Search results for: mathematics teaching knowledge

Authors: Judit Nagy

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Many scientific studies claim that financial education should start as early as possible. Children are much more capable of and willing to absorb new concepts than adults. If we introduce children to financial knowledge early, their behaviour and attitudes to this subject will change, increasing later success in this area of life. However, poor financial decisions may entail severe consequences, not only to individuals but even to the wider society. Good financial decisions and economic attitudes may contribute to economic growth and well-being. Whilst in several countries, education about financial awareness and fundamentals is available, the understanding and acquisition of complex economic knowledge and the development of children’s independent problem-solving skills are still lacking. The results suggest that teaching economic and financial knowledge through accounting and making lectures interactive by using special tools of positive education is critical to stimulating children’s interest. Eighty percent of the students in the study liked the combined and interactive lecture. Introducing this kind of knowledge to individuals is a relevant objective, even at the societal level.

Keywords: positive psychology, education innovation, primary school, gender, economics, accounting, finance, personal finance, mathematics, economic growth, well-being, sustainability

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Authors: Varong Pongsai

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The objective of this paper is introducing a new method of accounting posting which is called Matrix Method Posting. This method is based on the Matrix operation of pure Mathematics. Although, accounting field is classified as one of the social-science knowledge, many of accounting operations are placed by Mathematics sign and operation. Through the operation applying, it seems to be that the operations of Mathematics should be applied to accounting possibly. So, this paper tries to over-lap Mathematics logic to accounting logic smoothly. According to the context of discovery, deductive approach is employed to prove a simultaneously logical concept of both Mathematics and Accounting. The result proves that the Matrix can be placed to operate accounting perfectly, because Matrix and accounting logic also have a similarity concept which is balancing 2 sides during operations. Moreover, the Matrix posting also has a lot of benefit. It can help financial analyst calculating financial ratios comfortably. Furthermore, the matrix determinant which is a signature operation itself also helps auditors checking out the correction of clients’ recording. If the determinant is not equaled to 0, it will point out that the recording process of clients getting into the problem. Finally, the Matrix should be easily determining a concept of merger and consolidation far beyond the present day concept.

Keywords: matrix method posting, deductive approach, determinant, accounting application

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Authors: Surajo Isa

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In as much as mathematics is important to national development, it is regrettable to note that in Nigeria Students academic achievement especially in public examinations remains poor. Among the several factors responsible for such a poor performance is the lack of bringing cultural elements into the conventional school mathematics. The design for this study is triangulation in nature which is set to examined 800 students From 20 School (40 each from male and female schools). Ten (10) male and ten (10) female schools consisting of 400 male and 400 female students to formed the experiment and control groups with a further sub-groping of samples to represent urban and rural settings for both male and female groups. While the experimental groups were taught using ethnomathematics techniques, the control groups were taught using conventional techniques, the results of a t-test for independent samples at p =0.05 level of significance with tcritical = 1.968 showed that (a) boys performed significantly better than girls (b) there is no significantly difference in performance between urban and rural girls (c) significant difference in academic performance was obtained between urban and rural boys. Generally, it was observed that teaching mathematics with ethnomathematics technique would help in great achievement in mathematics.

Keywords: ethnomathematics, achievement, gender, settlement

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Authors: A. Tahar Djebbar

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Modern technologies have penetrated all spheres of human life, education being one of them. This paper focuses the attention on the integration of technology-based education in the Algerian classroom in teaching foreign languages. It sheds light on a specific area of ICT application: ICT in English learning and teaching. Some Algerian teachers or tutors of English face many challenges among which the lack of teaching materials which are indispensable for transmitting knowledge to learners. Thus, they find themselves compelled to use online e-books or download them in PDF form to support their lessons. Teachers even download such teaching materials like pictures, videos, audios, podcasts, and flash cards from the internet and store them in their Flash USBs to shape up the teaching-learning conditions. They use computers, data shows, and the internet so as to facilitate the teaching–learning process in the classroom. Hence, technology has become a must in the Algerian classroom especially in teaching English which has become a very important language in a national and an international level. This study aims at showing that Algerian tutors/teachers who take up the challenge of getting involved in the technology-enhanced language learning and teaching in the Algerian schools and universities face many obstacles.

