Search results for: elementary algebra classroom

Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista

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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.

Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom

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Authors: Takuma Yamamoto

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Present study investigated the relationship between elementary school children’s prosocial behavior in classroom and satisfaction with school life (approval and victimization from other children) with considering from the perspective of classroom social goal structures (prosocial and compliance goal structures). Participants were 755 elementary school children (393 boys, 362 girls, mean range= 10-12, 5th grader and 6th grader) who were living in Chugoku District, Japan. They filled up questionnaire which was consisted of Murakami, Nishimura and Sakurai’s (2016) prosocial behavior toward friend scale, Kawamura and Tagami’s (1997) satisfaction in classroom scale and Ohtani, Okada, Nakaya and Ito’s (2016) classroom social goal structures scale. Regression lines that satisfaction in classroom is dependent variable and prosocial behavior is independent variable for each class were drawn. There were two types of classroom which children’s prosocial behavior correlated with satisfaction positively and did not. Then one-way MANOVA was conducted to further describe two types of classroom which prosocial behavior increased satisfaction in classroom (type 1) and prosocial behavior decreased satisfaction (type 2). MANOVA for Prosocial goal structure was significant, type 1 > type 2. There were two key findings from this study. First, MANOVA for prosocial goal structure was significant. Second, high score of prosocial goal structure was not necessary condition for the classroom type which children’s prosocial behavior correlated with satisfaction. The implications from these key findings were: (1) in the low prosocial goal structure classroom, children will not behave prosocially because of their negative expectation for the effect of prosocial behavior, (2) this study can be a contribution for classroom management that teachers need to consider about the negative possibilities of prosocial behavior when they try to increase the amount of children’s positive behavior.

Keywords: elementary school children, classroom social goal structure, satisfaction with school life, prosocial behavior

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Authors: Tsai-Hsiu Lin

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Three dimensions of teacher culture hinder educational improvement: individualism, conservatism and presentism. To promote the professional development of teachers, these three aspects in teacher culture should be eliminated. Classroom observation may be a useful method of eliminating individualism. The Ministry of Education in Taiwan has attempted to reduce the isolation of teachers to promote their professional growth. Because classroom observation discourse varies, teachers are generally unwilling to allow their teaching to be observed. However, classroom observations take place in the country in the form of school evaluations. The main purpose of this study was to explore the differences in teachers’ conservatism, individualism and presentism after classroom observations had been conducted at an elementary school in Taiwan. The research method was a qualitative case study involving interviews with the school principal, the director of academic affairs, and two classroom teachers. The following conclusions were drawn: (1) Educators in different positions viewed classroom observations differently; (2) The classroom teachers did not highly value classroom observation; (3) There was little change in the teachers’ conservatism, individualism and presentism after classroom observation.

Keywords: classroom observation, Lortie’s Trinity, teacher culture, teacher professional development

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Authors: Muna Tabuni

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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

Procedia PDF Downloads 174

Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang

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The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.

Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications

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Authors: Michael Lousis

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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

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Authors: Mohamed Boubekri, Kristen Bub, Jaewook Lee, Kate Kurry

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In this study, we explored the impact of light, particularly daylight on sleep time and quality of elementary school children. Sleep actigraphy was used to measure objectively sleep time and sleep efficiency. Our data show a good correlation between light levels and sleep. In some cases, differences of up to 36 minutes were found between students in low light levels and those in high light level classrooms. We recommend, therefore, that classroom design need to pay attention to the daily daylight exposures elementary school children are receiving.

Keywords: light, daylight, actigraphy, sleep, circadian rhythm, sustainable architecture, elementary school, children

