Search results for: philosophy of mathematics

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: Marie-Josee Lavallee

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Adorno’s reputation as an abstract and pessimistic thinker who indulged in a critic of capitalist society and culture without bothering himself with opening prospects for change, and who has no interest in political activism, recently begun to be questioned. This paper, which has a twofold objective, will push revisionist readings a step further by putting forward the thesis that revolutionary praxis has been an enduring concern for Adorno, surfacing throughout his entire work. On the other hand, it will hold that his understanding of the relationships between theory and praxis, which will be explained by referring to Ernst Bloch’s distinction between the warm and cold currents of Marxism, can help to interpret the paralysis of revolutionary practice in our own time under a new light. Philosophy and its tasks have been an enduring topic of Adorno’s work from the 1930s to Negativ Dialektik. The writings in which he develops these ideas stand among his most obscure and abstract so that their strong ties to the political have remained mainly overlooked. Adorno’s undertaking of criticizing and ‘redeeming’ philosophy and metaphysics is inseparable from a care for retrieving the capacity to act in the world and to change it. Philosophical problems are immanent to sociological problems, and vice versa, he underlines in his Metaphysik. Begriff and Problem. The issue of truth cannot be severed from the contingent context of a given idea. As a critical undertaking extracting its contents from reality, which is what philosophy should be from Adorno's perspective, the latter has the potential to fully reveal the reification of the individual and consciousness resulting from capitalist economic and cultural domination, thus opening the way to resistance and revolutionary change. While this project, according to his usual method, is sketched mainly in negative terms, it also exhibits positive contours which depict a socialist society. Only in the latter could human suffering end, and mutilated individuals experiment with reconciliation in an authentic way. That Adorno’s continuous plea for philosophy’s self-critic and renewal hides an enduring concern for revolutionary praxis emerges clearly from a careful philosophical analysis of his writings on philosophy and a selection of his sociological work, coupled with references to his correspondences. This study points to the necessity of a serious re-evaluation of Adorno’s relationship to the political, which will impact on the interpretation of his whole oeuvre, is much needed. In the second place, Adorno's dialectical conception of theory and praxis is enlightening for our own time, since it suggests that we are experiencing a phase of creative latency rather an insurmountable impasse.

Keywords: Frankfurt school, philosophy and revolution, revolutionary praxis, Theodor W. Adorno

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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: Aleksandar Savanović

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In this paper we will analyze the relationship between the neo-liberal concept of property rights and redistribution policy. This issue is back in the focus of interest due to the crisis 2008. The crisis has reaffirmed the influence of the state on the free-market processes. The interference of the state with property relations re-opened a classical question: is it legitimate to redistribute resources of a man in favor of another man with taxes? The dominant view is that the neoliberal philosophy of natural rights is incompatible with redistributive measures. In principle, this view can be accepted. However, when we look into the details of the theory of natural rights proposed by some coryphaei of neoliberal philosophy, such as Hayek, Nozick, Buchanan and Rothbard, we can see that it is not such an unequivocal view.

Keywords: economic neoliberalism, natural law, property, redistribution

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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: Tripti Watwe

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Music or art of any country is its national heritage and represents the cultural personality of that region. Noble Laureate Rabindranath Tagore through his international educational endeavour called ‘Visva-Bharati’ established this concept that music can very much be a part of the mainstream education of a country because the purpose of both music and education is to bring in transformation in an individual. An individual with musical veins is more focused and meditative towards his or her goal in life. That is why in Tagore’s Visva-Bharati, one can observe even the brightest brains from various fields of economics, science, social sciences or literature equally verbal and efficient in Rabindra songs which the poet created under his own name.Tagore established this phenomenon that music if made a part of education and life, brings in profound transformation in the character and over-all personality of a person giving better and responsible citizens to a nation. It is expected that this hypothesis that music and education can be a nectarine combination can be established and proved with the help of various recorded observations containing Tagore’s educational philosophy, his experiments in his own institution ‘Visva-Bharati’ and through recorded research materials which have been gathered during the author’s field work in Visva-Bharati.

Keywords: Rabindranath Tagore, Visva-Bharati, education, music, philosophy

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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: 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: Itumeleng Phage

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Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

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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: Gülcan Taşkıran, Ayla Bayık Temel

