Search results for: mathematics concept acquisitions

Authors: Ezeamagu M.U, Madu B.C

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This study was designed to investigate the efficacy of 5Es constructivist-based instructional model on students’ retention in primary Mathematics. 5Es stands for Engagement, Exploration, Explanation, Elaboration and Evaluation. The study adopted the pre test post test non-equivalent control group quasi-experimental research design. The sample size for the study was one hundred and thirty four pupils (134), seventy six male (76) and fifty eight female (58) from two primary schools in Nsukka education zone. Two intact classes in each of the sampled schools comprising all the primary four pupils were used. Each of the schools was given the opportunity of being assigned randomly to either experimental or control group. The Experimental group was taught using 5Es model while the control group was taught using the conventional method. Two research questions were formulated to guide the study and three hypotheses were tested at p ≤ 0. 05. A Fraction Achievement Test (FAT) of ten (10) questions were used to obtain data on pupils’ retention. Research questions were answered using mean and standard deviation while hypotheses were tested using analysis of covariance (ANCOVA). The result revealed that the 5Es model was more effective than the conventional method of teaching in enhancing pupils’ performance and retention in mathematics, secondly there is no significant difference in the mean retention scores of male and female students taught using 5Es instructional model. Based on the findings, it was recommended among other things, that the 5Es instructional model should be adopted in the teaching of mathematics in primary level of the educational system. Seminar, workshops and conferences should be mounted by professional bodies, federal and state ministries of education on the use of 5Es model. This will enable the mathematics educator, serving teachers, students and all to benefit from the approach.

Keywords: constructivist, education, mathematics, primary, retention

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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: Ali Rashash Alzahrani, Elizabeth Stojanovski

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Data on various aspects of education are collected at the institutional and government level regularly. In Australia, for example, students at various levels of schooling undertake examinations in numeracy and literacy as part of NAPLAN testing, enabling longitudinal assessment of such data as well as comparisons between schools and states within Australia. Another source of educational data collected internationally is via the PISA study which collects data from several countries when students are approximately 15 years of age and enables comparisons in the performance of science, mathematics and English between countries as well as ranking of countries based on performance in these standardised tests. As well as student and school outcomes based on the tests taken as part of the PISA study, there is a wealth of other data collected in the study including parental demographics data and data related to teaching strategies used by educators. Overall, an abundance of educational data is available which has the potential to be used to help improve educational attainment and teaching of content in order to improve learning outcomes. A multivariate assessment of such data enables multiple variables to be considered simultaneously and will be used in the present study to help develop profiles of students based on performance in mathematics using data obtained from the PISA study.

Keywords: cluster analysis, education, mathematics, profiles

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Authors: Zsolt Lipcsey, Sampson Marshal Imeh

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We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basic element to be the maximal independent subset of a given semigroup. However, we construct examples for semigroups where finite basis exist and the basis is larger than the number of independent elements.

Keywords: generating sets, independent set, rank, cyclic semigroup, basis, commutative

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Aregamalage Sujeewa Vijayanthi Polgampala, Fang Huang

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This study explores the genesis and development of concept mapping as a useful tool for science education and its effectiveness as technique for teaching and learning and evaluation for secondary science in schools and the role played by National College of Education science teachers. Concept maps, when carefully employed and executed serves as an integral part of teaching method and measure of effectiveness of teaching and tool for evaluation. Research has shown that science concept maps can have positive influence on student learning and motivation. The success of concept maps played in an instruction class depends on the type of theme selected, the development of learning outcomes, and the flexibility of instruction in providing library unit that is equipped with multimedia equipment where learners can interact. The study was restricted to 6 male and 9 female respondents' teachers in third-year internship pre service science teachers in Gampaha district Sri Lanka. Data were collected through 15 item questionnaire provided to learners and in depth interviews and class observations of 18 science classes. The two generated hypotheses for the study were rejected, while the results revealed that significant difference exists between factors influencing teachers' choice of concept maps, its usefulness and problems hindering the effectiveness of concept maps for teaching and learning process of secondary science in schools. It was examined that concept maps can be used as an effective measure to evaluate students understanding of concepts and misconceptions. Even the teacher trainees could not identify, key concept is on top, and subordinate concepts fall below. It is recommended that pre service science teacher trainees should be provided a thorough training using it as an evaluation instrument.

