to learn and that it is exciting to learn along with my students.
Square Circles
Authors: Silver Judith A.
Published: December 2020

We cannot say, for example, that God can make a square circle or add two and two and get five or make a rock so big that He cannot lift it. This does not mean that there is something that God cannot do. Making square circles and the like is not doing something. It is literally nonsense. It implies no deficiency in divine power to say that God cannot do the logically impossible, not because the logically impossible lies beyond God's power, but because it is not anything “doable.”
Technology Reviews
Authors: Burke Maurice
Published: December 2020

Prices on software, books, and materials are subject to change. Consult the suppliers for the current prices.
Tides of Change: Teachers at the Helm
Authors: Lindquist Mary M.
Published: December 2020

Ten years ago, critics of our education system produced A Nation at Risk. Many charged that too little was being done to educate our youth. Standards were too low, and students were not prepared to embrace the challenges and opportunities of the world around us. As our nation rallied on the shoreline anticipating the tides of change, one message rang out loud and clear: “We must change the education we provide our students today if we want to ensure their success in the future.”
Graphing Powers and Roots of Complex Numbers
Authors: Embse Charles Vonder
Published: December 2020

Establishing mathematical connections is one of the most important themes that permeates the vision of mathematics teaching as outlined by the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). A graph has the power to help students make connections between the abstract algebraic representation and the visual representation of a concept, relationship, or pattern. With the introduction of sophisticated graphing utilities and graphing calculators, we can also make connections to the numerical representation as well as the algebraic and graphical representations. Even topics as abstract as complex numbers can now easily be visualized with a graph. Using De Moivre's theorem and a parametric graphing utility, we can graph the powers and roots of complex numbers. The “trace” feature of many graphing utilities moves a point along a graph and gives numerical output, helping students make the connection between the visual and numerical representation of the complex numbers. This rich technological environment allows students to conjecture and test many hypotheses on the way to “discovering” the propertieS of complex numbers represemed in the complex plane.
The Connections Challenge
Authors: Dickey Edwin M. , Raub-Hunt Margaret
Published: December 2020

[T]o help students broaden their perspective, to view mathematics as an integrated whole rather than as an isolated set of topics, and to acknowledge its relevance and usefulness both in and out of school.
Mathematics and Medical Indexes: A Life-saving Connection
Authors: Crouse Richard J. , Sloyer Clifford W.
Published: December 2020

Trauma is a medical term for any personal injury including either accidental or intentional wounds to the body. Trauma is the number-one killer of Americans up to age 38 and accounts for more years of life lost in the United States than cancer and heart disease combined. The material in this article should help students understand how mathematics is being used to fight this condition. Many of our students will become nurses, paramedics, or ambulance drivers. A number of students who enter other professions will work in one of these areas on a part-time or voluntary basis. This material should help these people understand how medical indexes are evaluated to determine the severity of an injury.
Aligning Assessment with the NCTM's Curriculum Standards
Authors: Schloemer Cathy G.
Published: December 2020

I recently found myself in the ideal situation of wanting to integrate the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) more fully into my teaching and, at the same time, being enrolled in a class that required me to research some aspect of assessment and then engage in a practical assessment project. As a result, I decided to find out more about standardsaligned assessment and then see if could use it with my high school precalculus students.
The relationships between moral distress and quality of nursing care in oncology nurses
Authors: Kim Sae Mi , Shin Yong Soon
Published: December 2020

Purpose: The study aimed to investigate the relationship between moral distress and the quality of nursing care.Methods: This cross-sectional correlation study included nurses working at oncology nursing units of two secondary general hospitals in Seoul and Gyeonggi-do, Korea. A total of 207 nurses participated. Moral distress was measured by the Moral Distress Scale-Revised Nurse Questionnaire and quality of nursing care was evaluated by the Quality of Oncology Nursing Care Scale. Data were collected from October 5 to 31, 2018. Data analysis included descriptive statistics, independent t-test, ANOVA, Pearson’s correlation coefficient and multiple regression analysis.Results: The quality of oncology nursing care showed a negative correlation with moral distress (r=-.19, p=.007). The factors affecting the quality of oncology nursing care were religion (β=-.22, p=.001), clinical experience in oncology units (β=.27, p=.007), and moral distress (β=-.16, p=.018). Moral distress showed a statistically significant predictive power of 13% in the regression model (F=8.70, p=<.001).Conclusion: The findings of this study suggest that management of moral distress is important to increase the quality of oncology nursing care.
Profile of the accelerated second-degree bachelor of science in nursing program graduates and analysis of relative efficiency of programs
Authors: Yang Seung-Hyeon , Lee Hyejung , Kim Hyo Yeong , Min Ari , Cho Euiyoung
Published: December 2020

Purpose: The purpose of this study was to describe the profile of graduates from accelerated second-degree Bachelor of Science in Nursing programs and to analyze the relative efficiency of nursing colleges using data envelopment analysis.Methods: An online survey link was emailed to the deans of nursing colleges, who were then asked to send the link to graduates of the respective colleges. The survey questionnaire included demographics, reasons for applying to the accelerated second-degree Bachelor of Science in Nursing program, employment after graduation, and nursing career satisfaction.Results: Sixty-two graduates of the accelerated second-degree Bachelor of Science in Nursing program responded to the survey. The mean age at admission was 24.28 (± 3.01) years. Reasons for applying to the accelerated second-degree Bachelor of Science in Nursing program were primarily increasing job security and using it as a stepping stone to another career. Nursing career job satisfaction was 4.81 (± 1.07) and more than 82% recommended this program. The data envelopment analysis found the average efficiency score to be 0.84 (± 0.20) and 4 nursing colleges to be relatively efficient.Conclusion: The accelerated second-degree Bachelor of Science in Nursing program can be considered to be an effective means to produce quality nurses with non-nursing bachelor degrees in a short time; however, outcomes of this program need to be systematically monitored to maintain quality level. Through this, competent nurses with knowledge of adjacent studies will be added to the nursing workforce.
Trends of the researches related to ethical topic in Korean nursing students
Authors: Jin Eunju , Kang Hyunju
Published: December 2020