Keywords: computer, communication, English, internet, learners, language acquisition, teaching, technology

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Authors: Leandro Marcos Alves Vaz

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In this article, we analyze the different approaches to the topic Magnetism of Matter in physics textbooks of Brazilian schools. For this, we compared the approach to the concepts of the magnetic characteristics of materials (diamagnetism, paramagnetism, ferromagnetism and antiferromagnetism) in different sources of information and in different levels of education, from Higher Education to High School. In this sense, we used as reference the theory of the Didactic Transposition of Yves Chevallard, a French educational theorist, who conceived in his theory three types of knowledge – Scholarly Knowledge, Knowledge to be taught and Taught Knowledge – related to teaching practice. As a research methodology, from the reading of the works used in teacher training and those destined to basic education students, we compared the treatment of a higher education physics book, a scientific article published in a Brazilian journal of the educational area, and four high school textbooks, in order to establish in which there is a greater or lesser degree of approximation with the knowledge produced by the scholars – scholarly knowledge – or even with the knowledge to be taught (to that found in books intended for teaching). Thus, we evaluated the level of proximity of the subjects conveyed in high school and higher education, as well as the relevance that some textbook authors give to the theme.

Keywords: Brazilian physics books, didactic transposition, magnetism of matter, teaching of physics

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Authors: Ekaterina A. Redkina

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The necessity and importance of teaching professionally oriented content in English needs no proof nowadays. Consequently, the ability to share personal ESP teaching experience seems of great importance. This paper is based on the 8-year ESP and EFL teaching experience at the Moscow State Linguistic University, Moscow, Russia, and presents theoretical analysis of specifics, possible problems, and perspectives of teaching Psychology in English to Russian psychology-students. The paper concerns different issues that are common for different ESP classrooms, and familiar to different teachers. Among them are: designing ESP curriculum (for psychologists in this case), finding the balance between content and language in the classroom, main teaching principles (the 4 C’s), the choice of assessment techniques and teaching material. The main objective of teaching psychology in English to Russian psychology students is developing knowledge and skills essential for professional psychologists. Belonging to international professional community presupposes high-level content-specific knowledge and skills, high level of linguistic skills and cross-cultural linguistic ability and finally high level of professional etiquette. Thus, teaching psychology in English pursues 3 main outcomes, such as content, language and professional skills. The paper provides explanation of each of the outcomes. Examples are also given. Particular attention is paid to the lesson structure, its objectives and the difference between a typical EFL and ESP lesson. There is also made an attempt to find commonalities between teaching ESP and CLIL. There is an approach that states that CLIL is more common for schools, while ESP is more common for higher education. The paper argues that CLIL methodology can be successfully used in ESP teaching and that many CLIL activities are also well adapted for professional purposes. The research paper provides insights into the process of teaching psychologists in Russia, real teaching experience and teaching techniques that have proved efficient over time.

Keywords: ESP, CLIL, content, language, psychology in English, Russian students

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Authors: Diriba Gemechu, Lamessa Abebe

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The aim of this study was to examine the effect of cooperative learning method on student’s academic achievement and on the achievement level over a usual method in teaching different topics of mathematics. The study also examines the perceptions of students towards cooperative learning. Cooperative learning is the instructional strategy in which pairs or small groups of students with different levels of ability work together to accomplish a shared goal. The aim of this cooperation is for students to maximize their own and each other learning, with members striving for joint benefit. The teacher’s role changes from wise on the wise to guide on the side. Cooperative learning due to its influential aspects is the most prevalent teaching-learning technique in the modern world. Therefore the study was conducted in order to examine the effect of cooperative learning on the academic achievement of grade 9 students in Mathematics in case of Mettu secondary school. Two sample sections are randomly selected by which one section served randomly as an experimental and the other as a comparison group. Data gathering instruments are achievement tests and questionnaires. A treatment of STAD method of cooperative learning was provided to the experimental group while the usual method is used in the comparison group. The experiment lasted for one semester. To determine the effect of cooperative learning on the student’s academic achievement, the significance of difference between the scores of groups at 0.05 levels was tested by applying t test. The effect size was calculated to see the strength of the treatment. The student’s perceptions about the method were tested by percentiles of the questionnaires. During data analysis, each group was divided into high and low achievers on basis of their previous Mathematics result. Data analysis revealed that both the experimental and comparison groups were almost equal in Mathematics at the beginning of the experiment. The experimental group out scored significantly than comparison group on posttest. Additionally, the comparison of mean posttest scores of high achievers indicates significant difference between the two groups. The same is true for low achiever students of both groups on posttest. Hence, the result of the study indicates the effectiveness of the method for Mathematics topics as compared to usual method of teaching.