Keywords: concept maps, evaluation, learning science, misconceptions

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Ahmet Erdoğan, Şahin Kesici, Mustafa Baloğlu

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Information technologies have lead to changes in the areas of communication, learning, and teaching. Besides offering many opportunities to the learners, these technologies have changed the teaching methods and beliefs of teachers. What the Technological Pedagogical Content Knowledge (TPACK) means to the teachers is considerably important to integrate technology successfully into teaching processes. It is necessary to understand how to plan and apply teacher training programs in order to balance students’ pedagogical and technological knowledge. Because of many inefficient teacher training programs, teachers have difficulties in relating technology, pedagogy and content knowledge each other. While providing an efficient training supported with technology, understanding the three main components (technology, pedagogy and content knowledge) and their relationship are very crucial. The purpose of this study is to determine whether motivational beliefs and self-regulated learning strategies are significant predictors of mathematics teacher candidates' TPACK perceptions. A hundred seventy five Turkish mathematics teachers candidates responded to the Motivated Strategies for Learning Questionnaire (MSLQ) and the Technological Pedagogical And Content Knowledge (TPACK) Scale. Of the group, 129 (73.7%) were women and 46 (26.3%) were men. Participants' ages ranged from 20 to 31 years with a mean of 23.04 years (SD = 2.001). In this study, a multiple linear regression analysis was used. In multiple linear regression analysis, the relationship between the predictor variables, mathematics teacher candidates' motivational beliefs, and self-regulated learning strategies, and the dependent variable, TPACK perceptions, were tested. It was determined that self-efficacy for learning and performance and intrinsic goal orientation are significant predictors of mathematics teacher candidates' TPACK perceptions. Additionally, mathematics teacher candidates' critical thinking, metacognitive self-regulation, organisation, time and study environment management, and help-seeking were found to be significant predictors for their TPACK perceptions.

Keywords: candidate mathematics teachers, motivational beliefs, self-regulated learning strategies, technological and pedagogical knowledge, content knowledge

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Authors: Mohammad Motiee

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From Kierkegaard to Sartre, the concept of 'being' was debated over various angles in the philosophy of being. Then, the futility, nothingness and absurdity of human condition in the world were all justified and led to a kind of solution by different approaches like Christianity, loss of faith, authentic existence and responsibility. In an extreme concern, the human condition in the world was pondered in different ways and the philosophy of thought tried to render an awareness of such condition for human beings. The present study aims at illustration of some approaches presented by prominent existentialists to justify the controversies in the concept of existence in human life.

Keywords: existence, existentialism, alienation, being

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Authors: S. Rawashdi, D. Bshouty

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This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: awakeness, awareness, learning mathematics, pupils

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Authors: G. A. Kuanaliyeva, G. T. Aigarinova, G. K. Shulanbekova

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This article is devoted to judicial control in criminal legal proceedings of the Republic of Kazakhstan in the light of the new Concept of legal policy till 2020. In article the general characteristic and concept of judicial control, and also its signs and types are considered. Different views of scientists are analyzed. Foreign experiment on application of judicial control is given. The author states also the point sight on this problem and gives the definition to concept of judicial control. The code of criminal procedure of the Republic of Kazakhstan (RK Criminal Procedure Code) doesn't consolidate concept of judicial control. The author in article suggests making change and addition to the existing Code of criminal procedure of the Republic of Kazakhstan by definition of judicial control. The decree of the President of the Republic of Kazakhstan of August 24, 2009 No. 858 approved the Concept of legal policy of the Republic for the period from 2010 to 2020. The new Concept of legal policy of the Republic of Kazakhstan, defines prospects of development of national legal system of the country on the following decade. The concept of legal policy completely mentions also institute of judicial control. Since finding of the independence by Kazakhstan the set of laws, including the rights directed on providing, freedoms and a legitimate interest of citizens was accepted. Certainly, in any country, whatever democratic it was, there are problems to human rights. However, it is obvious that Kazakhstan strongly intends to guarantee all Republic of Kazakhstan proclaimed in the Constitution the rights and freedoms of the citizens. Our country seeks for creation of the constitutional state, tries to provide a guarantee from various arbitrariness in activity of competent government bodies, officials. In the concept of legal policy of the Republic of Kazakhstan it is specified: "...priority of development of the criminal procedure right there is a further consecutive realization of the fundamental principles of the criminal legal proceedings directed on protection of the rights and freedoms of the person". Judicial control just also is such guarantee.

