Report of the Committee on Geometry

1931 ◽  
Vol 24 (5) ◽  
pp. 298-302
Keyword(s):  
Plane Geometry ◽  
National Council ◽  
College Entrance ◽  
Mathematical Association ◽  
Solid Geometry ◽  
Extensive Introduction ◽  
College Entrance Requirements

Early in 1929 a committee was appointed jointly by the Mathematical Association of America and the National Council of Teachers of Mathematics, to study the feasibility of a proposal that college entrance requirements in geometry should be modified so as to bring about the more extensive introduction of courses including the essentials of plane and solid geometry in a single year's work, in place of the traditional year of plane geometry. The Committee begs leave to report as follows:

College Entrance Requirements in Geometry

1929 ◽  
Vol 22 (8) ◽  
pp. 487-488
Author(s):  
Dunham Jackson
Keyword(s):  
Plane Geometry ◽  
Appreciable Amount ◽  
Entrance Examination ◽  
First Year ◽  
National Council ◽  
College Entrance Examination ◽  
College Entrance ◽  
Solid Geometry ◽  
Extensive Introduction ◽  
Examination Board

A proposal bas been made to the College Entrance Examination Board that it should modify its requirements so as to bring about the more extensive introduction of courses including an appreciable amount of solid geometry in the first year of geometry, in place of a part of the plane geometry ordinarily taught. In response to a request from the Board, a committee has been appointed by the Mathematical Associntion of America and the National Council of Teachers of Mathematics to discuss the feasibility of the proposal.

The 17th Annual Meeting of the National Council of Teachers of Mathematics

1936 ◽  
Vol 29 (4) ◽  
pp. 186-192
Author(s):  
Edwin W. Schreiber
Keyword(s):  
High School ◽  
New York ◽  
Secondary School ◽  
Annual Meeting ◽  
American Mathematical Society ◽  
School Mathematics ◽  
Annual Business ◽  
National Council ◽  
Mathematical Association ◽  
Solid Geometry

The Seventeenth Annual Meeting ofthe National Council of Teachers of Mathematics was held in St. Louis, Missouri, December 31, 1935 to January 1, 1936. This is the first annual meeting the National Council has held with the A.A.A.S. One hundred eighty-four registered for the meetings though the total attendance was well in excess of two hundred. A joint session with Section A of the A.A.A.S., the American Mathematical Society, and the Mathematical Association of America, was held on Tuesday morning, December 31, with approximately 250 in attendance. Professor Kenncth P. Williams of I ndiana University presented a temporary report of the Joint Commission on the Place of Mathematics in the Secondary School. “The Main Purposes and Objectives in Teaching High School Mathematics” was discussed by William Betz of Rochester, New York, representing the National Council, and W. W. Hart, representing the Mathematical Association of America. On Tuesday afternoon the National Council presented a Symposium on the Teaching of Geomcetry. Professor W. H. Roever of Washington University, St. Louis, discussed in a very thorough manner the 11Purpose, Nature, and use of Pictures in the Teaching of Solid Geometry.” John T. Rule, the Taylor School, Clayton, Missouri, presented an interesting paper on “Stereoscopy as an Aid to the Teaching of Solid Geometry.” The session closed with a stimulating discussion by Rolland R. Smith, Classical High School, Springfield, Mass., on “Developing the Meaning of Demonstration in Geometry.” The Tuesday evening session was opened by an address of welcome by the Rev. Father Robert S. Johnston, President of St. Louis University. The response was made by Miss Edith Woolsey of Minneapolis, Minnesota. Professor Edwin W. Schreiber, State Teachers College, Macomb, Illinois, presented an illustrated lecture on “The History of the Development of the Metric System.” Miss Ruth Lane, University High School, Iowa City, Iowa, presented an illuminating paper on “Mathematical Recreations, an Aid or a Relief?” On Wednesday morning, J anuary 1, the Annual Business session of the National Council was held. At this session Professor H. E. Slaught of the University of Chicago was honored in being elected Honorary President of the National Council. Secretary Schreiber as Chairman of the Ballot Committee announced the results of the annual election: President—Miss Martha Hildebrandt, Proviso Township High School, Maywood, Illinois; second Vice President-Miss Mary Kelly, Wichita, Kansas; three new members of the Board of Directors—E. R. Breslich, Chicago, Illinois, Leonard D. Haertter, Clayton, Missouri, and Virgil S. Mallory, Montclair, New Jersey. The morning session closed with two interesting papers: “Functiona! Thinking and Teaching in Secondary School Mathematics” by Professor H. C. Christofferson, Miami University, Oxford, Ohio; and “The Crisis in Mathematics—at Rome and Abroad— by Professor William D. Reeve, Teachers

A Reorganization of Geometry for Carryover

1941 ◽  
Vol 34 (4) ◽  
pp. 151-154
Author(s):  
Harold D. Aten
Keyword(s):  
High School ◽  
Plane Geometry ◽  
College Entrance ◽  
Series Form ◽  
American Council ◽  
The Third ◽  
Tenth Grade ◽  
College Entrance Requirements ◽  
Experimental Group ◽  
Geometry Test

“I enrolled in this course merely to complete the college entrance requirements … Now I wish that I could study geometry all the rest of the time I am in high school.” The fifteen-year-old writer of the preceding statement had little interest or ability in mathematics. Early in the course he tried to explain a postulate by a highly-prized “picture of one.” With I.Q. (Terman) 98, he ranked in the third quartile of eighty-five tenth grade pupils who formed our experimental group. He kept a detailed notebook of theorems and daily assignments, written up in his own words. At the end of the year he confided that he had never seen inside a geometry book. He took the Cooperative Plane Geometry test, Revised Series Form Q, of the American Council of Education with a score of 25.5, about 40 per cent above the standard for the country as a whole.