Keywords: academic achievement, comparison group, cooperative learning, experimental group

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Authors: Inuusah Mahama

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The study focused on the importance of diversity and the use of evidence-based practices and strategies in teaching learners with ASD. The study employed a mixed-methods design, including surveys, interviews, and observations. A total of 500 K-12 practitioners participated in the study, including teachers, administrators, and support staff. The study sought to investigate the current understanding and knowledge level of K-12 practitioners regarding diversity, evidence-based practices, and strategies for teaching learners with ASD. The study also examined the challenges that K-12 practitioners face in preparing learners with ASD and the resources they require to improve their practice. The results indicated that K-12 practitioners in Ghana have limited knowledge and skills in teaching learners with ASD, particularly in using evidence-based practices and strategies. Therefore, there is a need for providing training and professional development opportunities for K-12 practitioners, developing and implementing evidence-based practices and strategies, and increasing awareness of ASD and the need for effective teaching strategies. This would go a long way to improve the quality of education for learners with ASD in Ghana and ultimately lead to better outcomes for these students.

Keywords: autism, practitioners, diversity, evidence-based practises

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Authors: Yan Li

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Purpose: There is a lack of suitable recommendation systems to assist engineering teaching. The existing traditional engineering pedagogies lack learning interests for postgraduate students. The knowledge graph-based recommender system aims to enhance postgraduate students’ programming skills, with a focus on programming courses. Design/methodology/approach: The case study will be used as a major research method, and the two case studies will be taken in both two teaching styles of the universities (Zhejiang University and the University of Nottingham Ningbo China), followed by the interviews. Quantitative and qualitative research methods will be combined in this study. Research limitations/implications: The case studies were only focused on two teaching styles universities, which is not comprehensive enough. The subject was limited to postgraduate students. Originality/value: The study collected and analyzed the data from two teaching styles of universities’ perspectives. It explored the challenges of Engineering education and tried to seek potential enhancement.

Keywords: knowledge graph and recommender system, engineering pedagogy, programming skills, postgraduate students

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Authors: Narupot Putwattana

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Changes in global situation such as environmental and economic crisis brought the new perspective for science education called integrative biology. STEM has been increasingly mentioned for several educational researches as the approach which combines the concept in Science (S), Technology (T), Engineering (E) and Mathematics (M) to apply in teaching and learning process so as to strengthen the 21st-century skills such as creativity and critical thinking. Recent studies demonstrated STEM as the pedagogy which described the engineering process along with the science classroom activities. So far, pedagogical contents for STEM explaining the content in biology have been scarce. A qualitative literature review was conducted so as to gather the articles based on electronic databases (google scholar). STEM education, engineering design, teaching and learning of biology were used as main keywords to find out researches involving with the application of STEM in biology teaching and learning process. All articles were analyzed to obtain appropriate teaching and learning model that unify the core concept of biology. The synthesized model comprised of engineering design, inquiry-based learning, biological prototype and biologically-inspired design (BID). STEM content and context integration were used as the theoretical framework to create the integrative biology instructional model for STEM education. Several disciplines contents such as biology, engineering, and technology were regarded for inquiry-based learning to build biological prototype. Direct and indirect integrations were used to provide the knowledge into the biology related STEM strategy. Meanwhile, engineering design and BID showed the occupational context for engineer and biologist. Technological and mathematical aspects were required to be inspected in terms of co-teaching method. Lastly, other variables such as critical thinking and problem-solving skills should be more considered in the further researches.

Keywords: biomimicry, engineering approach, STEM education, teaching and learning model