Keywords: rights and freedoms of the person, concept, legal policy, court, judicial control

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Authors: Jay-R. Hosana Leonidas, Jayson A. Lucilo

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The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in Precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards Precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards Precalculus. Thus, the use of mobile phone applications in teaching Precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with Precalculus.

Keywords: bring your own device, mathematics education, mobile phone applications, senior high school

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Authors: A. Giannakopoulos, S. B. Buckley

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Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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Authors: Yi-Fung Lin, Yuan-Mei Liao

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Background: Pain is common among patients with cancer and is also one of the most disturbing symptoms. As this suffering is subjective, if patients proactively participate in their pain self-management, pain could be alleviated effectively. However, not everyone can carry out self-management very well because human behavior is a product of the cognition process. In this process, we can see that "self-efficacy" plays an essential role in affecting human behaviors. Methods: We used the eight steps of concept analysis proposed by Walker and Avant to clarify the concept of “self-efficacy for cancer pain management.” A comprehensive literature review was conducted for relevant publications that were published during the period of 1977 to 2021. We used several keywords, including self-efficacy, self-management, concept analysis, conceptual framework, and cancer pain, to search the following databases: PubMed, CINAHL, Web of Science, and Embase. Results: We identified three defining attributes for the concept of self-efficacy for cancer pain management, including pain management abilities, confidence, and continuous pain monitoring, and recognized six skills related to pain management abilities: problem-solving, decision-making, resource utilization, forming partnerships between medical professionals and patients, planning actions, and self-regulation. Five antecedents for the concept of self-efficacy for cancer pain management were identified: pain experience, existing cancer pain, pain-related knowledge, a belief in pain management, and physical/mental state. Consequences related to self-efficacy for cancer pain management were achievement of pain self-management, well pain control, satisfying quality of life, and containing motivation. Conclusions: This analysis provides researchers with a clearer understanding of the concept of “self-efficacy for cancer pain management.” The findings presented here provide a foundation for future research and nursing interventions to enhance self-efficacy for cancer pain management.

Keywords: cancer pain, concept analysis, self-efficacy, self-management

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Authors: Idha Novianti, Suci Nurhayati, Puryati, Elang Krisnadi

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Community service activities are activities of the academic community in practicing and cultivating science, knowledge, and technology to advance the general welfare and educate the nation's life as described in the Higher Education Law. Training activities on the use of GeoGebra software are an option because GeoGebra software is software that is easy to operate and complete in the presentation of graphic design. The training activity was held for 3 hours online via teams and 3 hours offline. Involving 15 junior high school mathematics teachers located around south Tangerang. As a result, all teachers were satisfied with the activity, and they had additional new knowledge and skills to teach mathematics in the topic of geometry and algebra. The existence of new knowledge made the participants increase their confidence in developing mathematical science for students at school.

Keywords: geogebra, Ms. teams, junior high school teacher, mathematics

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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: Valencia P. L. Rodrigo, Morita A. Adelina, Vargas V. Martin

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This proposal consists of an analysis of macro concepts involved within an organization growth using educational technologies, which will relate each concept, in a mathematical way with a vision of harmonic work. Working collaboratively, competitively and cooperatively so that this growth is harmonious and homogenous, coining a new term, Harmonic Work. The Harmonic Work ensures that the organization grows in all business directions, allowing managers to project a much more accurate growth, making clear the contribution of each department, resulting in an algorithm that analyzes each of the variables both endogenous and exogenous, establishing different performance indicators in its process of growth.