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Background: Florence Nightingale, the modern founder of the nursing, is most famous for her role as a nurse. But not so much known about her contributions as a mathematician and statistician. Aim: In this conceptual article it is aimed to examine Florence Nightingale's statistics education, how she used her passion for statistics and applied statistical data in nursing care and her scientific contributions to statistical science. Design: Literature review method was used in the study. The databases of Istanbul University Library Search Engine, Turkish Medical Directory, Thesis Scanning Center of Higher Education Council, PubMed, Google Scholar, EBSCO Host, Web of Science were scanned to reach the studies. The keywords 'statistics' and 'Florence Nightingale' have been used in Turkish and English while being screened. As a result of the screening, totally 41 studies were examined from the national and international literature. Results: Florence Nightingale has interested in mathematics and statistics at her early ages and has received various training in these subjects. Lessons learned by Nightingale in a cultured family environment, her talent in mathematics and numbers, and her religious beliefs played a crucial role in the direction of the statistics. She was influenced by Quetelet's ideas in the formation of the statistical philosophy and received support from William Farr in her statistical studies. During the Crimean War, she applied statistical knowledge to nursing care, developed many statistical methods and graphics, so that she made revolutionary reforms in the health field. Conclusions: Nightingale's interest in statistics, her broad vision, the statistical ideas fused with religious beliefs, the innovative graphics she has developed and the extraordinary statistical projects that she carried out has been influential on the basis of her professional achievements. Florence Nightingale has also become a model for women in statistics. Today, using and teaching of statistics and research in nursing care practices and education programs continues with the light she gave.

Keywords: Crimean war, Florence Nightingale, nursing, statistics

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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: R. M. Kashim

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The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: conceptual knowledge, primary school teachers, procedural knowledge, rational numbers

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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: Siriwan Chatmaneerungcharoen

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An emerging body of ‘21st century skills’-such as adaptability, complex communication skills, technology skills and the ability to solve non-routine problems--are valuable across a wide range of jobs in the national economy. Within the Thai context, a focus on the Philosophy of Sufficiency Economy is integrated into Science Education. Thai science education has advocated infusing 21st century skills and Philosophy of Sufficiency Economy into the school curriculum and several educational levels have launched such efforts. Therefore, developing science teachers to have proper knowledge is the most important factor to success of the goals. The purposes of this study were to develop 40 Cooperative Science teachers’ Technological Pedagogical Content Knowledge (TPACK) and to develop Professional Development Model integrated with Co-teaching Model and Coaching System (Co-TPACK). TPACK is essential to career development for teachers. Forty volunteer In-service teachers who were science cooperative teachers participated in this study for 2 years. Data sources throughout the research project consisted of teacher refection, classroom observations, Semi-structure interviews, Situation interview, questionnaires and document analysis. Interpretivist framework was used to analyze the data. Findings indicate that at the beginning, the teachers understood only the meaning of Philosophy of Sufficiency Economy but they did not know how to integrate the Philosophy of Sufficiency Economy into their science classrooms. Mostly, they preferred to use lecture based teaching and experimental teaching styles. While the Co- TPACK was progressing, the teachers had blended their teaching styles and learning evaluation methods. Co-TPACK consists of 3 cycles (Student Teachers’ Preparation Cycle, Cooperative Science Teachers Cycle, Collaboration cycle (Co-teaching, Co-planning, and Co-Evaluating and Coaching System)).The Co-TPACK enhances the 40 cooperative science teachers, student teachers and university supervisor to exchange their knowledge and experience on teaching science. There are many channels that they used for communication including online. They have used more Phuket context-integrated lessons, technology-integrated teaching and Learning that can explicit Philosophy of Sufficiency Economy. Their sustained development is shown in their lesson plans and teaching practices.

Keywords: technological pedagogical content knowledge, philosophy of sufficiency economy, professional development, coaching system

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Authors: Sisay Tamrat Ayalew

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This paper explores the concept of humanism as a guiding philosophy in education, specifically focusing on Ethiopian Higher Education Institutions (EHEIs). It highlights the perceived lack of humanistic elements within the educational system and the resulting intellectual and moral decay among students. The aim of this study is to critically reflect on the essence of humanism and its relevance to Ethiopian higher education. By examining the philosophy and practice of humanism, the paper seeks to evaluate the existing state of EHEIs in relation to this educational approach. The methodology employed in this research is qualitative. The study relies primarily on literature review and analysis of policy documents to gain insights into the subject matter. A hermeneutic approach is utilized to interpret the realities observed in various contexts. The key finding of this paper is that Ethiopian higher education institutions lack humanistic elements in their educational practices. This deficiency contributes to the overall moral and intellectual decay among students. The study accentuates that humanism is not merely an optional extra but an essential tool for creating a clean academic environment and fostering the holistic development of students.