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Authors: Anastasios Ntousas

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The purpose of the following paper is to analyze the relationship between the lexical quality and the self-teaching hypothesis and their impact on the reading ability. The following questions emerged, is there a correlation between the effective reading experience that the lexical quality hypothesis proposes and the self-teaching hypothesis, would the ability to read by analogy facilitate and create stable, synchronized four-word representational, and would word morphological knowledge be a possible extension of the self-teaching hypothesis. The lexical quality hypothesis speculates that words include four representational attributes, phonology, orthography, morpho-syntax, and meaning. Those four-word representations work together to make word reading an effective task. A possible lack of knowledge in one of the representations might disrupt reading comprehension. The degree that the four-word features connect together makes high and low lexical word quality representations. When the four-word representational attributes connect together effectively, readers have a high lexical quality of words; however, when they hardly have a strong connection with each other, readers have a low lexical quality of words. Furthermore, the self-teaching hypothesis proposes that phonological recoding enables printed word learning. Phonological knowledge and reading experience facilitate the acquisition and consolidation of specific-word orthographies. The reading experience is related to strong reading comprehension. The more readers have contact with texts, the better readers they become. Therefore, their phonological knowledge, as the self-teaching hypothesis suggests, might have a facilitative impact on the consolidation of the orthographical, morphological-syntax and meaning representations of unknown words. The phonology of known words might activate effectively the rest of the representational features of words. Readers use their existing phonological knowledge of similarly spelt words to pronounce unknown words; a possible transference of this ability to read by analogy will appear with readers’ morphological knowledge. Morphemes might facilitate readers’ ability to pronounce and spell new unknown words in which they do not have lexical access. Readers will encounter unknown words with similarly phonemes and morphemes but with different meanings. Knowledge of phonology and morphology might support and increase reading comprehension. There was a careful selection, discussion of theoretical material and comparison of the two existing theories. Evidence shows that morphological knowledge improves reading ability and comprehension, so morphological knowledge might be a possible extension of the self-teaching hypothesis, the fundamental skill to read by analogy can be implemented to the consolidation of word – specific orthographies via readers’ morphological knowledge, and there is a positive correlation between effective reading experience and self-teaching hypothesis.

Keywords: morphology, orthography, reading ability, reading comprehension

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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: Ricardo Merlo

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Attitude is a hypothetical construct that can be significantly measured to know the favorable or unfavorable predisposition that students have towards the teaching of sciences such as Physics. Although the state-of-the-art attitude test used in Physics teaching indicated different design and validation models in different groups of students, the analysis of the weight given to each dimension that supported the attitude was scarcely evaluated. Then, in this work, a methodology of attitude questionnaire construction process was proposed that allowed the teacher to design and validate the measurement instrument for different subjects of Physics at the university level developed in the classroom according to the weight considered to the affective, knowledge, and behavioural dimensions. Finally, questionnaire models were tested for the case of incoming university students, achieving significant results in the improvement of Physics teaching.

Keywords: attitude, physics teaching, motivation, academic performance

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Authors: Huseyin Demir

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This article is the results of a quantitative research about the effects of using interactive whiteboards in high school mathematics classroom. The aim of this article is to investigate the effects of using interactive whiteboards in high school mathematics classrooms. During the article the following questions are answered: 'What can we do with an interactive whiteboard?' and 'Do we really need those properties of the interactive whiteboard?' For the research part of the article, two groups of lessons are executed in Private Demirel College. In the first 6 weeks, the topics are taught on a normal blackboard. Starting from seventh week, we have used interactive whiteboard in the mathematics lessons. At the end of an eight week lectures with interactive whiteboards, a questionnaire is prepared and executed for the students. In the questionnaire 10 questions were asked about the benefits and differences of using the interactive whiteboards in mathematics lessons. By looking at the conclusion of the results of questionnaire and some discussions with the students we found some useful benefits of the usage of interactive whiteboards in mathematics lessons. This article will be helpful for the high school mathematics teachers.

Keywords: mathematics education, interactive whiteboard, blackboard, using interactive whiteboard in mathematics lessons

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Authors: Daniela Velichová

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Plenty of ideas on how to adopt active learning methods in education are available nowadays. Mathematics is a subject where the active involvement of students is required in particular in order to achieve desirable results regarding sustainable knowledge and deep understanding. The present article is based on the outcomes of an Erasmus+ project DrIVE-MATH, that was aimed at developing a novel and integrated framework to teach maths classes in engineering courses at the university level. It is fundamental for students from the early years of their academic life to have agile minds. They must be prepared to adapt to their future working environments, where enterprises’ views are always evolving, where all collaborate in teams, and relations between peers are thought for the well-being of the whole - workers and company profit. This reality imposes new requirements on higher education in terms of adaptation of different pedagogical methods, such as project-based and active-learning methods used within the course curricula. Active learning methodologies are regarded as an effective way to prepare students to meet the challenges posed by enterprises and to help them in building critical thinking, analytic reasoning, and insight to the solved complex problems from different perspectives. Fostering learning-by-doing activities in the pedagogical process can help students to achieve learning independence, as they could acquire deeper conceptual understanding by experimenting with the abstract concept in a more interesting, useful, and meaningful way. Clear information about learning outcomes and goals might help students to take more responsibility for their learning results. Active learning methods implemented by the project team members in their teaching practice, eduScrum and Jigsaw in particular, proved to provide better scientific and soft skills support to students than classical teaching methods. EduScrum method enables teachers to generate a working environment that stimulates students' working habits and self-initiative as they become aware of their responsibilities within the team, their own acquired knowledge, and their abilities to solve problems independently, though in collaboration with other team members. This method enhances collaborative learning, as students are working in teams towards a common goal - knowledge acquisition, while they are interacting with each other and evaluated individually. Teams consisting of 4-5 students work together on a list of problems - sprint; each member is responsible for solving one of them, while the group leader – a master, is responsible for the whole team. A similar principle is behind the Jigsaw technique, where the classroom activity makes students dependent on each other to succeed. Students are divided into groups, and assignments are split into pieces, which need to be assembled by the whole group to complete the (Jigsaw) puzzle. In this paper, analysis of students’ perceptions concerning the achievement of deeper conceptual understanding in mathematics and the development of soft skills, such as self-motivation, critical thinking, flexibility, leadership, responsibility, teamwork, negotiation, and conflict management, is presented. Some new challenges are discussed as brought by introducing active learning methods in the basic mathematics courses. A few examples of sprints developed and used in teaching basic maths courses at technical universities are presented in addition.