Models in Solid Geometry

1942 ◽  
Vol 35 (1) ◽  
pp. 05-07
Author(s):  
Miles C. Hartley
Keyword(s):  
Three Dimensional ◽  
Joint Commission ◽  
National Committee ◽  
National Council ◽  
Spatial Relationships ◽  
Mathematical Association ◽  
Solid Geometry ◽  
Long Time ◽  
Spatial Imagination ◽  
The Joint Commission

The development of the pupil's ability to visualize spatial relationships has for a long time been recognized as one of the problems confronting the teacher of Solid Geometry. In 1923, the National Committee on Mathematics Requirements wrote: “The aim of the work in Solid Geometry should be to exercise further the spatial imagination of the student and to give him both a knowledge of the fundamental relationships and the power to work with tbem.”1 In 1940, the Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics reported: “Much attention should be given to the visualization of spatial figmes and relations, to the representation of three dimensional figures on paper.…”2

Beginning Geometry and College Entrance

1928 ◽  
Vol 21 (1) ◽  
pp. 42-45
Author(s):  
Ralph Beatley
Keyword(s):  
Plane Geometry ◽  
Entrance Examination ◽  
National Committee ◽  
College Entrance Examination ◽  
College Entrance ◽  
Standard Requirement ◽  
Solid Geometry ◽  
One Year ◽  
Examination Board

In 1923 the College Entrance Examination Board published its Document 108 embodying a detailed statement of the revised requirements in plane and solid geometry. Those who were charged with the preparatjon cf this document gave heed to a suggestion of the National Committee on Mathematical Requirements1 with respect to the desirability of introducing the more elementary notions of solid geometry in connection with related ideas of plane geometry, and prepared accordingly the syllabus for Geometry cd, the so-called Minor Requirement in Plane and Solid Geometry. Document 108 states that “this requirement is designed to cover the most important parts of plane and solid geometry, in such a way that the preparation for it can be completed in the time usually devoted to the standard requirement in plane geometry,” i.e., one year.

scholarly journals III. On abstract geometry

1870 ◽  
Vol 18 (114-122) ◽  
pp. 122-123
Keyword(s):  
General Theory ◽  
Linear Function ◽  
Rational Functions ◽  
Plane Geometry ◽  
System Of Equations ◽  
Fundamental Notion ◽  
Solid Geometry

I submit to the Society the present exposition of some of the elementary principles of an Abstract m -dimensional geometry. The science presents itself in two ways,—as a legitimate extension of the ordinary two- and threedimensional geometries; and as a need in these geometries and in analysis generally. In fact whenever we are concerned with quantities connected together in any manner, and which are, or are considered as variable or determinable, then the nature of the relation between the quantities is frequently rendered more intelligible by regarding them (if only two or three in number) as the coordinates of a point in a plane or in space; for more than three quantities there is, from the greater complexity of the case, the greater need of such a representation; but this can only be obtained by means of the notion of a space of the proper dimensionality; and to use such representation, we require the geometry of such space. An important instance in plane geometry has actually presented itself in the question of the determination of the curves which satisfy given conditions: the conditions imply relations between the coefficients in the equation of the curve; and for the better understanding of these relations it was expedient to consider the coefficients as the coordinates of a point in a space of the proper dimensionality. A fundamental notion in the general theory presents itself, slightly in plane geometry, but already very prominently in solid geometry; viz. we have here the difficulty as to the form of the equations of a curve in space, or (to speak more accurately) as to the expression by means of equations of the twofold relation between the coordinates of a point of such curve. The notion in question is that of a k -fold relation,—as distinguished from any system of equations (or onefold relations) serving for the expression of it,—and giving rise to the problem how to express such relation by means of a system of equations (or onefold relations). Applying to the case of solid geometry my conclusion in the general theory, it may be mentioned that I regard the twofold relation of a curve in space as being completely and precisely expressed by means of a system of equations (P = 0, Q = 0, . . T = 0), when no one of the func ions P, Q, ... T, as a linear function, with constant or variable integral coefficients, of the others of them, and when every surface whatever which passes through the curve has its equation expressible in the form U = AP + BQ ... + KT., with constant or variable integral coefficients, A, B ... K. It is hardly necessary to remark that all the functions and coefficients are taken to be rational functions of the coordinates, and that the word integral has reference to the coordinates.

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