The Art Of Teaching: You Can Make Them

1942 ◽  
Vol 35 (4) ◽  
pp. 182-183
Author(s):  
Clara O. Larson
Keyword(s):  
Plane Geometry ◽  
Art Of Teaching

To handle things or to touch them gives a significance and concreteness that no amount of looking, drawing or thinking can give. For optional work in my plane geometry classes some of the boys made models, some from old erector sets and some from wood.

The Art of Teaching: A Device for Teaching Locus

1941 ◽  
Vol 34 (6) ◽  
pp. 279
Author(s):  
Margaret C. Amig
Keyword(s):  
Plane Geometry ◽  
Key Points ◽  
Art Of Teaching ◽  
Set Of Points

By the time the pupil has reached locus problems (about the beginning of the second semester of plane geometry), he is pretty well acquainted with figures and has learned to observe relationships between their parts—points, lines, and angles. He has been taught to pick the hypothesis out of a statement and draw a figure to illustrate it. With the figure before him, his task is then to discover or to prove certain conclusions about the figure. Locus problems must be approached in a very different way. No description of the figure is presented to the pupil nor is he expected to draw a figure all at once. The problem is to use certain key points or lines in order to locate a set of points which obey certain given conditions. In other words the pupil is to show how a figure grows rather than merely to produce one.

The Art of Teaching: A New Technique in Handling the Congruence Theorems in Plane Geometry

1943 ◽  
Vol 36 (5) ◽  
pp. 237-239
Author(s):  
Ralph C. Miller
Keyword(s):  
Isosceles Triangle ◽  
Usual Method ◽  
Plane Geometry ◽  
New Technique ◽  
The Third ◽  
Art Of Teaching ◽  
A New Technique ◽  
Congruence Theorem

The Usual method of proof employed in the congruence theorems kills, rather than stimulates, the interest of many students being introduced to geometry. The customary method of superposition applies some very nice axioms and postulates, but leaves the student mystified as to what it is all about. The fact the assumption, that an angle can be bisected, is used to prove the isosceles triangle theorem, which is used to prove the third congruence theorem (s.s.s. equals s.s.s.), which in turn is used to prove the original assumption (that an angle can be bisected) should contribute much to the added confusion of an alert student.

The Art of Teaching: The Use of Models in the Teaching of Plane Geometry

1944 ◽  
Vol 37 (6) ◽  
pp. 272-277
Author(s):  
Frances M. Burns
Keyword(s):  
Plane Geometry ◽  
Visual Impression ◽  
Solid Geometry ◽  
Art Of Teaching ◽  
Accepted Practice ◽  
Third Dimension ◽  
Beginning Students ◽  
Use Of Models

The use of models in the teaching of solid geometry has long been an accepted practice, but in plane geometry they have found little favor. Although not complicated by a third dimension, many of the relationships of plane geometry are difficult for beginning students to understand. The visual impression created by a model often clarifies the meaning of a proposition or leads to a generalization. The purpose of this article is not to present a case to justify their use, but rather to indicate some ways in which the writer's plane geometry classes have found them helpful.

The Art of Teaching: Vocabulary in Plane Geometry

1942 ◽  
Vol 35 (7) ◽  
pp. 331
Author(s):  
Earl R. Keesler
Keyword(s):  
Plane Geometry ◽  
New Words ◽  
Extra Effort ◽  
Technical Vocabulary ◽  
Art Of Teaching ◽  
Integration Project

Since the technical vocabulary of geometry is composed largely of derivatives from Latin and Greek words, the teaching of their history together with pronunciation, meaning, spelling and use should be included as an important part of the course. English equivalents make it much easier to remember definitions which otherwise may be memorized mechanically. For this reason it is sound practice to discuss derivations whenever they may aid in the assimilation of new words. The Latin and history departments are always more than willing to cooperate in such an integration project, while the increased interest and understanding are well worth the extra effort and planning.

The Art of Teaching A New Department

1936 ◽  
Vol 29 (7) ◽  
pp. 346
Author(s):  
Margaret Amig
Keyword(s):  
Isosceles Triangle ◽  
Plane Geometry ◽  
Formal Proofs ◽  
Common Error ◽  
Formal Geometry ◽  
Art Of Teaching

I have found a very slight departure from the usual arrangement of a proposition in plane geometry, very effective in helping pupils to surmount a common difficulty and to avoid a common error. Most beginners find it hard to see why formal proofs of geometric facts are necessary and some are openly rebellious at the idea of giving tedious demonstrations of the truth of very obvious conclusions. Furthermore many pupils approach formal geometry with a background of intuitive geometry and facts retained from that study are likely to increase the pupil's reluctance to substitute reasoning for inspection. The accepted a rrangement of a proposition—first theorem, then figure, then proof—adds, it seems to me, to his confusion. Why, he asks, should one write at the top of the page or recite that the base angles of an isosceles triangle are equal and then proceed to prove that it is true?

The Art of Teaching

1938 ◽  
Vol 31 (2) ◽  
pp. 78-80
Author(s):  
Daniel Luzon Morris
Keyword(s):  
Plane Geometry ◽  
Solid Geometry ◽  
Art Of Teaching

After a person has passed through the “discipline” of plane geometry, solid geometry, and trigonometry, he sometimes realizes the transcendent beauty of plane geometry. Why should he not realize this while he is learning it?

Spacetime Geometry

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Coordinate System ◽  
Special Relativity ◽  
Displacement Vector ◽  
Proper Time ◽  
Plane Geometry ◽  
Spatial Displacement ◽  
Spacetime Geometry ◽  
Space And Time ◽  
Displacement Vectors

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.

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