Keywords: active learning methods, collaborative learning, conceptual understanding, eduScrum, Jigsaw, soft skills

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Authors: Irina Peterburgsky

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We have been working on finding internship positions for our math and computer science majors. Among many other positive outcomes of internship for students majoring in mathematics, there are: students see new applications of mathematics to real life and see new scientific problems; they learn new methods, tools, etc. that they have not seen in their classes; they appreciate the power of mathematics that increases their interest in learning mathematics; they make decisions to take more advanced math courses; students understand better what their potentials, strong points, and limitations are; learn what work ethic is; learn how to work as a member of a team at a workplace; understand better how to offer their help and how to ask for help; start building their professional relationship; build self-confidence as young professionals, and what is the most important - they get a better understanding of their goals in their future professional careers.

Keywords: internship, mathematics, positive outcoms for students, workplace

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Authors: Wichuda Kunnu, Aungkana Sukwises

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Audio-lingual method (ALM) is a teaching approach that is claimed that ineffective for teaching second/foreign languages. Because some linguists and second/foreign language teachers believe that ALM is a rote learning style. However, this study is done on a belief that ALM will be able to solve Thais’ English speaking problem. This paper aims to report the findings on teaching English speaking to adult learners with an “adapted ALM”, one distinction of which is to use Thai as the medium language of instruction. The participants are consisted of 9 adult learners. They were allowed to speak English more freely using both the materials presented in the class and their background knowledge of English. At the end of the course, they spoke English more fluently, more confidently, to the extent that they applied what they learnt both in and outside the class.

Keywords: teaching English, audio lingual method, cognitive science, psychology

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Authors: Krongthong Khairiree

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The purpose of this research study is to explore mathematics project-based learning approach and the use of technology in the context of school mathematics in Thailand. Data of the study were collected from 6 sample secondary schools and the students were 6-14 years old. Research findings show that through mathematics project-based learning approach and the use of GSP, students were able to make mathematics learning fun and challenging. Based on the students’ interviews they revealed that, with GSP, they were able to visualize and create graphical representations, which will enable them to develop their mathematical thinking skills, concepts and understanding. The students had fun in creating variety of graphs of functions which they can not do by drawing on graph paper. In addition, there are evidences to show the students’ abilities in connecting mathematics to real life outside the classroom and commercial products, such as weaving, patterning of broomstick, and ceramics design.

Keywords: mathematics, project-based learning, Geometer’s Sketchpad (GSP), commercial products

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Authors: Saeedeh Shafiee Nahrkhalaji

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Metacognitive knowledge increases EFL students’ ability to be successful learners. Although this relationship has been investigated by a number of scholars, EFL teachers’ explicit awareness of their cognitive knowledge has not been sufficiently explored. The aim of this study was to examine the role of EFL teachers’ metacognitive knowledge in their pedagogical performance. Furthermore, the role played by years of their academic education and teaching experience was also studied. Fifty female EFL teachers were selected. They completed Metacognitive Awareness Inventory (MAI) that assessed six components of metacognition including procedural knowledge, declarative knowledge, conditional knowledge, planning, evaluating, and management strategies. Near the end of the academic semester, the students of each class filled in ‘the Language Teacher Characteristics Questionnaire’ to evaluate their teachers’ pedagogical performance. Four elements of MAI, declarative knowledge, planning, evaluating, and management strategies were found to be significantly correlated with EFL teachers’ pedagogical success. Significant correlation was also established between metacognitive knowledge and EFL teachers’ years of academic education and teaching experience. The findings obtained from this research have contributing implication for EFL teacher educators. The discussion concludes by setting out directions for future research.