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Md. Shah Alam

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Mushfiq Ahmad has defined a Mixed Number, which is the sum of a scalar and a Cartesian vector. He has also defined the elementary group operations of Mixed numbers i.e. the norm of Mixed numbers, the product of two Mixed numbers, the identity element and the inverse. It has been observed that Mixed Number is consistent with Pauli matrix algebra and a handy tool to work with Dirac electron theory. Its use as a mathematical method in Physics has been studied. (1) We have applied Mixed number in Quantum Mechanics: Mixed Number version of Displacement operator, Vector differential operator, and Angular momentum operator has been developed. Mixed Number method has also been applied to Klein-Gordon equation. (2) We have applied Mixed number in Electrodynamics: Mixed Number version of Maxwell’s equation, the Electric and Magnetic field quantities and Lorentz Force has been found. (3) An associative transformation of Mixed Number numbers fulfilling Lorentz invariance requirement is developed. (4) We have applied Mixed number algebra as an extension of Complex number. Mixed numbers and the Quaternions have isomorphic correspondence, but they are different in algebraic details. The multiplication of unit Mixed number and the multiplication of unit Quaternions are different. Since Mixed Number has properties similar to those of Pauli matrix algebra, Mixed Number algebra is a more convenient tool to deal with Dirac equation.

Keywords: mixed number, special relativity, quantum mechanics, electrodynamics, pauli matrix

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Authors: Benjamin Lee Warren

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Many problems exist in additive number theory which is essential to determine the primes that are the sum of two elements from a given single-variable polynomial sequence, and most of them are unattackable in the present day. Here, we determine solutions for this problem to a few certain sequences (certain binomial coefficients and power sums) using only elementary algebra and some algebraic factoring methods (as well as Euclid’s Lemma and Faulhaber’s Formula). In particular, we show that there are finitely many primes as sums of two of these types of elements. Several cases are fully illustrated, and bounds are presented for the cases not fully illustrated.

Keywords: binomial coefficients, power sums, primes, algebra

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Authors: Zolzaya Badmaavanchig, Shoko Miyamoto

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In recent years, universal design for learning (hereinafter referred to as "UDL"), which aims to establish an inclusive education system and to make all children, regardless of their disabilities, experts in learning, has been attracting attention, and there have been some attempts to incorporate it into regular classrooms where children with developmental disabilities and those who show such tendencies are enrolled. The purpose of this study was to examine the effectiveness and challenges of implementing UDL in Japanese elementary schools based on the previous literature. As a method, we first searched for articles on UDL for learning and UDL in the classroom from 2010 to 2022. In addition, we selected practice studies that targeted children with special educational support needs and the classroom as a whole. In response to the extracted literature, this bridge examined the following five perspectives: (1) subjects and grades in which UDL was practiced, (2) methods to grasp the actual conditions of the children, (3) consideration for children with special needs during class, (4) form of class, and (5) effects of the practice. Based on the results, we would like to present issues related to future UDL efforts in Japanese elementary schools.

Keywords: universal design for learning, regular elementary school class, children with special education needs, special educational support

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Authors: Fu-Chi Chuang, Yu-Liang, Chang, Wen-Der Wang

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Our environment has been contaminated by many artificial chemicals, such as plastics, pesticides. Many of them have hormone-like activity and are classified as 'environmental hormone (also named endocrine disruptors)'. These chemicals interfere with or mimic hormones have adverse effects that persist into adulthood. Environmental education is an important way to teach students to become engaged in real-world issues that transcend classroom walls. Elementary education is the first stage to perform environmental education and it is an important component to help students develop adequate environmental knowledge, attitudes, and behavior. However, elementary teachers' knowledge plays a critical role in this mission. Therefore, we use a questionnaire to survey the knowledge of environmental hormone of elementary school teachers and their learning motivation of the environmental hormone-regarding knowledge. We collected 218 questionnaires from Taiwanese elementary teachers and the results indicate around 73% of elementary teachers do not have enough knowledge about environmental hormones. Our results also reveal the in-service elementary teachers’ learning motivation of environmental hormones knowledge is positively enhanced once they realized their insufficient cognitive ability of environmental hormones. We believe our study will provide the powerful reference for Ministry of Education to set up the policy of environmental education to enrich all citizens sufficient knowledge of the effects of the environmental hormone on organisms, and further to enhance our correct environmental behaviors.

Keywords: elementary teacher, environmental hormones, learning motivation, questionnaire

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Authors: Alireza Gilani

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In this paper, we consider the fuzzification of implicative pseudo-ideal in a pseudo-BCK algebra, and then we investigate some of their properties. We prove that the family of fuzzy implicative pseudo-ideal is completely distributive lattice.