Keywords: humanism, higher education, human dignity, intellectual decadence, moral sickness

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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: Eugenia Vomvoridi-Ivanovic

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It is broadly assumed that participation in field experiences will help pre-service teachers (PSTs) bridge theory to practice. However, this is often not the case since PSTs who are placed in classrooms with large numbers of students from diverse linguistic, cultural, racial, and ethnic backgrounds (culturally diverse students (CDS)) usually observe ineffective mathematics teaching practices that are in contrast to those discussed in their teacher preparation program. Over the past decades, the educational research community has paid increasing attention to investigating out-of-school learning contexts and how participation in such contexts can contribute to the achievement of underrepresented groups in Science, Technology, Engineering, and mathematics (STEM) education and their expanded participation in STEM fields. In addition, several research studies have shown that students display different kinds of mathematical behaviors and discourse practices in out-of-school contexts than they do in the typical mathematics classroom since they draw from a variety of linguistic and cultural resources to negotiate meanings and participate in joint problem solving. However, almost no attention has been given to exploring these contexts as field experiences for pre-service mathematics teachers. The purpose of this study was to explore how participation in a community based after-school field experience promotes understanding of the content pedagogy concepts introduced in elementary mathematics methods courses, particularly as they apply to teaching mathematics to CDS. This study draws upon a situated, socio-cultural theory of teacher learning that centers on the concept of learning as situated social practice, which includes discourse, social interaction, and participation structures. Consistent with exploratory case study methodology, qualitative methods were employed to investigate how a cohort of twelve participating pre-service teacher's approach to pedagogy and their conversations around teaching and learning mathematics to CDS evolved through their participation in the after-school field experience, and how they connected the content discussed in their mathematics methods course with their interactions with the CDS in the after-school. Data were collected over a period of one academic year from the following sources: (a) audio recordings of the PSTs' interactions with the students during the after-school sessions, (b) PSTs' after-school field-notes, (c) audio-recordings of weekly methods course meetings, and (d) other document data (e.g., PST and student generated artifacts, PSTs' written course assignments). The findings of this study reveal that the PSTs benefitted greatly through their participation in the after-school field experience. Specifically, after-school participation promoted a deeper understanding of the content pedagogy concepts introduced in the mathematics methods course and gained a greater appreciation for how students learn mathematics with understanding. Further, even though many of PSTs' assumptions about the mathematical abilities of CDS were challenged and PSTs began to view CDSs' cultural and linguistic backgrounds as resources (rather than obstacles) for learning, some PSTs still held negative stereotypes about CDS and teaching and learning mathematics to CDS in particular. Insights gained through this study contribute to a better understanding of how informal mathematics learning contexts may provide a valuable context for pre-service teacher's learning to teach mathematics to CDS.

Keywords: after-school mathematics program, pre-service mathematical education of teachers, qualitative methods, situated socio-cultural theory, teaching culturally diverse students

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Authors: Onesimus Bulus Shiaki

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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

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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: Boran Akin Demir

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Notions such as ‘I’, ‘self’, and ‘mind’ are typically used synonymously in Western dualist philosophy, in a way that distances itself from the material world. This has rendered it increasingly difficult for the dualist Western philosopher to truly understand the Vedantic claim that all is one, and ultimately that ‘I am Brahman’. In Advaita Vedanta, we are introduced to one of the most exhilarating theories of non-dualism through its Doctrine of Illusion. This paper approaches the issue through a comparative study between seemingly unrelated thinkers – namely, Jalaluddin Rumi, Lao Tzu, and Plato. The broadness of this research in such alternative schools of thought aims to show the underlying unity that successfully presents itself through time and space, thus upholding the philosophy of Advaita Vedanta from all corners of the world.

Keywords: Advaita Vedanta, Brahman, Lao Tzu, Plato, Rumi

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Authors: Napasri Suwanajote

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The purposes of this research were to analyze and evaluate successful factors in OTOP production process for the developing of learning center on OTOP production process based on Sufficiency Economic Philosophy for sustainable life quality. The research has been designed as a qualitative study to gather information from 30 OTOP producers in Bangkontee District, Samudsongkram Province. They were all interviewed on 3 main parts. Part 1 was about the production process including 1) production, 2) product development, 3) the community strength, 4) marketing possibility, and 5) product quality. Part 2 evaluated appropriate successful factors including 1) the analysis of the successful factors, 2) evaluate the strategy based on Sufficiency Economic Philosophy, and 3) the model of learning center on OTOP production process based on Sufficiency Economic Philosophy for sustainable life quality. The results showed that the production did not affect the environment with potential in continuing standard quality production. They used the raw materials in the country. On the aspect of product and community strength in the past 1 year, it was found that there was no appropriate packaging showing product identity according to global market standard. They needed the training on packaging especially for food and drink products. On the aspect of product quality and product specification, it was found that the products were certified by the local OTOP standard. There should be a responsible organization to help the uncertified producers pass the standard. However, there was a problem on food contamination which was hazardous to the consumers. The producers should cooperate with the government sector or educational institutes involving with food processing to reach FDA standard. The results from small group discussion showed that the community expected high education and better standard living. Some problems reported by the community included informal debt and drugs in the community. There were 8 steps in developing the model of learning center on OTOP production process based on Sufficiency Economic Philosophy for sustainable life quality.