Keywords: metacognotive knowledge, pedagogical performance, language teacher characteristics questionnaire, metacognitive awareness inventory

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Authors: Eish Sharma

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Literature around Mathematics education suggests that democratic attitudes can be strengthened through teaching and learning Mathematics. Furthermore, connections between critical education and Mathematics education are observed in the light of critical pedagogy to locate Critical Mathematics Education (CME) as the theoretical framework. Critical pedagogy applied to Mathematics education is identified as one of the key themes subsumed under Critical Mathematics Education. Through the application of critical pedagogy in mathematics, unequal power relations and social injustice can be identified, analyzed, and challenged. The research question is: have educational policies in India viewed the role of critical pedagogy applied to mathematics education (i.e., critical mathematics education) to ensure social justice as an educational aim? The National Curriculum Framework (NCF), 2005 upholds education for democracy and the role of mathematics education in facilitating the same. More than this, NCF 2005 rests on Critical Pedagogy Framework and it recommends that critical pedagogy must be practiced in all dimensions of school education. NCF 2005 visualizes critical pedagogy for social sciences as well as sciences, stating that the science curriculum, including mathematics, must be used as an “instrument for achieving social change to reduce the divide based on economic class, gender, caste, religion, and the region”. Furthermore, the implementation of NCF 2005 led to a reform in the syllabus and textbooks in school mathematics at the national level, and critical pedagogy was applied to mathematics textbooks at the primary level. This intervention led to ethnomathematics and critical mathematics education in the school curriculum in India for the first time at the national level. In October 2022, the Ministry of Education launched the National Curriculum Framework for Foundational Stage (NCF-FS), developed in light of the National Education Policy, 2020, for children in the three to eight years age group. I want to find out whether critical pedagogy-based education and critical pedagogy-based mathematics education are carried forward in NCF 2022. To find this, an argument analysis of specific sections of the National Curriculum Framework 2022 document needs to be executed. Des Gasper suggests two tables: The first table contains four columns, namely, text component, comments on meanings, possible reformulation of the same text, and identified conclusions and assumptions (both stated and unstated). This table is for understanding the components and meanings of the text and is based on Scriven’s model for understanding the components and meanings of words in the text. The second table contains four columns i.e., claim identified, given data, warrant, and stated qualifier/rebuttal. This table is for describing the structure of the argument, how and how well the components fit together and is called ‘George Table diagram based on Toulmin-Bunn Model’.

Keywords: critical mathematics education, critical pedagogy, social justice, etnomathematics

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Authors: Guangzhuang Yu, Chun-Chu Liu

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With the advent of the Internet era in recent years, social music education has gradually shifted from the original entity education mode to the mode of entity plus network teaching. No matter for school music education, professional music education or social music education, the teaching quality is the most important evaluation index. Regarding the research on teaching quality evaluation, scholars at home and abroad have contributed a lot of research results on the basis of multiple methods and evaluation subjects. However, to our best knowledge the complete evaluation model for the virtual teaching interaction mode of the emerging network music education Application (APP) has not been established. This research firstly found out the basic dimensions that accord with the teaching quality required by the three parties, constructing the quality evaluation index system; and then, on the basis of expounding the connotation of each index, it determined the weight of each index by using method of fuzzy analytic hierarchy process, providing ideas and methods for scientific, objective and comprehensive evaluation of the teaching quality of network education APP.

Keywords: network music education APP, teaching quality evaluation, index and connotation

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Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. In this study, we examine a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data was collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers were self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used.

Keywords: teacher learning, professional development, pedagogical content knowledge, geometry

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Authors: Aroona Hashmi

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Student’s success in Mathematics and Science depends upon their learning attitude towards both subjects. It also influences the participation rate of the learner. The present study was based on a survey of high school students about their attitude towards Mathematics and Science at Secondary level. Students of the both gender constitute the population of this study. Sample of the study was 276 students and 20 teachers from 10 Government schools from Lahore District. Questionnaire and interview were selected as tool for data collection. The results showed that Pakistani students’ positive attitude towards learning Mathematics and Science. There was a significance difference between the students’ attitude towards learning Mathematics and no significance difference was found in the students’ attitude towards learning Science at Secondary level.