Purpose: The purpose of this study is to explore the trends of research related to ethical topics in Korean nursing students.Methods: A total of 131 articles that were published from 2000 to 2020 were analyzed and summarized according to publishing type, research design, subject, data analysis method, main research topic, research variables and instrument.Results: Most studies were journal articles (93.9%) and their most frequent research design was survey (75.7%). The research subjects covered all grades (35.1%) or they were divided between clinical nursing practicum (29.8%) or not (21.4%). The main research topics were biomedical ethics, ethical values, moral judgment and ethics education. Recently, ethical decision making and practical ability in nursing practice were reported. The instruments for measuring variables were limited and the same tools were used several times.Conclusion: Based on the findings of this study, it is suggested that the selection of various research topics and the application of research methods related to ethics for nursing students will continue in response to rapidly changing social phenomena in the future. In particular, it is necessary that research related to ethical and practical ability as well as ethical attitudes and perceptions of nursing students be actively carried out.
(Counter-)Narrating European integration
Authors: Seeliger Martin
Published: December 2020

In order to maintain social standards within the European Union, trade unions have to overcome national differences to form common political positions. Especially against the background of the recent enlargement rounds, the crafting of such positions has become a daunting task. In this context, the European Services Directive has posed an important challenge to trade unions: The so-called ‘country of origin principle’ implied that workers were supposed to be employed in line with the standards of the sending- and not the receiving country. After lengthy discussions between representatives from Eastern and Western Europe, the trade unionists managed to form a joint political line and forced the European Commission to remove the principle. In order to challenge the hegemonic neoliberal narrative of the common market bringing freedom and prosperity to the countries of Europe, the article will show how the counternarrative of a European Social Model served as a reference frame for this joint position.
Odpowiedzialność przedsiębiorcy za niedostarczanie informacji i dokumentów na żądanie Prezesa UOKiK – kilka refl eksji po decyzji w sprawie Engie
Authors: Kanton Krzysztof
Published: December 2020

The article contains an analysis of the solutions adopted in the Polish legal system governing the procedure for requesting information and documents by the President of the Office of Competition and Consumer Protection (President of UOKiK). In the first part of the article, the author discusses the basic standards that should be met by a request of the UOKiK, with regard to the scope of the request and its purpose, taking into account, in particular, the guidelines which follow from EU case-law. The author considers the scope of the obligation under Article 50 Section 1 of the Act on Competition and Consumer Protection (the Act), criticizing the solution that makes it impossible in practice to challenge the demands of the President of UOKiK without a risk of exposure to severe financial sanctions. The proposals for amendments of applicable regulations are also discussed, the aim of which would be to provide business undertakings with an adequate standard of protection of their fundamental rights in connect in with the procedure for submitting information and documents requested by the President of UOKiK. The second part of the article is devoted to issues concerning financial penalties for a breach of the obligation referred to in Article 50 Section 1 of the Act. The author discusses the current legal framework and indicates the need to introduce certain legislative changes in the future. The analysis also covers the practice of the Polish competition authority to impose penalties for a breach of the obligation under Article 50 Section 1 of the Act
“T.N. GRANOVSKY AS A SCHOLAR OF HISTORY (ON THE CENTENARY OF HIS DEATH 1855-1955)” (the Report Written by Associate Member of the USSR Academy of Sciences, Doctor of Historical Sciences, Professor Sergei Ivanovich Arkhangelsky (1882-1958), Read by Him on November 23, 1955)
Authors: Fedoseeva Kseniia Vladimirovna
Published: December 2020

This paper consists of an introductory article and an original source text with the author's commentary. It introduces into scientific circulation S. I. Archangelsky's report "T. N. Granovsky as a Scholar of History", prepared for public reading in 1955. The research object of the introductory article is the scientific work of Doctor of Historical Sciences, Professor and Associate Member of the USSR Academy of Sciences S. I. Arkhangelsky (1882-1958). The research subject is his work focused on the history of historical sciences and the place that he assigned to himself in the framework of the Moscow school of scholars at that time. The author also attempts to delimit S.I. Arkhangelsky's texts, conducted within the framework of cooperation with Nizhny Novgorod and Moscow scientific organizations. The work of S.I. Arkhangelsky is considered through the prism of an analysis of the scientific schools and corporations of scholars. The author applied the comparative-historical and biographical methods, as well as the general scientific methods of analysis and synthesis. The novelty of the presented research lies in the fact that, in the first place, it introduces into scientific circulation the previously unknown text of S.I. Arkhangelsky, dedicated to the work of T.N. Granovsky, which is important both for the further development of the history of Russian historical sciences and for the reconstruction of the scientific biography of S.I. Arkhangelsky; secondly, the author significantly enhances the picture of the initial formation of S.I. Arkhangelsky as a specialist in world history, differentiating between his research on domestic and foreign history; the author also reveals the role and place of the scientist within the corporation of scholars.