Keywords: production process, OTOP, sufficiency economic philosophy, language choice

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Authors: Han Hyuk Cho, Hanik Jo

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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: Tao Peng

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This paper presents a holistic model of political economy based on Daoism – the foundational philosophy of classical Chinese epistemology. Daoism is both comprehensive and subtle in its manifestations and applications in all aspects of nature and society. Based on Daoist creation theory of the universe, life theory and five element functioning theory, a holistic model in economics with minimal assumptions and independent of ideology are constructed. Under this framework, different schools of economics, such as neo-liberal, Marxism, and Austrian school, are explored and shed new light on. Economic and financial predictions can be realized in applications to Qi Men Dun Jia. This framework can provide guidelines and inspirations to economic modelling, economic policies formulation and strategy development and guide society towards a more sustainable future.

Keywords: daoism, economics, holistic, philosophy

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Authors: Joanne Hardman

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South Africa’s crisis in mathematics attainment is well documented. To meet the need to develop students’ mathematical performance in schools the government has launched various initiatives using computers to impact on mathematical attainment. While it is clear that computers can change pedagogical practices, there is a dearth of qualitative studies indicating exactly how pedagogy is transformed with Information Communication Technologies (ICTs) in a teaching activity. Consequently, this paper addresses the following question: how, along which dimensions in an activity, does pedagogy alter with the use of computer drill and practice software in four disadvantaged grade 6 mathematics classrooms in the Western Cape province of South Africa? The paper draws on Cultural Historical Activity Theory (CHAT) to develop a view of pedagogy as socially situated. Four ideal pedagogical types are identified: Reinforcement pedagogy, which has the reinforcement of specialised knowledge as its object; Collaborative pedagogy, which has the development of metacognitive engagement with specialised knowledge as its object; Directive pedagogy, which has the development of technical task skills as its object, and finally, Defensive pedagogy, which has student regulation as its object. Face-to-face lessons were characterised as predominantly Reinforcement and Collaborative pedagogy and most computer lessons were characterised as mainly either Defensive or Directive.

Keywords: computers, cultural historical activity theory, mathematics, pedagogy

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Authors: Joel S. Mtebe, Aron Kondoro, Mussa M. Kissaka, Elia Kibga

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Sub-Saharan Africa is described as the second fastest growing mobile phone penetration in the world more than in the United States or the European Union. Mobile phones have been used to provide a lot of opportunities to improve people’s lives in the region such as in banking, marketing, entertainment, and paying various bills such as water, TV, and electricity. However, the potential of using mobile phones to enhance teaching and learning has not been explored. This study presents an experience of developing and delivering SMS quizzes questions that were used to assess mastery of the subject content knowledge of science and mathematics secondary school teachers in Tanzania. The SMS quizzes were used as a follow up support mechanism to 500 teachers who participated in a project to upgrade subject content knowledge of science and mathematics subjects. Quizzes of 10-15 questions were sent to teachers each week for 8 weeks and the results were analyzed using SPSS. The results showed that chemistry and biology had better performance compared to mathematics and physics. Teachers reported some challenges that led to poor performance, invalid answers, and non-responses and they are presented. This research has several practical implications for those who are implementing or planning to use mobile phones for teaching and learning especially in rural secondary schools in sub-Saharan Africa.

Keywords: mobile learning, elearning, educational technolgies, SMS, secondary education, assessment

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Authors: Luana Mathias Souto

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The situation about women’s rights it’s a sensitive issue when it’s talking about human rights. More difficult its find a way to protect these rights. Aware of this problem, this article aims to analyze the women’s rights in the Brazilian context, mainly, the reproductive rights. So, to achieve this purpose, this paper through the combination of Law, philosophy, and Literature tries to rethinking why women can’t have a voice when the decisions about their rights are taken. Methodologically, it was used as an interdisciplinary bibliographical revision between Law, philosophy, and Literature. From Literature it brings the contributions from the life-narratives as an instrument to promote human rights. Besides the life-narratives theory, it’s also used the novel The Handmaid’s tale from Margaret Atwood, which became a symbol to reflect about reproductive rights. From philosophy, it’s adopted the concepts of Homo sacer and state of exception developed by the philosopher Giorgio Agamben. The contributions of these different researches fields made possible to conclude that women are Homo sacer because governments ignore their voices and opinions when they talk about abortion. The control of the human body, mainly, women bodies it’s more important than preserving some fundamental rights and because of this, it’s so difficult to preserve and promote the human rights. Based on these conclusions, it is understood that when the state is incapable or does not want to guarantee the adequate protection of human rights, it is up to society through its various means to find ways to protect them, and this is the main proposal sought by this article.

Keywords: dystopian fiction, human rights, life-narratives, state of exception

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