Keywords: attitude, mathematics, science, secondary level

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Authors: Mitat Uysal, Aynur Uysal

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Artificial Intelligence (AI) is fundamentally driven by mathematics, with many of its core algorithms rooted in mathematical principles such as linear algebra, probability theory, calculus, and optimization techniques. This paper explores the deep connection between AI and mathematics, highlighting the role of mathematical concepts in key AI techniques like machine learning, neural networks, and optimization. To demonstrate this connection, a case study involving the implementation of a neural network using Python is presented. This practical example illustrates the essential role that mathematics plays in training a model and solving real-world problems.

Keywords: AI, mathematics, machine learning, optimization techniques, image processing

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Authors: Jaya Bishnu Pradhan

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Weaving mat is one of the common activities performed in different community generally in the rural part of Nepal. Mat weavers’ practice mathematical ideas and concepts implicitly in order to perform their job. This study is intended to uncover the mathematical ideas embedded in mat weaving that can help teachers and students for the teaching and learning of school geometry. The ethnographic methodology was used to uncover and describe the beliefs, values, understanding, perceptions, and attitudes of the mat weavers towards mathematical ideas and concepts in the process of mat weaving. A total of 4 mat weavers, two mathematics teachers and 12 students from grade level 6-8, who are used to participate in weaving, were selected for the study. The whole process of the mat weaving was observed in a natural setting. The classroom observation and in-depth interview were taken with the participants with the help of interview guidelines and observation checklist. The data obtained from the field were categorized according to the themes regarding mathematical ideas embedded in the weaving activities, and its possibilities in teaching learning of school geometry. In this study, the mathematical activities in different sectors of their lives, their ways of understanding the natural phenomena, and their ethnomathematical knowledge were analyzed with the notions of pluralism. From the field data, it was found that the mat weaver exhibited sophisticated geometrical ideas in the process of construction of frame of mat. They used x-test method for confirming if the mat is rectangular. Mat also provides a good opportunity to understand the space geometry. A rectangular form of mat may be rolled up when it is not in use and can be converted to a cylindrical form, which usually can be used as larder so as to reserve food grains. From the observation of the situations, this cultural experience enables students to calculate volume, curved surface area and total surface area of the cylinder. The possibilities of incorporation of these cultural activities and its pedagogical use were observed in mathematics classroom. It is argued that it is possible to use mat weaving activities in the teaching and learning of school geometry.

Keywords: ethnography, ethnomathematics, geometry, mat weaving, school pedagogy

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Authors: Ali Yaro Kankia

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Millennium Development Goals are eight goals set by the 189 United Nations member States with 2015 as its target year of achievement. Since its signing in September 2000, individual nations have been finding ways and means of actualizing them. This paper consider how a refocused basic Mathematics curriculum could serve as an appropriate tool in achieving these goals. This was done by considering the theme in the following sub-headings. Basic Mathematics curriculum before now, basic Mathematics curriculum and the millennium development Goals and challenges of a refocused basic Mathematics curriculum for the MDGs. The appropriate conclusion was reached.

Keywords: actualizing, curriculum, MDGs, refocused

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Authors: Fatimah Alsaleh, Glenda Anthony

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The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs’ sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs’ sense of preparedness was investigated via a mixed-methods approach combining a survey (N = 105) and in-depth interviews with survey volunteers (N = 16). Statistical analysis in SPSS was used to explore the quantitative data, and thematic analysis was applied to the qualitative interviews data. The results revealed that the PSTs perceived the practicum experience to have played a dominant role in shaping their feelings of preparedness and efficacy. However, despite the generally positive influence of practicum, the PSTs also reported numerous challenges that lessened their feelings of preparedness. These challenges were often related to the classroom environment and the school culture. For example, about half of the PSTs indicated that the practicum schools did not have the resources available or the support necessary to help them learn the work of teaching. In particular, the PSTs expressed concerns about translating the theoretical knowledge learned at the university into practice in authentic classrooms. These challenges engendered PSTs feeling less prepared and suggest that more support from both the university and the school is needed to help PSTs develop a stronger sense of preparedness. The area in which PSTs felt least prepared was that of classroom and behavior management, although the results also indicated that PSTs only felt a moderate level of general teaching efficacy and were less confident about how to support students as learners. Again, feelings of lower efficacy were related to the dissonance between the theory presented at university and real-world classroom practice. In order to close this gap between theory and practice, PSTs expressed the wish to have more time in the practicum, and more accountability for support from school-based mentors. In highlighting the challenges of the practicum in shaping PSTs’ sense of preparedness and efficacy, the study argues that better communication between the ITE providers and the practicum schools is necessary in order to maximize the benefit of the practicum experience.