Keywords: BCK-algebra, pseudo-BCK algebra, pseudo-ideal, implicative pseudo-ideal

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Authors: Salvatore Triolo

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We discuss the possibility of extending the well-known Gelfand-Naimark-Segal representation to modules over a C*algebra. We focus our attention on the case of Hilbert modules. We consider, in particular, the problem of the existence of a faithful representation. Non-commutative Lᵖ-spaces are shown to constitute examples of a class of CQ*-algebras. Finally, we have shown that any semisimple proper CQ*-algebra (X, A#), with A# a W*-algebra can be represented as a CQ*-algebra of measurable operators in Segal’s sense.

Keywords: Gelfand-Naimark-Segal representation, CQ*-algebras, faithful representation, non-commutative Lᵖ-spaces, operator in Hilbert spaces

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Authors: Yassir I. Dinar

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We computed the weights of the adjoint action of distinguished sl2-triples in Lie algebra of type Dn using mathematical induction.

Keywords: lie algebra, root systems, representation theory, nilpotent orbits

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Natalia Kasatkina

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In an ever-increasing globalization, one’s grasp of diversity and tolerance has never been more indispensable, and it is a vital duty for all those in the field of foreign language teaching to help children cultivate such values. The present study explores the role of DIVERSITY and TOLERANCE in the language classroom and elementary, middle, and high school students’ perceptions of these two concepts. It draws on several theoretical domains of language acquisition, cultural awareness, and school psychology. Relying on these frameworks, the major findings are synthesized, and a paradigm of teaching tolerance through language-teaching is formulated. Upon analysing how tolerant our children are with ‘others’ in and outside the classroom, we have concluded that intolerance and aggression towards the ‘other’ increase with age, and that a feeling of supremacy over migrants and a sense of fear towards them begin to manifest more apparently when the students are in high school. In addition, we have also found that children in elementary school do not exhibit such prejudiced thoughts and behavior, which leads us to the believe that tolerance as well as intolerance are learned. Therefore, it is within our reach to teach our children to be open-minded and accepting. We have used the novel ‘Uncle Tom’s Cabin’ by Harriet Beecher Stowe as a springboard for lessons which are not only targeted at shedding light on the role of language in the modern world, but also aim to stimulate an awareness of cultural diversity. We equally strive to conduct further cross-cultural research in order to solidify the theory behind this study, and thus devise a language-based curriculum which would encourage tolerance through the examination of various literary texts.

Keywords: literary text, tolerance, EFL classroom, word-association test

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Authors: Natalia Pacheco Rego

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The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.

Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation

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Authors: Chin-Wen Chien

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Protocols are tools that help teachers inquire into the teaching and professional learning during the professional dialogue. This study focused on the integration of protocols into elementary school English teachers’ professional dialogue and discussed the influence of protocols on teachers’ teaching and learning. Based on the analysis of documents, observations, and interviews, this study concluded that with the introduction of protocols to elementary school English teachers, three major protocols were used during their professional dialogue. These protocols led the teachers to gain professional learning in content knowledge and pedagogical content knowledge. However, the facilitators’ lack of experience in using protocols led to interruptions during the professional dialogue. Suggestions for effective protocol-based professional dialogue are provided.

Keywords: protocols, professional learning, professional dialogue, classroom practice

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Authors: Carolina S. Correia, Thalita V. Thomé, Andersen Boniolo, Dhayana I. Veiga

