For a better mathematics program 2) In high-school geometry

1956 ◽  
Vol 49 (2) ◽  
pp. 100-111
Author(s):  
F. Lynwood Wren
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Teacher ◽  
High School Teacher ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Program

Euclidean geometry is now under attack from well-informed centers. “What should be done about it?” is a very real question for the high-school teacher.

Fixed Point Theorems in Euclidean Geometry

1973 ◽  
Vol 66 (4) ◽  
pp. 324-330
Author(s):  
Stanley R. Clemens
Keyword(s):  
High School ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Euclidean Geometry ◽  
Transformation Theory ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Points Of View ◽  
Modern Mathematics

The direction of future high school geometry courses is currently the subject of much discussion. One frequent suggestion is that high school geometry should be presented with transformation theory as the unifying theme. In support of this new direction, we shall illustrate that transformations can be employed to bring theorems from classical synthetic geometry into the so-called mainstream of modern mathematics. The thread tying these two points of view together will be the application of fixed point theorems.

The Forum: What Should Become of the High School Geometry Course?: The Present Year-Long Course in Euclidean Geometry Must Go

1972 ◽  
Vol 65 (2) ◽  
pp. 102-154
Author(s):  
Howard F. Fehr
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Mathematics ◽  
Study Group ◽  
High School Geometry ◽  
School Year ◽  
School Geometry ◽  
Long Course ◽  
Coordinate Geometry

It is assumed that the geometey course refers to one that is commonly taught in the tenth school year. It is traditional Euclidean synthetic geometry, 2- and 3-space, modified by an introduction of ruler and protractor axioms into the usual synthetic axioms. A unit of coordinate geometry of the plane is usually appended. It is a course that is reflected in textbooks prepared by the School Mathematics Study Group and in most commercial textbooks.

Neutral and Non-Euclidean Geometry— A High School Course

1977 ◽  
Vol 70 (4) ◽  
pp. 310-314
Author(s):  
Peter A. Krauss ◽  
Steven L. Okolica
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry

Report of a promising classroom-tested alternative in high school geometry.

The Emergence of Foundational Study

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
School Teacher ◽  
High School Teacher ◽  
The Other ◽  
Non Euclidean Geometry ◽  
Higher Institutions ◽  
Hermann Graßmann

This chapter looks at how modern foundational study has twofold mathematical roots. One is the discovery of non-Euclidean geometries, especially the proof of independence of the parallel postulate by Eugenio Beltrami in 1868, in his Saggio di interpretazione della geometria non-euclidea (Treatise on the interpretation of non-Euclidean geometry). The other root is arithmetical, retraceable through Peano and others to the 1861 book Lehrbuch der Arithmetik für höhere Lehranstalten (Arithmetic for higher institutions of learning) by the high school teacher Hermann Grassmann. In each of these two cases, one has to set things straight: To prove independence in geometry, one has to ask what the axioms are, and maybe even the principles of proof.

The Lessons Non-Euclidean Geometry Can Teach

1940 ◽  
Vol 33 (2) ◽  
pp. 73-79
Author(s):  
Kenneth B. Henderson
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
Real Difference ◽  
Seventh Grade ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry ◽  
Plane Passing ◽  
Length Width ◽  
Better Than

So YOU want to teach mathematics! Why you selected college geometry is more than I know because college geometry is about as useless as high school geometry. Seriously now, did the fact that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles ever make any real difference in your behavior? And were you thrilled to find out that a line is tangent to a circle if it is perpendicular to the radius drawn to the point of contact? Let me warn you in advance t hat when you find out a line is perpendicular to a plane if it is perpendicular to all lines in the plane passing through its foot, you will be apathetic. Furthermore, when you prove that the volume of a rectangular solid is really the product of the length, width, and height you will probably be disgusted, for you knew t hat ever since you were in the seventh grade. The fact that you proved it is really silly, isn't it? You have gotten along pretty well so far just taking somebody's, a teacher's or author's, word for it. And after all, what difference does it make whether you assume this is so in the first place or whether you assume something else, and from this prove the theorem for finding this volume. None of you would try to make me believe that you can calculate the area of the floor of this room better than Fred Fable whose schedule conflicts prevented him from being one of your classmates in geometry in high school.

Introduction to non-Euclidean Geometry

1964 ◽  
Vol 57 (7) ◽  
pp. 457-461
Author(s):  
Wesley W. Maiers
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
Non Euclidean Geometry

A teacher of high school geometry describes a successful unit that convinces pupils that what we prove depends on what we assume.

Euclid and Descartes: A Partnership

1991 ◽  
Vol 84 (9) ◽  
pp. 706-709
Author(s):  
Dorothy Hoy Wasdovich
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
And Algebra ◽  
First Time ◽  
Coordinate Geometry

Although Descartes developed the application of algebra to geometry over 400 years ago, his work has had little impact on the high school geometry course. Geometry and algebra are still taught as separate, unrelated subjects rather than as complementary approaches to mathematics. Any coordinate geometry that is included in a course in Euclidean geometry is apt to be placed in one chapter or unit with the implication that it is “optional” and the material covers theorems that have already been proved. If methods of proof are to be compared, why not do it the first time a theorem is encountered?

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