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Full-Text Articles in Mathematics

Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce Sep 2005

Algebraic Insight Underpins The Use Of Cas For Modelling, Robyn Pierce

The Mathematics Enthusiast

Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathematical solutions to mathematically formulated problems. Controlling and monitoring the use of CAS to perform the necessary routine processes requires the mathematical thinking referred to as algebraic insight. This paper sets out a framework of the aspects, and elements of algebraic insight and illustrates the importance of students …


A Comparison Of The Danish And The Virginia Secondary Teacher Education System: Their Values And Emphasis On Mathematics Content Knowledge, Bettina Dahl Sep 2005

A Comparison Of The Danish And The Virginia Secondary Teacher Education System: Their Values And Emphasis On Mathematics Content Knowledge, Bettina Dahl

The Mathematics Enthusiast

In this paper I will first examine an example of secondary mathematics teacher education in the USA, namely Virginia, then compare it with the secondary teacher education in Denmark. The purpose is both to investigate how much mathematics the students get in the respective systems and secondly to see what this type of teacher education communicates about the values emphasized in the various countries’ education systems. I spent more time on explaining the Danish education system than that of the USA and the single states since it is assumed that the reader is familiar with these systems. One cannot necessarily …


Call For Papers Sep 2005

Call For Papers

The Mathematics Enthusiast

No abstract provided.


Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi Sep 2005

Problem Solving And Problem Posing In A Dynamic Geometry Environment, Constantinos Christou, Nicholas Mousoulides, Marios Pittalis, Demetra Pitta-Pantazi

The Mathematics Enthusiast

In this study, we considered dynamic geometry software (DGS) as the tool that mediates students’ strategies in solving and posing problems. The purpose of the present study was twofold. First, to understand the way in which students can solve problems in the setting of a dynamic geometry environment, and second, to investigate how DGS provides opportunities for posing new problems. Two mathematical problems were presented to six pre-service teachers with prior experience in dynamic geometry. Each student participated in two interview sessions which were video recorded. The results of the study showed that DGS, as a mediation tool, encouraged students …


Meet The Authors Sep 2005

Meet The Authors

The Mathematics Enthusiast

No abstract provided.


Von Neumann And Computers, Steve Humble Sep 2005

Von Neumann And Computers, Steve Humble

The Mathematics Enthusiast

The title of this paper should not be Von Neumann and computers, but Von Neumann and the Von Neumann machine. Von Neumann may be famous for many things but humility was not one of them. Yet no one had anything bad to say about 'good time' Johnny Von Neumann; he just was too likeable. He gave massive parties and loved women, fast cars, jokes, noise, Mexican food, fine wine, and, most of all, mathematics. 'Unbelievable', said one of Von Neumann's old friends, 'He knew how to have a good time. His parties were once if not twice a week at …


Tme Statistics Sep 2005

Tme Statistics

The Mathematics Enthusiast

No abstract provided.


Tme Volume 2, Number 2 Sep 2005

Tme Volume 2, Number 2

The Mathematics Enthusiast

No abstract provided.


Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman Sep 2005

Editorial: Globalization, History, Technology And Mathematics Education, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.


A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott Apr 2005

A Preface To Gutstein Generalized: A Philosophical Debate, Johnny W. Lott

The Mathematics Enthusiast

The National Council of Teachers of Mathematics (NCTM) has taken a very firm stand on the issue of equity in mathematics education. Not only is equity incorporated in the Curriculum and Evaluation Standards for School Mathematics (1989) and Principles and Standards for School Mathematics (2000), equity is the first plank of NCTM’s legislative platform.


Editorial, Bharath Sriraman Apr 2005

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.


