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.

Some Considerations Appertaining to the Content of High School Mathematics

1934 ◽  
Vol 27 (1) ◽  
pp. 41-52
Author(s):  
Gordon R. Mirick
Keyword(s):  
High School ◽  
Point Of View ◽  
School Mathematics ◽  
First Year ◽  
Analytic Geometry ◽  
High School Mathematics ◽  
First Year Students ◽  
Mathematics Courses ◽  
Solid Geometry ◽  
The Subject

Recent years have witnessed a change in the content of courses in mathematics for the seventh, eighth and ninth grades. There has been a change not only in content but in the point of view in the teaching of the subject. A study of the mathematics courses offered to first-year students in our various colleges reveals two important changes. First, the elements of analytic geometry and of the calculus are introduced earlier, and second, there is much less emphasis on Euclidean solid geometry. Pupils who do not take this subject in high school often miss it in college, for the number of colleges offering a course in Euclidean solid geometry is fast diminishing.

What Should High School Geometry Be?

1968 ◽  
Vol 61 (5) ◽  
pp. 466-471
Author(s):  
Charles Buck
Keyword(s):  
High School ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
College Mathematics ◽  
High School Geometry ◽  
School Geometry ◽  
Mathematics Curricula ◽  
School Mathematics Curriculum

The question “What to do about geometry?” has for decades beset the planners of both high school and college mathematics curricula. Until the nature of the first course in high school geometry is settled, the high school mathematics curriculum cannot stabilize. If the high school geometry question could be answered, this would help the colleges to reset geometry in their curricula.

Integrating Transformation Geometry into Traditional High School Geometry

1992 ◽  
Vol 85 (9) ◽  
pp. 716-719
Author(s):  
Steve Okolica ◽  
Georgette Macrina
Keyword(s):  
High School ◽  
Mathematics Curriculum ◽  
School Mathematics ◽  
High School Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry ◽  
Transformation Geometry ◽  
To Receive ◽  
School Mathematics Curriculum

The grades 9-12 section of NCTM's Curriculum and Evaluation Standards for School Mathematics defines transformation geometry as “the geometric counterpart of functions” (1989, 161). Further, the Standards document recognizes the importance of this topic to the high school mathematics curriculum by listing it among the “topics to receive increased attention” (p. 126). Also included on this list is the integration of geometry “across topics.”

Interest of Pupils in High School Mathematics and Factors in Securing It

1927 ◽  
Vol 20 (1) ◽  
pp. 26-38
Author(s):  
Alfred Davis
Keyword(s):  
High School ◽  
Present Status ◽  
School Mathematics ◽  
High School Mathematics ◽  
Single Class ◽  
Class A ◽  
The Subject

A few years ago attention was attracted to the high percentage of failures among pupils taking high school mathematics. Sometimes as many as 50% or even more would fail in a single class. A little consideration would have convinced the teachers that such a situation must soon attract unfavorable criticism, and that this might be expected from those who were not most favorably disposed towards the subject. At a time when every subject was to be tried and judged, not according to its past achievements, nor according to its future possibilities, but according to present status alone, someone was certain to take a one-eyed view of high school mathematics and condemn it as an unsuitable subject to be required of all high school pupils.

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.

Experimental Programs: Coordinate Geometry with an Affine Approach

1964 ◽  
Vol 57 (6) ◽  
pp. 404-405
Author(s):  
Harry Sitomer
Keyword(s):  
High School ◽  
High School Teachers ◽  
School Mathematics ◽  
Study Group ◽  
School Teachers ◽  
High School Geometry ◽  
School Geometry ◽  
Coordinate Geometry

In the spring of 1961, the School Mathematics Study Group convened a group of college mathematicians and high school teachers of mathematics to consider plans for writing an alternate high school geometry course, in which coordinates would be introduced and used as early as feasible.

Prove It

1998 ◽  
Vol 91 (8) ◽  
pp. 726-728
Author(s):  
Amy A. Prince
Keyword(s):  
High School ◽  
School Mathematics ◽  
Evaluation Standards ◽  
High School Geometry ◽  
School Geometry

Ask anyone who has taken high school geometry, and he or she will have a notion of a proof— generally, a two-column proof of statements and reasons. The two-column proof has fallen out of favor in such reform documents as the NCTM's Curriculum and Evaluation Standards for School Mathematics, which seeks to emphasize “deductive arguments expressed orally or in sentence or paragraph form” (NCTM 1989, 126). The two-column proof is a somewhat rigid form, yet it demonstrates to the students that they may not just give statements or draw conclusions without sound mathematical reasons.

Election of High School Mathematics by Females and Males: Attributions and Attitudes

1981 ◽  
Vol 18 (2) ◽  
pp. 207-218 ◽  
Author(s):  
Joan Daniels Pedro ◽  
Patricia Wolleat ◽  
Elizabeth Fennema ◽  
Ann DeVaney Becker
Keyword(s):  
High School ◽  
Mathematics Performance ◽  
School Mathematics ◽  
Advanced Mathematics ◽  
High School Mathematics ◽  
Mathematics Courses ◽  
Small Set ◽  
Advanced Mathematics Courses

Males, more than females, elect advanced mathematics courses. This differential in the number of mathematics courses elected has been cited as a major explanation of sex-related differences in adults' mathematics performance and in their participation in mathematics-related careers. Knowledge about some of the variables that enter into the decision to persist in the study of mathematics is essential for those who are interested in encouraging females, as well as males, to adequately prepare themselves in mathematics. This study identified some attitudinal and attributional variables that relate to the election of mathematics courses by females and males. A small set of variables was found to explain some of the variance in female and male mathematics plans. These results might help in understanding why females do not continue in as large a proportion as males to elect mathematics and/or to enter mathematics-related careers.

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