Some Experiments Testing the Most Rapid Method of Factoring the Type ax2 + bx + c

1911 ◽  
Vol 4 (1) ◽  
pp. 32-34
Author(s):  
Fiske Allen
Keyword(s):  
High School ◽  
Rapid Method ◽  
Mathematics Teachers ◽  
Cross Product ◽  
Middle Term ◽  
The Third ◽  
Considerable Debate ◽  
Product Method ◽  
Quadratic Trinomial ◽  
The Cross

For some time there has been considerable debate among the mathematics teachers of Horace Mann High School as to the best method of factoring the quadratic trinomial of the type ax2 + bx + c. It was rather generally agreed that the so-called “cross-product” method is most easily made rational to the pupil and that the method of “splitting the middle term” is least easily taught; also that guessing is involved in all the methods. But it is insisted that either the “splitting-middle-term” method or “multiply-by-a” method is more scientific than the “cross-product” method because a definite system of guessing can be given for the first two which does not apply to the third. This last argument is denied, with no possibility of proof or conviction, but a disagreement upon the question of which method is most rapid was more easily tested and the following experiments made.

ABOUT THE PROBLEM OF CLASSIFICATION OF THE CONCEPTS OF INFORMATICS STUDIED AT SECONDARY SCHOOL

2018 ◽  
pp. 4-7
Author(s):  
S. I. Zenko
Keyword(s):  
Secondary School ◽  
Foreign Language ◽  
Computer Science ◽  
Parts Of Speech ◽  
The Third ◽  
The Cross ◽  
Definition Of

The article raises the problem of classification of the concepts of computer science and informatics studied at secondary school. The efficiency of creation of techniques of training of pupils in these concepts depends on its solution. The author proposes to consider classifications of the concepts of school informatics from four positions: on the cross-subject basis, the content lines of the educational subject "Informatics", the logical and structural interrelations and interactions of the studied concepts, the etymology of foreign-language and translated words in the definition of the concepts of informatics. As a result of the first classification general and special concepts are allocated; the second classification — inter-content and intra-content concepts; the third classification — stable (steady), expanding, key and auxiliary concepts; the fourth classification — concepts-nouns, conceptsverbs, concepts-adjectives and concepts — combinations of parts of speech.

THE EFFECT OF APPLYING DEMONSTRATION METHOD ON STUDENTS’ ACHIEVEMENT IN SPEAKING SKILL AT THE THIRD GRADE OF SMK PAB 3 MEDAN ESTATE

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Meryanti Napitupulu And Anni Holila Pulungan
Keyword(s):  
High School ◽  
Control Group ◽  
Vocational High School ◽  
Control Groups ◽  
Speaking Test ◽  
The Third ◽  
Speaking Skill ◽  
The Subject ◽  
And Control ◽  
Experimental Group

This study was conducted as an attempt to discover the effect of applying Demonstration Method on students’ achievement in speaking skill. It was an experimental research. The subject was students of Grade XII, Vocational High School (Sekolah Menengah Kejuruan: SMK), which consisted of 79 students. The research was divided into two groups: experimental and control groups. The instrument used to collect the data was speaking test. To obtain the reliability of the test, the writer applied Kuder Richardson 21 formula. The result of the reliability was 0.7, and it was found that the test was reliable. The data were analyzed by using t-test formula. The analysis showed that the scores of the students in the experimental group were significantly higher than the scores of the students in the control group at the level of significant m = 0.05 with the degree of freedom (df) 77, t-observed value 8.9 > t-table value 1.99. The findings indicate that using Demonstration Method significantly affected the students’ achievement in speaking skill. So, English teachers are suggested to use Demonstration Method in order to improve students’ achievement in speaking skill.

Identifying Barriers to Integration of Technology into Traditional Approach of Teaching: A Case Study of Mathematics Teachers in Former Transkei in the Eastern Cape

10.31355/12 ◽  
2017 ◽  
Vol 1 ◽  
pp. 063-071
Author(s):  
Agyei Fosu
Keyword(s):  
High School ◽  
Mathematics Teachers ◽  
Traditional Approach ◽  
High School Education ◽  
Eastern Cape ◽  
High School Mathematics ◽  
Policy Makers ◽  
The Past ◽  
Integration Of Technology ◽  
Teaching Of Mathematics