Keywords: business projection, collaboration, competitiveness, educational technology, harmonious growth

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Lizette Grobler

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Although the notion of environmental citizenship has become an established concept linked to scholarship on sustainability internationally, it is not the case in South Africa. This literature review aims to investigate whether the concept is a viable construct in the South African household waste management context. This literature review firstly examines different approaches to environmental citizenship and the normative notions of environmental values, attitudes, and behaviour advocated by proponents of each tradition. Secondly, this paper deals with the application of environmental citizenship as a measure to address household waste. Thirdly, this paper interrogates the utilization of the concept in South African scholarly literature on waste management. The paper argues for the introduction of the concept as a potential approach to behavioural change in the household waste management context.

Keywords: environmental citizenship, environmental responsibility, household waste, ownership of waste

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Authors: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: Sangram A. Sathe, Neha A. Madgulkar, Shruti S. Raut, S. P. Wadkar

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Transforaminal lumbar interbody fusion (TLIF) surgeries have nowadays became popular for treatment of degenerated spinal disorders. The interbody fusion technique like TLIF maintains load bearing capacity of the spine and a suitable disc height. Currently many techniques have been introduced to cure Spondylolisthesis. This surgery provides greater rehabilitation of degenerative spines. While performing this TLIF surgery existing methods use guideway, which is a troublesome surgery technique as the use of two separate instruments is required to perform this surgery. This paper presents a concept which eliminates the use of guideway. This concept also eliminates problems that occur like reverting the cage. The concept discussed in this paper also gives high accuracy while performing surgery.

Keywords: TLIF, spondylolisthesis, spine, instruments

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Authors: Nazir Amir

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Teaching approaches to present science and mathematics content amongst academically-low-achieving students may need to be different than approaches that are adopted for the more academically-inclined students, primarily due to the different learning needs and learning styles of these students. In crafting out lessons to motivate and engage these students, teachers need to consider the backgrounds of these students and have a good understanding of their interests so that lessons can be presented in ways that appeal to them, and made relevant not just to the world around them, but also to their personal experiences. This presentation highlights how the author worked with a Professional Learning Community (PLC) of teachers in crafting out fun and feasible classroom teaching approaches to present science and mathematics content in ways that are made Relevant, Appealing, and Personal (RAP) to groups of academically-low-achieving students in Singapore. Feedback from the students and observations from their work suggest that they were engaged through the RAP-modes of instruction, and were able to appreciate the role of science and mathematics through a variety of low-cost design-based STEM (Science, Technology, Engineering, and Mathematics) activities. Such results imply that teachers teaching academically-low-achieving students, and those in under-resourced communities, could consider infusing RAP-infused instructions into their lessons in getting students develop positive attitudes towards STEM subjects.

Keywords: STEM Education, STEAM Education, Curriculum Instruction, Academically At-Risk Students, Singapore

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Authors: Guorong Sui, Xingwei Jia, Chenhui Yin, Xiumin Gao

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In the processing of camera-based high precision and non-contact measurement, the geometric-optical aberration is always inevitably disturbing the measuring system. Moreover, the aberration is different with the different focal length, which will increase the difficulties of the system’s calibration. Therefore, to understand the relationship between the focal length as a function of aberration properties is a very important issue to the calibration of the measuring systems. In this study, we propose a new mathematics model, which is based on the plane calibration method by Zhang Zhengyou, and establish a relationship between the focal length and aberration coefficient. By using the mathematics model and carefully modified compensation templates, the calibration precision of the system can be dramatically improved. The experiment results show that the relative error is less than 1%. It is important for optoelectronic imaging systems that apply to measure, track and position by changing the camera’s focal length.

Keywords: camera calibration, aberration coefficient, vision measurement, focal length, mathematics model

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Authors: Yun-Ju Chiu, Feng-Yi Chen