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Evidence-based practices (EBP) in education is a set of principles and practices used to raise educational policy, it involves the integration of professional expertise in education with the best empirical evidence in making decisions about how to deliver instruction. The purpose of this presentation is to describe and characterize studies about EBP in education in elementary classroom setting. Data here presented is part of an ongoing systematic review research. Articles were searched and selected from four academic databases: ProQuest, Scielo, Science Direct and Capes. The search terms were evidence-based practices or program effectiveness, and education or teaching or teaching practices or teaching methods. Articles were included according to the following criteria: The studies were explicitly described as evidence-based or discussed the most effective practices in education, they discussed teaching practices in classroom context in elementary school level. Document excerpts were extracted and recorded in Excel, organized by reference, descriptors, abstract, purpose, setting, participants, type of teaching practice, study design and main results. The total amount of articles selected were 1.185, 569 articles from Proquest Research Library; 216 from CAPES; 251 from ScienceDirect and 149 from Scielo Library. The potentially relevant references were 178, from which duplicates were removed. The final number of articles analyzed was 140. From 140 articles, are 47 theoretical studies and 93 empirical articles. The following research design methods were identified: longitudinal intervention study, cluster-randomized trial, meta-analysis and pretest-posttest studies. From 140 articles, 103 studies were about regular school teaching and 37 were on special education teaching practices. In several studies, used as teaching method: active learning, content acquisition podcast (CAP), precision teaching (PT), mediated reading practice, speech therapist programs and peer-assisted learning strategies (PALS). The countries of origin of the studies were United States of America, United Kingdom, Panama, Sweden, Scotland, South Korea, Argentina, Chile, New Zealand and Brunei. The present study in is an ongoing project, so some representative findings will be discussed, providing further acknowledgment on the best teaching practices in elementary classroom setting.

Keywords: best practices, children, evidence-based education, elementary school, teaching methods

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Authors: Rabi Abdullahi Danjuma, Fatima Binta Attahir

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Classroom discourse is important, and it is worth examining what the phenomena is and how it helps both the teacher and students in a classroom situation. This paper looks at the classroom as a traditional social setting which has its own norms and values. The paper also explains what discourse is, as extended communication in speech or writing often interactively dealing with some particular topics. It also discusses classroom discourse as the language which teachers and students use to communicate with each other in a classroom situation. The paper also looks at some strategies for effective classroom discourse. Finally, implications and recommendations were drawn.

Keywords: classroom, discourse, learning, student, strategies, communication

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Authors: Mahdi Taheri Asl

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Using a variety of strategies to read text plays an important role to make students strategic independent, strategic, and metacognitive readers. Given the importance of comprehension instruction (CI), it is essential to support the fostering comprehension skills at elementary age students, particularly those who struggle with or dislike reading. One of the main components of CI is activating metacognitive skills, which double function of elementary students. Thus, it’s important to evaluate the implemented comprehension interventions to inform reading specialist and teachers. There has been limited review research in the area of CI, so the conduction review research is required. The purpose of this review is to examine the effectiveness of metacognitive reading strategies in a regular classroom environment with elementary aged students. We develop five inclusion criteria to identify researches relevant to our research. First, the article had to be published in a peer-reviewed journal from 2000 to 2023. second, the study had to include participants in elementary school it could include of special education students. Third, the intervention needed to be involved with metacognitive strategies. Fourth, the articles had to use experimental or quasi experimental design. The last one needed to include measurement of reading performance in pre and post intervention. We used computer data-based site like Eric, PsychoINFO, and google scholar to search for articles that met these criteria. we used the following search terms: comprehension instruction, meta cognitive strategies, and elementary school. The next step was to do an ancestral search that get in reviewing the relevant studies cited in the articles that were found in the database search. We identified 30studies in the initial searches. After coding agreement, we synthesized 13 with respect to the participant, setting, research design, dependent variables, measures, the intervention used by instructors, and general outcomes. The finding show metacognitive strategies were effective to empower student’s comprehension skills. It also showed that linguistic instruction will be effective if got mixed with metacognitive strategies. The research provides a useful view into reading intervention. Despite the positive effect of metacognitive instruction on students’ comprehension skills, it is not widely used in classroom.

Keywords: comprehension instruction, metacogntion, metacognitive skills, reading intervention

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Authors: Wagneur Edouard

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Tropical algebra is the algebra constructed over an idempotent semifield S. We show here that every m-dimensional tropical module M over S with strongly independent basis can be embedded into Sm, and provide an algebraic invariant -the Γ-matrix of M- which characterises the isomorphy class of M. The strong independence condition also yields a significant improvement to the Whitney embedding for tropical torsion modules published earlier We also show that the strong independence of the basis of M is equivalent to the unique representation of elements of M. Numerous examples illustrate our results.