Keywords: impact, mathematics, practicum experience, pre-service teachers, sense of preparedness

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Authors: Irfan Ahmed Rind

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Science education has recently become the top priority of government of Pakistan. Number of schemes has been initiated for the improvement of science teaching and learning at primary and secondary levels of education, most importantly training in-service science teachers on inquiry based teaching and learning to empower students and encourage creativity, critical thinking, and innovation among them. Therefore, this approach has been promoted in the recent continuous professional development trainings for the in-service teachers. However, the follow ups on trained science teachers and educators suggest that these teachers fail to implement the inquiry based teaching and learning in their classes. In addition, these trainings also fail to bring any significant change in students’ science content knowledge and understanding as per the annual national level surveys conducted by government and independent agencies. Research suggests that science has been taught using scientific positivism, which supports objectivity based on experiments and mathematics. In contrary, the inquiry based teaching and learning are based on constructivism, which conflicts with the positivist epistemology of science teachers. It was, therefore, assumed that science teachers struggle to implement the inquiry based teaching approach as it conflicts with their basic epistemological beliefs. With this assumption, this research aimed to (i) understand how science teachers conceptualize the nature of science, and how this influence their understanding of learning, learners, their own roles as teachers and their teaching strategies, (ii) identify the conflict of science teachers’ epistemological beliefs with the inquiry based teaching approach, and (iii) find the ways in which science teachers epistemological beliefs may be developed from positivism to constructivism, so that they may effectively use the inquiry based teaching approach in teaching science. Using qualitative case study approach, thirty six secondary and higher secondary science teachers (21 male and 15 female) were selected. Data was collected using interviewed, participatory observations (sixty lessons were observed), and twenty interviews from students for verifications of teachers’ responses. The findings suggest that most of the science teacher were positivist in defining the nature of science. Most of them limit themselves to one fix answer that is provided in the books and that there is only one 'right' way to teach science. There is no room for students’ or teachers’ own opinion or bias when it comes to scientific concepts. Inquiry based teaching seems 'no right' to them. They find it difficult to allow students to think out of the box. However, some interesting exercises were found to be very effective in bringing the change in teachers’ epistemological beliefs. These will be discussed in detail in the paper. The findings have major implications for the teachers, educators, and policymakers.

Keywords: science teachers, epistemology, metacognition, inquiry based teaching

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Authors: Muhammad Jawwad, Riffat Iqbal

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The Socratic method, also known as the dialectical method and elenctic method, has significant relevance in the contemporary educational system. It can be incorporated into modern-day educational systems theoretically as well as practically. Being interactive and dialogue-based in nature, this teaching approach is followed by critical thinking and innovation. The pragmatic value of the Dialectical Method has been discussed in this article, and the limitations of the Socratic method have also been highlighted. The interactive Method of Socrates can be used in many subjects for students of different grades. The Limitations and delimitations of the Method have also been discussed for its proper implementation. This article has attempted to elaborate and analyze the teaching method of Socrates with all its pre-suppositions and Epistemological character.

Keywords: Socratic method, dialectical method, knowledge, teaching, virtue

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Authors: Duygu Özdemir, Bilal Özçakır

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Usage of augmented reality in education helps students to make sense of the three-dimensional world of mathematics. In this study, it was aimed to develop activities about fractions for 5th-grade students by augmented reality and also aimed to assess these activities in terms of students’ understanding and views. Data obtained from 60 students in a private school in Marmaris, Turkey was obtained through classroom observations, students’ worksheets and semi-structured interviews during two weeks. Data analysis was conducted by using constant-comparative analysis which leads to meaningful categories of findings. Findings of this study indicated that usage of augmented reality is a facilitator to make concretize and provide real-life application for fractions. Moreover, students’ opinions about its usage were lead to categories as benefit for learning, enjoyment and creating awareness of usage of augmented reality in mathematics education. In general, this study could be a bridge to show the contributions of augmented reality applications to mathematics education and also highlights that augmented reality could be used with subjects like fractions rather than subjects only in geometry learning domain.

Keywords: augmented reality, mathematics, fractions, students

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