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Kinematics is the beginning to learn mechanics in physics course. The concept of acceleration plays an important role in learning kinematics. Teachers usually instruct the conception through the formulas and graphs of kinematics and the well-known law F = ma. However, over the past few decades, a lot of researchers reveal numerous students’ difficulties in learning acceleration. One of these difficulties is that students frequently confuse acceleration with velocity and force. Why is the concept of acceleration so difficult to learn? The aim of this study is to understand the conceptual evolution of acceleration through the historical textual analysis. Text analysis and one-to-one interviews with high school students and teachers are used in this study. This study finds the history of science constructed from textbooks is usually quite different from the real evolution of history. For example, most teachers and students believe that the best-known law F = ma was written down by Newton. The expression of the second law is not F = ma in Newton’s best-known book Principia in 1687. Even after more than one hundred years, a famous Cambridge textbook titled An Elementary Treatise on Mechanics by Whewell of Trinity College did not express this law as F = ma. At that time of Whewell, the early mid-nineteenth century Britain, the concept of acceleration was not only ambiguous but also confused with the concept of force. The process of learning the concept of acceleration is analogous to its conceptual development in history. The study from the perspective of historical textual analysis will promote the understanding of the concept learning difficulties, the development of professional physics teaching, and the improvement of the context of physics textbooks.

Keywords: acceleration, textbooks, mechanics, misconception, history of science

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Authors: Onesimus Bulus Shiaki

Abstract:

The study investigated the effect of cooperative learning strategy on mathematics achievement and retention among senior secondary school students of different abilities in Taraba State Nigeria. Cooperative learning strategy could hopefully contribute to students’ achievement which will spur the teachers to develop strategies for better learning. The quasi-experimental of pretest, posttest and control group design was adopted in this study. A sample of one hundred and sixty-four (164) Senior Secondary Two (SS2) students were selected from a population of twelve thousand, eight hundred and seventy-three (12,873) SS2 Students in Taraba State. Two schools with equivalent mean scores in the pre-test were randomly assigned to experimental and control groups. The experimental group students were stratified according to ability levels of low, medium and high. The experimental group was guided by the research assistants using the cooperative learning instructional package. After six weeks post-test was administered to the two groups while the retention test was administered two weeks after the post-test. The researcher developed a 50-item Mathematics Achievement Test (MAT) which was validated by experts obtaining the reliability coefficient of 0.87. Mean scores and standard deviations were used to answer the research questions while the Analysis of Co-variance (ANCOVA) was used to test the hypotheses. Major findings from the statistical analysis showed that cooperative learning strategy has a significant effect on the mean achievement of students as well as retention among students of high, medium and low ability in mathematics. However, cooperative learning strategy has no effect on the interaction of ability level and retention. Based on the results obtained, it was therefore recommended that the adoption of the use of cooperative learning strategy in the teaching and learning of mathematics in senior secondary schools be initiated, maintained and sustained for the benefit of senior secondary school students in Taraba State. Periodic Government sponsored in-service training in form of long vacation training programme, workshops, conferences and seminars on the nature, scope, and use of cooperative learning strategy should be organized for senior secondary school mathematics teachers in Taraba state.

Keywords: ability level, cooperative learning, mathematics achievement, retention

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Authors: Cristina-Maria Păcurar

Abstract:

The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: Ahmed Amin Mousa, M. Abd El Salam

Abstract:

The current study presents a proposed program for acquisition the skills and techniques needed to produce concept cartoon. The proposed program has been prepared for non-specialist students who have never used neither graphics nor animating software. It was presented to postgraduates in Faculty of Education for Early Childhood, Cairo University, during the spring term of the 2014-2015 academic year. The program works in three different aspects: Drawing and images editing, sound manipulation, and creating animation. In addition, the researchers have prepared a questionnaire for measuring the quality of the concept cartoons produced by the students. The questionnaire was used as a pre-test and post-test, and at the end of the study, a significant difference was determined in favour of post-test results.

Keywords: cartoon, concept cartoon, kindergarten, animation

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Authors: Han Hyuk Cho, Hanik Jo

Abstract:

In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

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Authors: Mogens Frank Mikkelsen

Abstract:

Special Relativity Theory (SRT) includes only one characteristic of light, the speed is equal to all observers, and by excluding other relevant characteristics of light, the common interpretation of SRT should be regarded as merely an approximative theory. By rethinking the iconic double light cones, a revised version of SRT can be developed. The revised concept of light cones acknowledges an asymmetry of past and future light cones and introduced a concept of the extended past to explain the predictions as something other than the future. Combining this with the concept of photon-paired events, led to the inference that Special Relativity theory can support the existence of Now.

Keywords: relativity, light cone, Minkowski, time

Procedia PDF Downloads 49