Keywords: classification, idempotent semi-modules, strong independence, tropical algebra

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Authors: Ariel B. Domagsang

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This study dealt with the physical fitness activities for elementary school pupils of Matacon Elementary School, Polangui South District, Albay Division are presented in this chapter. Specifically, it looked into the pre-post test performance based on the Physical Fitness Test which were subjected to statistical significant test of difference including health- and skill-related improvement. Finally, it came up with physical fitness activities to improve the physical fitness performance of the pupils. The descriptive method through survey using questionnaire-checklist, unstructured interview and document(ary) analysis were utilized in this research. There were 171 grades five and six pupil participants in this undertaking.

Keywords: Matakon, fitness acitivities, elementary schools, physical fitness of pupils

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Authors: Ranjit Biswas

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The existing subject Algebra is incomplete to support mathematical computations being done by scientists of all areas: Mathematics, Physics, Statistics, Chemistry, Space Science, Cosmology etc. even starting from the era of great Einstein. A huge hidden gap in the subject ‘Algebra’ is unearthed. All the scientists today, including mathematicians, physicists, chemists, statisticians, cosmologists, space scientists, and economists, even starting from the great Einstein, are lucky that they got results without facing any contradictions or without facing computational errors. Most surprising is that the results of all scientists, including Nobel Prize winners, were proved by them by doing experiments too. But in this paper, it is rigorously justified that they all are lucky. An algebraist can define an infinite number of new algebraic structures. The objective of the work in this paper is not just for the sake of defining a distinct algebraic structure, but to recognize and identify a major gap of the subject ‘Algebra’ lying hidden so far in the existing vast literature of it. The objective of this work is to fix the unearthed gap. Consequently, a different algebraic structure called ‘Region’ has been introduced, and its properties are studied.

Keywords: region, ROR, RORR, region algebra

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Authors: Jhemson C. Elis, Alvin S. Magadia

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Our world is full of numbers, shapes, and figures that illustrate the wholeness of a thing. Indeed, this statement signifies that mathematics is everywhere. Mathematics in its broadest sense helps people in their everyday life that is why in education it is a must to be taken by the students as a subject. The study aims to determine the profile of the respondents in terms of gender and age, performance of the control and experimental groups in the pretest and posttest, impact of the instructional game used as instructional intervention in teaching algebra for high school students, significant difference between the level of performance of the two groups of respondents in their pre–test and post–test results, and the instructional intervention can be proposed. The descriptive method was also utilized in this study. The use of the certain approach was to that it corresponds to the main objective of this research that is to determine the effectiveness of the instructional game used as an instructional intervention in teaching algebra for high school students. There were 30 students served as respondents, having an equal size of the sample of 15 each while a greater number of female teacher respondents which totaled 7 or 70 percent and male were 3 or 30 percent. The study recommended that mathematics teacher should conceptualize instructional games for the students to learn mathematics with fun and enjoyment while learning. Mathematics education program supervisor should give training for teachers on how to conceptualize mathematics intervention for the students learning. Meaningful activities must be provided to sustain the student’s interest in learning. Students must be given time to have fun at the classroom through playing while learning since mathematics for them was considered as difficult. Future researcher must continue conceptualizing some mathematics intervention to suffice the needs of the students, and teachers should inculcate more educational games so that the discussion will be successful and joyful.

Keywords: instructional game in algebra, mathematical intervention, joyful, successful

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Authors: Reiko Yamamoto

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This paper reports on how synchrony occurs between children and their teacher, and what prevents or facilitates synchrony. The aim of the experiment conducted in this study was to precisely analyze their movements and synchrony and reveal the process of synchrony in a real-world classroom. Specifically, the experiment was conducted for around 20 minutes during an English as a foreign language (EFL) lesson. The participants were 11 fourth-grade school children and their classroom teacher in a public elementary school in Japan. Previous researchers assert that synchrony causes the state of flow in a class. For checking the level of flow, Short Flow State Scale (SFSS) was adopted. The experimental procedure had four steps: 1) The teacher read aloud the first half of an English storybook to the children. Both the teacher and the children were at their own desks. 2) The children were subjected to an SFSS check. 3) The teacher read aloud the remaining half of the storybook to the children. She made the children remove their desks before reading. 4) The children were again subjected to an SFSS check. The movements of all participants were recorded with a video camera. From the movement analysis, it was found that the children synchronized better with the teacher in Step 3 than in Step 1, and that the teacher’s movement became free and outstanding without a desk. This implies that the desk acted as a barrier between the children and the teacher. Removal of this barrier resulted in the children’s reactions becoming synchronized with those of the teacher. The SFSS results proved that the children experienced more flow without a barrier than with a barrier. Apparently, synchrony is what caused flow or social emotions in the classroom. The main conclusion is that synchrony leads to cognitive outcomes such as children’s academic performance in EFL learning.

