Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3

Algebra Related Abstracts

3 Mathematical Anxiety and Misconceptions in Algebra of Grade Vii Students in General Emilio Aguinaldo National High School

Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

Abstract:

This is a descriptive research on the level of math anxiety and mathematics misconceptions in algebra. This research is composed of four parts: (1) analysis of the level of anxiety of the respondents; (2) analysis of the common mathematical misconceptions in algebra; (3) relationship of socio-demographic profile in math anxiety and mathematical misconceptions and (4) analysis of the relationship of math anxiety and misconceptions in algebra. Through the demographic profile questionnaire it was found out that most of the respondents were female. Majority had ages that ranged from 13-15. Most of them had parents who finished secondary education. The biggest portion of Grade Seven students where from families with annual family income ranging from PhP 100, 000 to PhP 299, 999. Most of them came from public school. Mathematics Anxiety Scale for Secondary and Senior Secondary School Students (MAS) and set of 10 open-ended algebraic expressions and polynomials were also administered to determine the anxiety level and the common misconceptions in algebra. Data analysis revealed that respondents had high anxiety in mathematics. Likewise, the common mathematical misconceptions of the Grade Seven students were: combining unlike terms; multiplying the base and exponents; regarding the variable x as 0; squaring the first and second terms only in product of two binomials; wrong meaning attached to brackets; writing the terms next to each other but not simplifying in using the FOIL Method; writing the literal coefficient even if the numerical coefficient is 0; and dividing the denominator by the numerator when the numerical coefficient in the numerator is smaller than the numerical coefficient of the denominator. Results of the study show that the socio-demographic characteristics were not related to mathematics anxiety and misconceptions. Furthermore, students from higher section had high anxiety than those students on the lower section. Thus, belonging to higher or lower section may affect the mathematical misconceptions of the respondents.

Keywords: Algebra, math anxiety, grade 7 math, math misconceptions

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2 Dual Duality for Unifying Spacetime and Internal Symmetry

Authors: David C. Ni

Abstract:

The current efforts for Grand Unification Theory (GUT) can be classified into General Relativity, Quantum Mechanics, String Theory and the related formalisms. In the geometric approaches for extending General Relativity, the efforts are establishing global and local invariance embedded into metric formalisms, thereby additional dimensions are constructed for unifying canonical formulations, such as Hamiltonian and Lagrangian formulations. The approaches of extending Quantum Mechanics adopt symmetry principle to formulate algebra-group theories, which evolved from Maxwell formulation to Yang-Mills non-abelian gauge formulation, and thereafter manifested the Standard model. This thread of efforts has been constructing super-symmetry for mapping fermion and boson as well as gluon and graviton. The efforts of String theory currently have been evolving to so-called gauge/gravity correspondence, particularly the equivalence between type IIB string theory compactified on AdS5 × S5 and N = 4 supersymmetric Yang-Mills theory. Other efforts are also adopting cross-breeding approaches of above three formalisms as well as competing formalisms, nevertheless, the related symmetries, dualities, and correspondences are outlined as principles and techniques even these terminologies are defined diversely and often generally coined as duality. In this paper, we firstly classify these dualities from the perspective of physics. Then examine the hierarchical structure of classes from mathematical perspective referring to Coleman-Mandula theorem, Hidden Local Symmetry, Groupoid-Categorization and others. Based on Fundamental Theorems of Algebra, we argue that rather imposing effective constraints on different algebras and the related extensions, which are mainly constructed by self-breeding or self-mapping methodologies for sustaining invariance, we propose a new addition, momentum-angular momentum duality at the level of electromagnetic duality, for rationalizing the duality algebras, and then characterize this duality numerically with attempt for addressing some unsolved problems in physics and astrophysics.

Keywords: Algebra, Quantum Mechanics, General Relativity, string theory, Symmetry‎, Duality, correspondence, momentum-angular-momentum

Procedia PDF Downloads 223
1 Conspicuous and Significant Learner Errors in Algebra

Authors: Michael Lousis

Abstract:

The kind of the most important and conspicuous errors the students made during the three-years of testing of their progress in Algebra are presented in this article. The way these students’ errors changed over three-years of school Algebra learning also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students, who were purposefully culled according to their participation in each occasion of testing in the development of the three-year Kassel Project in England and Greece, in both domains at once of Arithmetic and Algebra. Hence, for each of these English and Greek students, six test-scripts were available and corresponded to the three occasions of testing in both Arithmetic and Algebra respectively.

Keywords: Algebra, Errors, Kassel Project, progress of learning

Procedia PDF Downloads 131