Tips for Beginners: Optional proofs of theorems in plane geometry

1955 ◽  
Vol 48 (8) ◽  
pp. 578-580
Author(s):  
Francis G. Lankford
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Deductive Proof

This department of The Mathematics Teacher for October contained an article on “Helping Pupils Use Proofs of Theorems in Geometry.” There, some suggestions were given for helping pupils to understand the nature of a deductive proof and to develop the ability to prove theorems independently.

The War on Euclid

1942 ◽  
Vol 35 (5) ◽  
pp. 205-207
Author(s):  
Charles Salkind
Keyword(s):  
Mathematics Teacher ◽  
Progressive Education ◽  
Turn Of The Century ◽  
Joint Commission ◽  
Plane Geometry ◽  
Education Association ◽  
History Of ◽  
The Joint Commission

To recite the history of the attempts, since even before the turn of the century, to modify the method and content of the Plane Geometry Course or “Euclid,” is to invite upon oneself the charge of banality. From the early efforts of Perry and Russell in England, of Laisant in France, of Klein in Germany, of Moore and Hedrick in our own country, to the two most recent reports by the Progressive Education Association and the Joint Commission, through article after article in The Mathematics Teacher and other professional magazines, the battle for reform has been and still is raging.

Proving the Equkaity of the Base Angles of an Isosceles Triangle

1929 ◽  
Vol 22 (6) ◽  
pp. 318-319
Author(s):  
Joseph A. Nyberg
Keyword(s):  
Mathematics Teacher ◽  
Isosceles Triangle ◽  
Plane Geometry ◽  
Angle Bisector ◽  
Significant Step

In a recent paper (A Different Beginning for Plane Geometry, by H. C. Christofferson, MATHEMATICS TEACHER, Dec., 1928) much emphasis is placed on the fact that the existence of an angle bisector must be assumed in proving that tho base angles of an isosceles triangle are equal. Because of this assumption it is argued that, we could better begin by assuming triangles congruent if the corresponding sides are equal. The following is a proof of the equality of the base angles of an isosceles triangle without the use of tho angle bisector. Since the quqestion seems important I present the proof with some detail. Step 4 is the significant step.

A Reply to Mr. Nygaard

1942 ◽  
Vol 35 (4) ◽  
pp. 179-181
Author(s):  
Norman N. Royall
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
National Council ◽  
School Year ◽  
Student Chapter ◽  
Group I

I have read, with ever increasing incredulity, an article in the October (1941) issue of The Mathematics Teacher entitled “A Functional Revision of Plane Geometry” by P. H. Nygaard. Mr. Nygaard's article is such a glaring example of the type of discussion which finds its way into print today to the mortal harm of sound instruction in mathematics that I can not let it pass unchallenged. We have here at Winthrop a student chapter of the National Council of Teachers of Mathematics into the hands of whose members there comes each month during the school year a copy of The Mathematics Teacher. Since I am the faculty sponsor of this group I can for them correct the enors in Mr. Nygaard's essay. The effect of this correction is, however, limited by the range of my voice; therefore, I hope that my reply may have full publicity in The Mathematics Teacher to the end that I may reach the audience afforded to Mr. Nygaard.

More new exercises in plane geometry

1957 ◽  
Vol 50 (5) ◽  
pp. 330-339
Author(s):  
_ _
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Similar Material ◽  
Wide Range ◽  
Mathematics Student ◽  
New Type

The stock of geometrical exercises of the new type introduced in the February 1957 issue of The Mathematics Teacher is here increased so that a wide range of suggested problems is opened to the teacher of geometry.This paper, the last in a series of five devoted to the cutting of squares, also supplements similar material inThe Mathematics Student Journal for April1957.

Tessellations and the Art of M. C. Escher

1984 ◽  
Vol 31 (5) ◽  
pp. 54-55
Author(s):  
Betty K. Zurstadt
Keyword(s):  
Mathematics Teacher ◽  
Plane Geometry ◽  
Upper Elementary ◽  
Elementary Years ◽  
The World

Relating mathematics to the world around us is one of the goals of the mathematics teacher. Plane geometry can be made relevant in the upper elementary years with a study of Escher's tessellations and how he created them.

What is Going On in Your School? The influence of the study of plane geometry on critical thinking

1956 ◽  
Vol 49 (2) ◽  
pp. 151-153
Author(s):  
Carmen C. Massimiano
Keyword(s):  
Critical Thinking ◽  
Plane Geometry ◽  
Classroom Teachers ◽  
Deductive Proof ◽  
Teaching Geometry ◽  
Clear Thinking ◽  
The One ◽  
Precise Expression

In studies that have surveyed the purposes of teaching geometry, such reasons as, “to teach the students to think logically,” and, “to understand the meaning of deductive proof,” were most frequently mentioned. In one important survey that tabulated the opinions of 500 classroom teachers concerning the important objectives of teaching geometry, the one receiving the highest rating was, “to develop the habit of clear thinking and precise expression.”

The Case for the Syllogism in Plane Geometry

1953 ◽  
Vol 46 (5) ◽  
pp. 311-325
Author(s):  
James F. Ulrich
Keyword(s):  
Transfer Of Training ◽  
Plane Geometry ◽  
Deductive Proof ◽  
Reflective Thought ◽  
The Many ◽  
The Mind

It is generally agreed that one of the chief objectives of plane geometry is to foster reflective thought in the mind of the pupil. At various times and in various places it has been clearly stated that the achievement of this objective demands a clear and explicit treatment of the components of reflective thought itself, if the desired benefits from transfer of training are to accrue. The writer will make no attempt to reconcile the many forms of the term “reflective thought”; this has been done elsewhere.1 Whenever the elements of reflective thought are listed in a discussion of the objectives of plane geometry, one of those elements will be similar to this: Plane geometry should help the student to understand the nature of and develop an appreciation for deductive proof. Few would deny that this is an important mission of geometry. It is the approach made by the teacher in presenting the deductive proof to which the remainder of this article is devoted.

Individual Work in Plane Geometry

1930 ◽  
Vol 23 (3) ◽  
pp. 155-160
Author(s):  
Jas. H Zant
Keyword(s):  
High School ◽  
Mathematics Teacher ◽  
Ninth Grade ◽  
The State ◽  
Plane Geometry ◽  
Text Book ◽  
Teachers College ◽  
Individual Work ◽  
Individual Instruction ◽  
Work Done

In the October 1929 number of the Mathematics Teacher there appeared a report of individual work done in ninth grade algebra1. The following report may be of interest as a description of an attempt to teach plane geometry by an individual instruction method. It was used in the Russell High School of the Southeastern State Teachers College, Durant, Oklahoma during the winter and spring of 1927-28. The class used was composed of about twentyfive members which were all the pupils taking geometry in this particular school. The text book in use was the state adopted text of Oklahoma, Newell and Harper's Plane Geometry, published by RowPeterson and Company.

Tips for Beginners: An aid to writing deductive proofs in plane geometry

1958 ◽  
Vol 51 (4) ◽  
pp. 303-305
Author(s):  
John F. Schacht
Keyword(s):  
High School ◽  
High School Students ◽  
Mathematics Teacher ◽  
Recent Article ◽  
Plane Geometry ◽  
School Students

In a recent article in The Mathematics Teacher, Rosskopf and Exner suggest that “… teachers and textbooks should do a better job of introducing high school students to the concepts of logic.”1

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