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Full-Text Articles in Mathematics
Editorial, Bharath Sriraman
Action: Tell Me More Albert!, Jerry T. Baty, Virginia A.H. Mcclendon
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.
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
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 …
Commentary On Ballou's Paper: Galois - The Myths And The Man, Catherine Degrandpre
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 …
The Nature Of Proof In Today's Classroom. Book Review Of The Nature Of Proof, Erica Lane
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 …
Analogies And Mathematics: What Is The Connection? Book Review Of Mathematical And Analogical Reasoning Of Young Learners, Bharath Sriraman
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
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
Regular Polytopes, Jonathan Comes
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
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.
Teaching Symmetry In The Elementary Curriculum, Christy Knuchel
Teaching Symmetry In The Elementary Curriculum, Christy Knuchel
The Mathematics Enthusiast
Symmetry is a fundamental part of geometry, nature, and shapes. It creates patterns that help us organize our world conceptually. We see symmetry every day but often don’t realize it. People use concepts of symmetry, including translations, rotations, reflections, and tessellations as part of their careers. Examples of careers that incorporate these ideas are artists, craftspeople, musicians, choreographers, and not to mention, mathematicians.
It is important for students to grasp the concepts of geometry and symmetry while at the elementary level as a means of exposing them to things they see everyday that aren’t obviously related to mathematics but have …
Radius, Diameter, Circumference, Pi, Geometer's Sketchpad, And You!, Scott Edge
Radius, Diameter, Circumference, Pi, Geometer's Sketchpad, And You!, Scott Edge
The Mathematics Enthusiast
I truly believe learning mathematics can be a fun experience for children of all ages. It is up to us, the teachers, to present math as an interesting application. The addition of computers into our ever-changing world has given us an important tool, which can assist us on our journey to teach math in new fun and interesting ways. The Program Geometer’s Sketchpad© is one of many mathematic programs we as teachers can use to better help kids understand different geometric concepts. I would like to use Geometer’s Sketchpad© in my classroom to help teach my students about circles and …
Editorial, Bharath Sriraman
Understanding Polygons And Polyhedrons Using Flexagons, Aaron Tekulve
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 …
Exploring Perimeter And Area With 4th Graders, Amber Lieberg Winkler
Exploring Perimeter And Area With 4th Graders, Amber Lieberg Winkler
The Mathematics Enthusiast
I am going to teach basic introductory geometry skills to 4th graders using Geometry’s Sketchpad. At this age, children are only beginning to learn about geometry in their math classes, and I would like for the students to understand these basic concepts using technology. This problem is so important for the students to learn early, and learn correctly. These skills will involve finding the area and perimeter of regular polygons, basic skills using Geometry’s Sketchpad, and activities that will apply these introductory concepts; directly correlating within the national geometry standards of mathematics. Children use geometry everyday, even when they don’t …