Some Simple Logical Notions Encountered in Elementary Mathematics

1931 ◽  
Vol 24 (7) ◽  
pp. 436-443
Author(s):  
Carl A. Garabedian
Keyword(s):  
Elementary Mathematics ◽  
Solving Equations ◽  
Formal Algebra

It is a serious shortcoming of our elementary texts that they fail to explain the logical notions which underlie the processes employed in proving identities and in solving equations. The situation might be less embarrassing were it not met so early. But it is at the very beginning of the study of formal algebra that it becomes necessary to distinguish between, and to deal with, identical equations and conditional equations; and, following closely upon the course in algebra, comes trigonometry with its chapter on identities.

scholarly journals APPLICATION OF INVARIANCE PROPERTIES IN PROBLEMS DEPENDING ON THE PARAMETER

2020 ◽  
Vol 70 (2) ◽  
pp. 47-52
Author(s):  
О.D. Apyshev ◽  
◽  
R.О. Nurkanova ◽  
F.S. Аmenova ◽  
◽  
...  
Keyword(s):  
Elementary Mathematics ◽  
Sufficient Conditions ◽  
Solutions To Equations ◽  
Systems Of Equations ◽  
Invariance Properties ◽  
Solution Of Equations ◽  
Single Solution ◽  
Solving Equations ◽  
Necessary And Sufficient ◽  
Invariant Properties

In this paper, we comprehensively consider the problems that depend on the parameter. The necessary and sufficient conditions for the existence of a unique solution of equations and systems of equations that depend on the parameter are investigated. Finding solutions to equations and systems of equations that depend on parameters is one of the most difficult areas of elementary mathematics. To solve them, you need to find ways that require special logical thinking, which must satisfy some additional conditions, for example, to determine a single solution, a solution in a set of all possible values of unknowns, cases when all the solutions of one system are solutions of another, and so on. One of these cases is the use of invariant properties. The article uses various examples of using invariant properties of transformations to consider methods and techniques for solving equations and systems of equations that depend on a single parameter. As a result, due to the presence of invariant properties of transformations, we see that the desired solution is found quickly and easily.

STUDI DESKRIPTIF MINAT CALON GURU SEKOLAH DASAR TERHADAP PENGGUNAAN ALAT PERAGA MATEMATIKA SETELAH PERKULIAHAN MEDIA DAN MODEL PEMBELAJARAN MATEMATIKA SD

2015 ◽  
Vol 8 (1) ◽  
pp. 19
Author(s):  
Isna Rafianti ◽  
Etika Khaerunnisa
Keyword(s):  
Elementary Teachers ◽  
Elementary Mathematics ◽  
Mathematics Learning ◽  
Learning Model ◽  
Prospective Elementary Teachers ◽  
Descriptive Research ◽  
Learning Mathematics ◽  
Mathematical Problems ◽  
The Subject ◽  
Object Of Study

This research is motivated by the lack of interest of teachers in the use of props in the process of learning mathematics in elementary school. In accordance with the demands of the curriculum in 2013 and supported by the developed learning theory, learning mathematics is abstract object of study, students need an intermediary that props math-ematics, so that students can more easily understand the concepts that will be pre-sented, and in the end it can deliver students to solve mathematical problems, not only that proposed by the teacher but also the problems in life. The purpose of this study was to determine the interest of prospective elementary teachers on the use of props mathematics after getting lectures media and elementary mathematics learning model. By knowing the interest of prospective elementary teachers will be developed further realization of the state of the subject being studied. The method used is descriptive research, then the instruments used were questionnaires and interviews. The results of this study stated that the interest of prospective elementary teachers on the use of props after attending lectures media and elementary mathematics learning model is high over-all with a percentage of 76.70%.Keywords : Interest, Props Mathematics

Some aspects of familiarization with binomial coefficients

2019 ◽  
pp. 49-53
Author(s):  
Abdulkarim Magomedov ◽  
S.A. Lavrenchenko
Keyword(s):  
Elementary Mathematics ◽  
Binomial Coefficients ◽  
Computational Aspects

New laconic proofs of two classical statements of combinatorics are proposed, computational aspects of binomial coefficients are considered, and examples of their application to problems of elementary mathematics are given.

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