Keywords: engagement in a class, English as a foreign language (EFL) learning, interactional synchrony, social emotions

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Authors: Abigail Gragg

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The goal of this research study was to adjudicate if implementing Howard Gardner’s multiple levels of intelligence would enhance student achievement levels in an Algebra 1 College Preparatory class. This was conducted within every class by incorporating one level of the eight levels of intelligence into small group work in stations. Every class was conducted utilizing small-group instruction. Achievement levels were measured through various forms of collected data that expressed student understandings in class through formative assessments versus student understandings on summative assessments. The data samples included: assessments (i.e. summative and formative assessments), observable data, video recordings, a daily log book, student surveys, and checklists kept during the observation periods. Formative assessments were analyzed during each class period to measure in-class understanding. Summative assessments were dissected per question per accuracy to review the effects of each intelligence implemented. The data was collated into a coding workbook for further analysis to conclude the resulting themes of the research. These themes include 1) there was no correlation to multiple levels of intelligence enhancing student achievement, 2) bodily-kinesthetic intelligence showed to be the intelligence that had the most improvement on test questions and 3) out of all of the bits of intelligence, interpersonal intelligence enhanced student understanding in class.

Keywords: stations, small group instruction, multiple levels of intelligence, Mathematics, Algebra 1, student achievement, secondary school, instructional Pedagogies

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Authors: Karl Erickson I. Ebora

Abstract:

Science and technology are two inseparable terms which bring wonders to all aspects of life such as education, medicine, food production and even the environment. In education, technology has become an integral part as it brings many benefits to the teaching-learning process. However, in the Philippines, being one of the developing countries resources are scarce and not all schools enjoy the fruits brought by technology. Much of this ordeal impacts that of multigrade instruction. These schools are often the last priority in resources allocation since these have limited number of students. In fact, it is not surprising that these schools do not have even a single computer unit much more a computer laboratory. This paper sought to present a plan on how public schools would receive its e-classroom. Specifically, this paper sought to answer questions like the level of the school readiness in terms of facilities and equipment; the attitude of the respondents towards the use of e-classroom; level of teacher’s familiarity in using different e-classroom software and the plans of interventions undertaken by the school to make it e-classroom ready. After gathering and analysing the necessary data, this paper came up with the following conclusions that in terms of facilities and equipment, Guisguis Talon Elementary School (Main), though a multigrade school, is ready to receive e-classroom.; that the respondents show positive disposition in technology utilization in teaching after they strongly agree that technology plays essential role in the teaching-learning process. Also, they strongly agree that technology is a good motivator; it makes the teaching and learning more interesting and effective; it makes teaching easy; and that technology enhances student’s learning. Additionally, Teacher-respondents in Guisguis Talon Elementary School (Main) show familiarity in using software. They are very familiar with MS Word; MS Excel; MS PowerPoint; and internet and email. Moreover, they are very familiar with basic e-classroom computer operations and basic application software. They are very familiar with MS office and can do simple editing and formatting; in accessing and saving information from CD/DVD, external hard drives, USB and the like; and in browsing effectively different search engines and educational sites, download and upload files. Likewise respondents strongly agree to the interventions undertaken by the school to make it e-classroom ready. They strongly agree that funding and support are needed by the school; that stakeholders should be encouraged to consider donating of equipment; and that school and community should try to mobilize their resources in order to help the school; that the teachers should be provided with trainings in order for them to be technologically competent; and that principals and administrators should motivate their teachers to undergo continuous professional development.

Keywords: e-classroom, multi-grade school, DCP, classroom computers

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