NOTE: THIS ARTICLE WAS PUBLISHED WITH THE INFORMING SCIENCE INSTITUTE. Aim/Purpose................................................................................................................................................................................................. The main aim of the study is to identify some of the barriers to the integration of technology into the teaching of mathematics in high schools. Background................................................................................................................................................................................................. Writing on chalkboards as a method of transferring knowledge is a key feature of traditional approach to teaching may have been successful in the past, but the minds of the current generation vary from those of the previous generation. Today’s students are immersed in technology. They are much more up-to-date on the latest technology and gadgets. Technology has certainly changed how students access and integrate information, so it plausible that technology has also changed the way students thinks. Growing up with cutting-edge technologies has left them thinking differently than students of past generations. This call for new innovative approaches to teaching that will cater to the students of today. Of course it is not wise to discard the traditional way of teaching that the past teachers have painstakingly created because of its past and some current success. This is why it is recommended to use this approach as a base for the new ones. Thus, if there is a way to transfer the advantages of this approach of teaching to new innovative approach then teachers should do everything in their power to merge the past and the present into one innovative teaching approach. Methodology................................................................................................................................................................................................. Purposeful sampling was used to survey a total of 116 high school mathematics teachers in the former Transkei Homelands. But only 97 questionnaires were deemed usable because of the way they have answered the questions. Microsoft excel was used in the descriptive statistics Contribution................................................................................................................................................................................................. To identify some barriers that need to be addressed by stakeholders, policy makers in high school education so that high school mathematics teachers will be able to integrate technology into their classroom teaching to meet today students’ learning needs. Findings...................................................................................................................................................................................................... The results indicated that the participating teachers need to be trained and supported in the use of the new technologies applicable to teaching mathematics. Recommendations for Practitioners.......................................................................................................................................................... The Eastern Cape department of education needs to consider the lacked of technology training as a barrier to the integration of technology into the teaching of mathematics and take necessary steps to address it. Recommendation for Researchers........................................................................................................................................................... There is the need to explore in depth whether the factors of gender and age also act as barriers. Impact on Society....................................................................................................................................................................................... The research will assist stakeholders, policy makers of high school education to identify the needs of mathematics teachers. That is to say, the skill sets, experience and expertise, as well as teaching equipment and classroom design and environment required by mathematics teachers. Future Research........................................................................................................................................................................................... More work needs to be done to check whether gender, age of the teachers have some effects on their attitude towards technology integration as well as evaluate the role played by choice of teaching methodology and teaching objectives.

Confidence Estimation of the Cross-Product Ratio of Binomial Proportions under Different Sampling Schemes

2021 ◽  
Vol 42 (2) ◽  
pp. 435-450
Author(s):  
Chanakan Sungboonchoo ◽  
Thuntida Ngamkham ◽  
Wararit Panichkitkosolkul ◽  
Andrei Volodin
Keyword(s):  
Cross Product ◽  
Confidence Estimation ◽  
Sampling Schemes ◽  
Product Ratio ◽  
Binomial Proportions ◽  
The Cross

scholarly journals The Baum-Connes conjecture, noncommutative Poincaré duality, and the boundary of the free group

2003 ◽  
Vol 2003 (38) ◽  
pp. 2425-2445 ◽  
Author(s):  
Heath Emerson
Keyword(s):  
Free Group ◽  
Homology Class ◽  
Hyperbolic Group ◽  
Cross Product ◽  
Direct Connection ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Duality Map ◽  
The Cross ◽  
Gromov Boundary

For every hyperbolic groupΓwith Gromov boundary∂Γ, one can form the cross productC∗-algebraC(∂Γ)⋊Γ. For each such algebra, we construct a canonicalK-homology class. This class induces a Poincaré duality mapK∗(C(∂Γ)⋊Γ)→K∗+1(C(∂Γ)⋊Γ). We show that this map is an isomorphism in the case ofΓ=𝔽2, the free group on two generators. We point out a direct connection between our constructions and the Baum-Connes conjecture and eventually use the latter to deduce our result.

scholarly journals Angular Vectors in the Theory of Vectors

2017 ◽  
Vol 9 (5) ◽  
pp. 71
Author(s):  
Yevhen Mykolayovych Kharchenko
Keyword(s):  
Angular Velocity ◽  
Cross Product ◽  
Vector Form ◽  
Coordinate Vector ◽  
The Cross ◽  
Definition Of ◽  
Physical Quantities

The theory of angular vectors, which allows modelling of the properties of angular physical quantities, is considered. The meaning of the cross product of vectors was radically revised and changed. Formulas for finding torque and angular velocity in a coordinate-vector form with a correct mapping of their directions were deduced. Described definition of the inverse vector and its properties. The inversed vector allows us to perform vector division operations.

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