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: A New Technique in Plane Geometry

1948 ◽  
Vol 41 (4) ◽  
pp. 189-190
Author(s):  
D. A. Zarlengo
Keyword(s):  
Subject Matter ◽  
Plane Geometry ◽  
New Technique ◽  
Visual Instruction ◽  
The Past ◽  
The World ◽  
The Future ◽  
A New Technique ◽  
Future Education ◽  
Major Emphasis

With the ending of the war, many of us feel that the world and the life of earlier years will never return. The rapid developments in all fields during the past several years will leave their results with us, and we shall feel and live them long into the future. Education has had its share in this transition. During the training of American youth all methods of presentation of subject matter had to be tried for the quickest and best method. Needless to say visual instruction received a major emphasis; enough to make it a definite part of modern teaching.

The Influence of Direct Instruction on Student Self-appraisals: A Hierarchical Analysis of Treatment and Aptitude-Treatment Interaction Effects

1981 ◽  
Vol 18 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Lyn Corno ◽  
Alexis Mitman ◽  
Larry Hedges
Keyword(s):  
Locus Of Control ◽  
Self Esteem ◽  
New Technique ◽  
Hierarchical Analysis ◽  
Learning Skills ◽  
The Third ◽  
Class Level ◽  
Treatment Interaction ◽  
Aptitude Treatment Interaction ◽  
A New Technique

The study analyzed student self-appraisal data from an instructional experiment in the third grade. Treatment and aptitude-treatment interaction (ATI) effects were assessed on self-esteem, attitude, anxiety, and locus of control Analyses were performed at the student and class levels to accommodate the hierarchical character of the data. Results showed the instruction favorably influenced self-esteem, attitude, and anxiety. In particular, parent instruction in learning skills resulted in significantly higher average scores on self-esteem and attitude and lower scores on anxiety. Class-level ATI's were also evidenced among the parent instruction and selected student aptitudes. Second-order ATI's are illustrated with a new technique developed by Hedges.

scholarly journals A new technique for forearm X-photo (The third report)

1996 ◽  
Vol 52 (2) ◽  
pp. 161
Author(s):  
T. Ugajin ◽  
N. Sugiyama ◽  
Y. Hishikawa ◽  
S. Mori ◽  
T. Itou
Keyword(s):  
New Technique ◽  
The Third ◽  
A New Technique

scholarly journals Semilinear Transformations in Coding Theory: A New Technique in Code-Based Cryptography

2022 ◽  
Author(s):  
Wenshuo Guo ◽  
Fang-Wei Fu
Keyword(s):  
Linear Space ◽  
Coding Theory ◽  
Linear Codes ◽  
New Technique ◽  
Compact Representation ◽  
The Public ◽  
The Third ◽  
Public Keys ◽  
A New Technique ◽  
Code Based Cryptography

Abstract This paper presents a new technique for disturbing the algebraic structure of linear codes in code-based cryptography. Specifically, we introduce the so-called semilinear transformations in coding theory and then apply them to the construction of code-based cryptosystems. Note that Fqm can be viewed as an Fq -linear space of dimension m , a semilinear transformation φ is therefore defined as an Fq -linear automorphism of Fqm . Then we impose this transformation to a linear code C over Fqm . It is clear that φ (C) forms an Fq -linear space, but generally does not preserve the Fqm -linearity any longer. Inspired by this observation, a new technique for masking the structure of linear codes is developed in this paper. Meanwhile, we endow the underlying Gabidulin code with the so-called partial cyclic structure to reduce the public-key size. Compared to some other code-based cryptosystems, our proposal admits a much more compact representation of public keys. For instance, 2592 bytes are enough to achieve the security of 256 bits, almost 403 times smaller than that of Classic McEliece entering the third round of the NIST PQC project.

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?

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