Gutstein Generalized- A Philosophical Debate: A Critical Commentary On Gutstein's (2003) Thesis For The Incorporation Of Social Justice In The Mathematics Curriculum, Seth Braver, Jane Micklus, Sheila Bradley, Hillary Van Spronsen, Samantha Allen, Vicki Campbell Apr 2005

Gutstein Generalized- A Philosophical Debate: A Critical Commentary On Gutstein's (2003) Thesis For The Incorporation Of Social Justice In The Mathematics Curriculum, Seth Braver, Jane Micklus, Sheila Bradley, Hillary Van Spronsen, Samantha Allen, Vicki Campbell

The Mathematics Enthusiast

The Scene: A Courtroom
The Year: 2004 (old style), 15 (new style - After Standards)

The Grand Inquisitor mounts the podium, and addresses the Debaters standing silently before him. A large crowd fills the hall.

Inquisitor:
Ladies and Gentlemen! You have been summoned here today to present the final arguments for and against these propositions which have so vexed our society in recent months. Each of you represents a vision of the future of mathematics education. Ere the sun sets we shall fix our resolve to one vision or the other. The victors, I doubt not, shall lead us into …


Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein Apr 2005

Response To Gutstein Generalized- A Philosophical Debate, Eric Gutstein

The Mathematics Enthusiast

It is a pleasure, challenge, and an honor to respond to the thoughtful and innovative debate started by Braver, Micklus, Bradley, van Spronsen, Allen, & Campbell on teaching mathematics for social justice. They take seriously the issues in, and raise many interesting views about, my article, Teaching and Learning Mathematics for Social Justice in an Urban Latino School (JRME, January, 2003). I would like to respond to (connected) two points in particular: the relationship of functional to critical literacies, and the relationship of “critical thinking” in mathematics to learning mathematics for social justice. However, I would first like to clarify …


Taxi Cab Geometry: History And Applications!, Chip Reinhardt Apr 2005

Taxi Cab Geometry: History And Applications!, Chip Reinhardt

The Mathematics Enthusiast

We will explore three real life situations proposed in Eugene F. Kraus e's book Taxicab Geometry. First a dispatcher for Ideal City Police Department receives a report of an accident at X = (-1,4). There are two police cars located in the area. Car C is at (2,1) and car D is at (-1,-1). Which car should be sent? Second there are three high schools in Ideal city. Roosevelt at (2,1), Franklin at ( -3,-3) and Jefferson at (-6,-1). Draw in school district boundaries so that each student in Ideal City attends the school closet to them. For the third …


Commentary On Ballou's Paper: Galois - The Myths And The Man, Catherine Degrandpre Apr 2005

Commentary On Ballou's Paper: Galois - The Myths And The Man, Catherine Degrandpre

The Mathematics Enthusiast

mathematics curriculum. As seen in her paper, the solution of the cubic essentially involves the use of a clever substitution in the general cubic in order to reduce it into a cubic without the square term, which in turn is factorable as a quadratic provided one makes another substitution. A natural question to ask ourselves, which mathematicians in the colorful theory of equations undoubtedly did as well, is how far can we push this technique of cle ver substitutions to solve higher degree equations. These substitutions are called Tschirnhaus transformations and have a pattern of the form x = y …


Tme Volume 2, Number 1 Apr 2005

Tme Volume 2, Number 1

The Mathematics Enthusiast

No abstract provided.


Action: Tell Me More Albert!, Jerry T. Baty, Virginia A.H. Mcclendon Apr 2005

Action: Tell Me More Albert!, Jerry T. Baty, Virginia A.H. Mcclendon

The Mathematics Enthusiast

The new school year opens with the instructor cheerfully announcing to the students on the first day, “Good morning, class! Welcome to the fun of a new language called algebra”. He continues, “Today we are going to have a conversation about your success in this classroom. First, is the area of mathematics called algebra, necessary for your future?"

None of the students responds.


Meet The Authors Apr 2005

Meet The Authors

The Mathematics Enthusiast

No abstract provided.


Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou Apr 2005

Cardano's Solution To The Cubic: A Mathematical Soap Opera, Kacee Ballou

The Mathematics Enthusiast

Through this research into the solution of the cubic, I hope to learn the thoughts of mathematicians during this period of history. This knowledge must be conveyed in a way that is historically and mathematically accurate, yet comprehensible and readily available to use in a class of eighth grade math students. It is my wish that as we begin to delve into the world of algebraic and graphical solutions to the problems in the eighth grade text, students will be able to make a connection with this information to that they are currently using to solve their problems. They should …


Call For Papers Apr 2005

Call For Papers

The Mathematics Enthusiast

No abstract provided.


