Introduction

2006 ◽  
Vol 100 (3) ◽  
pp. 164
Author(s):  
Johnny W. Lott
Keyword(s):  
High School ◽  
Panel Discussion ◽  
High School Geometry ◽  
School Geometry ◽  
Original Question ◽  
The Subject ◽  
February Issue ◽  
Question Today ◽  
School Curricula

In 1972, the Mathematics Teacher published a series of three articles in “The Forum,” a section of the journal devoted to diverging opinions with respect to the role of geometry and the best approach to it. The February issue addressed the question “What should become of the high school geometry course?” The articles in “The Forum” in February were written by Howard F. Fehr, Frank M. Eccles, and Bruce E. Meserve. I chose the article by Fehr as one that has had an effect on high school curricula and still poses some answers to the original question today. The question was the subject of a panel discussion at the August 2006 MathFest of the Mathematical Association of America sponsored by the NCTM/MAA Joint Committee on Mutual Concerns.

Let’s Use Trigonometry

1975 ◽  
Vol 68 (2) ◽  
pp. 157-160
Author(s):  
John J. Rodgers
Keyword(s):  
High School ◽  
Subject Matter ◽  
School Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject ◽  
Order Of Presentation

All too often in the teaching of high school mathematics courses, we overlook the inherent flexibility and interdependence of the subject matter. It is easy to fall into the trap of presenting algebra, trigonometry, geometry, and so on, as separate areas of study. It is because they were taught this way traditionally. With relatively minor changes in the order of presentation, we can demonstrate to the student the vital interconnectiveness of mathematics. For example, many courses in high school geometry include a unit on trigonometry. The student learns three trigonometric ratios, namely, the sine, the cosine, and the tangent. He also learns to use the trigonometric tables to solve for an unknown side of a right triangle. Generally this material comes quite late in the year.

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.

Demonstrative Algebra

1946 ◽  
Vol 39 (6) ◽  
pp. 255-260
Author(s):  
E. R. Stabler
Keyword(s):  
High School ◽  
Junior High School ◽  
Junior High ◽  
College Algebra ◽  
Logical Structure ◽  
Senior High School ◽  
High School Geometry ◽  
School Geometry ◽  
Standard Terminology ◽  
The Subject

High School or college algebra, in comparison with high school geometry, is commonly recognized as a loosely organized subject. In algebra, the usual emphasis is on generalization of the concepts and rules of arithmetic, and on the use of a more powerful symbolism to solve numerical problems, but not on the systematic, logical development of the subject from a set of postulates and undefined terms. Standard terminology distinguishes between informal geometry of the junior high school and demonstrative geometry of the senior high school, but in the field of algebra we generally have only such designations as elementary, intermediate, advanced, or college algebra. These various courses certainly differ in the complexity of topics considered, and in the later courses somewhat more attention is probably paid to such fundamental postulates as commutative and associative laws, and more proofs of specific thorems may be given. But it can hardly be said that under usual conditions the logical structure of the subject, as a whole, is significantly much more advanced in the later than in the earlier courses. Somehow, we do not hear of courses entitled “demonstrative algebra.”

scholarly journals High school students interpretations and use of diagrams in geometry proofs

2017 ◽  
Author(s):  
◽  
Ruveyda Karaman
Keyword(s):  
High School ◽  
High School Students ◽  
School Students ◽  
Clinical Interviews ◽  
High School Geometry ◽  
Geometrical Reasoning ◽  
School Geometry ◽  
Study Participants ◽  
Reasoning Study

In high school geometry, proving theorems and applying them to geometry problems is an expectation from high school students (CCSSI, 2010). Diagrams are considered as an essential part of the geometry proofs because diagrams are included in a typical geometric statement such as a claim or problem (Manders, 2008; Shin et al., 2001). This interview-based study investigated how high school students interpret and use diagrams during the process of proving geometric claims. Particular attention is given to the semiotic resources such as symbols, visuals, and gestures that students draw from the diagrams to develop their proving activities. Hence, the goal of the current study is to contribute to the mathematics education field by providing insights into the details of semiotic aspects of diagrammatic reasoning. Study participants were grade 10-12 high school students and data was collected through one-on-one task- based clinical interviews. In general, students focused on the figural properties of the diagrams more frequently than the conceptual properties of the diagrams in their proofs even when they produced a new diagram or multiple diagrams. Regarding the semiotic structure of students' proving process, gesture resources were prominent in the semiotic structure of students' proving process in diagram-given tasks. The findings also suggested that, in general, some visual resources such as drawing a new figure or multiple figures occurred regularly in particular tasks such as diagram-free tasks with non- diagrammatic register or truth-unknown features. Overall, the frameworks used in this study showed how important it is to consider the mathematics as multi semiotic, understanding the role of gestures in students' geometrical reasoning.

A Chain of Influence in the Development of Geometry

1991 ◽  
Vol 84 (1) ◽  
pp. 15-19
Author(s):  
James E. Lightner
Keyword(s):  
High School ◽  
Next Generation ◽  
Deductive Argument ◽  
Human Needs ◽  
High School Geometry ◽  
School Geometry ◽  
History Of ◽  
The Subject ◽  
A Chain

Teachers of high school geometry are confronted daily with the problem of making the subject as interesting as possible for their students. We teachers, of course, find the challenge of producing a logical deductive argument enough to keep us interested and motivated, but, unfortunately, it may be insufficient for our students. Perhaps sharing with them some of the history of the development of geometry, especially introducing them to some of the great mathematicians, will get them to appreciate the fact that mathematics is the product of human minds, created in response to human needs. Let us look at some of these early “giants” of geometry to see their role in the development of this field of mathematics and to note how each had a tremendous influence on the next generation of geometers.

When Is a Quadrilateral a Parallelogram?

1994 ◽  
Vol 87 (3) ◽  
pp. 208-211
Author(s):  
Charalmpos Toumasis
Keyword(s):  
High School ◽  
High School Geometry ◽  
School Geometry ◽  
The Subject

In most high school geometry textbooks the subject of parallelograms is usually treated in the following manner. First the definition is given: “A quadrilateral in which the opposite sides are parallel is called a parallelogram.” After this definition, some properties of parallelograms are mentioned that can serve as criteria for determining when a quadrilateral is a parallelogram.

Sign in / Sign up

Export Citation Format

Share Document