Editorial, Bharath Sriraman Oct 2004

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.


The Nature Of Proof In Today's Classroom. Book Review Of The Nature Of Proof, Erica Lane Oct 2004

The Nature Of Proof In Today's Classroom. Book Review Of The Nature Of Proof, Erica Lane

The Mathematics Enthusiast

Harold Fawcett. The Nature of Proof. New York City: Bureau of Publications, Columbia University, 1938. Re-printed by the National Council of Teachers of Mathematics in 1995.

Throughout the world, children are taught new ideas and concepts in a variety of ways, and the advocates of the different approaches claim that their method is the most effective and profitable for the students. In addition to the different teaching styles, each individual learns the material in a distinct manner. Teachers, therefore, must be aware of the diverse techniques of both teaching and learning in an effort to optimize the learning experience …


Regular Polytopes, Jonathan Comes Oct 2004

Regular Polytopes, Jonathan Comes

The Mathematics Enthusiast

In the last proposition of the Elements Euclid proved that there are only five regular polyhedra, namely the tetrahedron, octahedron, icosahedron, cube, and dodecahedron. To show there can be no more than five he used the fact that in a polyhedra, the sum of the interior angles of the faces which meet at each vertex must be less than 360.


The Morley Trisector Theorem, Grant Swicegood Oct 2004

The Morley Trisector Theorem, Grant Swicegood

The Mathematics Enthusiast

This paper deals with an unannounced theorem by Frank Morley that he originally published amid a collection of other, more general, theorems. Having intrigued mathematicians for the past century, it is now simply referred to as Morley’s trisector theorem:

The three intersections of the angles of a triangle, lying near the three sides respectively, form an equilateral triangle.


Tme Volume 1, Number 2 Oct 2004

Tme Volume 1, Number 2

The Mathematics Enthusiast

No abstract provided.


Author Information Oct 2004

Author Information

The Mathematics Enthusiast

No abstract provided.


Analogies And Mathematics: What Is The Connection? Book Review Of Mathematical And Analogical Reasoning Of Young Learners, Bharath Sriraman Oct 2004

Analogies And Mathematics: What Is The Connection? Book Review Of Mathematical And Analogical Reasoning Of Young Learners, Bharath Sriraman

The Mathematics Enthusiast

Lyn English (Ed). Mathematical and Analogical Reasoning of Young Learners. New Jersey: Lawrence Erlbaum & Associates, 2004. ISBN 0-8058-4945-9.

In the last decade and a half mathematics education literature has shown a rapid increase in books and articles that focus on the social and cultural issues related to mathematics learning and teaching. Although the social and cultural dimensions are important and relevant, the cognitive dimension of mathematical learning is equally important and received less attention. Mathematical and Analogical Reasoning of Young Learners takes us back to the very roots of learning and investigates foundational questions on the nature of …


Voronoi Diagrams, Michael Mumm Oct 2004

Voronoi Diagrams, Michael Mumm

The Mathematics Enthusiast

Suppose we have a finite number of distinct points in the plane. We refer to these points as sites. We wish to partition the plane into disjoint regions called cells, each of which contains exactly one site, so that all other points within a cell are closer to that cell's site than to any other site.


Editorial, Bharath Sriraman Apr 2004

Editorial, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.


Understanding Polygons And Polyhedrons Using Flexagons, Aaron Tekulve Apr 2004

Understanding Polygons And Polyhedrons Using Flexagons, Aaron Tekulve

The Mathematics Enthusiast

The goal of this paper is to help students understand simple polygons and simple polyhedrons. First the project within this paper involves having students look at polygons. Though much of this information should have been learned in the fourth grade it is still important to review this material. Having the students define certain shapes illustrates their true understanding of the subject. The second part to the project within this paper is to use the student’s knowledge of polygons and build polyhedrons. In this paper the students will only have to concern themselves with squares and equilateral triangles. Here they will …