Search results for: philosophy of mathematics

Authors: Lisa Kasmer

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Teachers’ instructional decisions shape the structure and content of mathematics lessons and influence the mathematics that students are given the opportunity to learn. Therefore, it is important to better understand how teachers make instructional decisions and thus find new ways to help practicing and future teachers give their students a more effective and robust learning experience. Understanding the relationship between teachers’ instructional decisions and their goals, resources, and orientations (beliefs) is important given the heightened focus on geometric transformations in the middle school mathematics curriculum. This work is significant as the development and support of current and future teachers need more effective ways to teach geometry to their students. The following research questions frame this study: (1) As middle school mathematics teachers plan and enact instruction related to teaching transformations, what thinking processes do they engage in to make decisions about teaching transformations with or without a coordinate system and (2) How do the goals, resources and orientations of these teachers impact their instructional decisions and reveal about their understanding of teaching transformations? Teachers and students alike struggle with understanding transformations; many teachers skip or hurriedly teach transformations at the end of the school year. However, transformations are an important mathematical topic as this topic supports students’ understanding of geometric and spatial reasoning. Geometric transformations are a foundational concept in mathematics, not only for understanding congruence and similarity but for proofs, algebraic functions, and calculus etc. Geometric transformations also underpin the secondary mathematics curriculum, as features of transformations transfer to other areas of mathematics. Teachers’ instructional decisions in terms of goals, orientations, and resources that support these instructional decisions were analyzed using open-coding. Open-coding is recognized as an initial first step in qualitative analysis, where comparisons are made, and preliminary categories are considered. Initial codes and categories from current research on teachers’ thinking processes that are related to the decisions they make while planning and reflecting on the lessons were also noted. Surfacing ideas and additional themes common across teachers while seeking patterns, were compared and analyzed. Finally, attributes of teachers’ goals, orientations and resources were identified in order to begin to build a picture of the reasoning behind their instructional decisions. These categories became the basis for the organization and conceptualization of the data. Preliminary results suggest that teachers often rely on their own orientations about teaching geometric transformations. These beliefs are underpinned by the teachers’ own mathematical knowledge related to teaching transformations. When a teacher does not have a robust understanding of transformations, they are limited by this lack of knowledge. These shortcomings impact students’ opportunities to learn, and thus disadvantage their own understanding of transformations. Teachers’ goals are also limited by their paucity of knowledge regarding transformations, as these goals do not fully represent the range of comprehension a teacher needs to teach this topic well.

Keywords: coordinate plane, geometric transformations, instructional decisions, middle school mathematics

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Authors: Musa Auwal Mamman, S. G. Isa

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This study was carried out in order to investigate the effectiveness of GeoGebra software in teaching and learning of linear and quadratic equations amongst senior secondary school students in Fagge Local Government Area, Kano State–Nigeria. Five research items were raised in objectives, research questions and hypotheses respectively. A random sampling method was used in selecting 398 students from a population of 2098 of SS2 students. The experimental group was taught using the GeoGebra software while the control group was taught using the conventional teaching method. The instrument used for the study was the mathematics performance test (MPT) which was administered at the beginning and at the end of the study. The results of the study revealed that students taught with GeoGebra software (experimental group) performed better than students taught with traditional teaching method. The t- test was used to analyze the data obtained from the study.

Keywords: GeoGebra Software, mathematics performance, random sampling, mathematics teaching

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Authors: Maria Belen C. Costa, Liza C. Costa

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Teachers have an important influence on students’ academic achievement. Teachers play a crucial role in educational attainment because they stand in the interface of the transmission of knowledge, values, and skills in the learning process through the instructional strategies they employ in the classroom. The level of achievement of students in school depends on the degree of effectiveness of instructional strategies used by the teacher. Thus, this study was conceptualized and conducted to examine the instructional strategies preferred and used by the Science and Mathematics teachers and the impact of those strategies in their teaching performance and students’ academic achievement in Science and Mathematics. The participants of the study comprised a total enumeration of 61 teachers who were chosen through total enumeration and 610 students who were selected using two-stage random sampling technique. The descriptive correlation design was used in this study with a self-made questionnaire as the main tool in the data gathering procedure. Relationship among variables was tested and analyzed using Spearman Rank Correlation Coefficient and Wilcoxon Signed Rank statistics. The teacher participants under study mainly belonged to the age group of ‘young’ (35 years and below) and most were females having ‘very much experienced’ (16 years and above) in teaching. Teaching performance was found to be ‘very satisfactory’ while academic achievement in Science and Mathematics was found to be ‘satisfactory’. Demographic profile and teaching performance of teacher participants were found to be ‘not significant’ to their instructional strategy preferences. Results implied that age, sex, level of education and length of service of the teachers does not affect their preference on a particular instructional strategy. However, the teacher participants’ extent of use of the different instructional strategies was found to be ‘significant’ to their teaching performance. The instructional strategies being used by the teachers were found to have a direct effect on their teaching performance. Academic achievement of student participants was found to be ‘significant’ to the teacher participants’ instructional strategy preferences. The preference of the teachers on instructional strategies had a significant effect on the students’ academic performance. On the other hand, teacher participants’ extent of use of instructional strategies was showed to be ‘not significant’ to the academic achievement of students in Science and Mathematics. The instructional strategy being used by the teachers did not affect the level of performance of students in Science and Mathematics. The results of the study revealed that there was a significant difference between the teacher participants’ preference of instructional strategy and the student participants’ instructional strategy preference as well as between teacher participants’ extent of use and student participants’ perceived level of use of the different instructional strategies. Findings found a discrepancy between the teaching strategy preferences of students and strategies implemented by teachers.

Keywords: academic achievement, extent of use, instructional strategy, preferences

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Authors: Marion G. Ben-Jacob, David Wang

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There is a mathematics requirement for entry level college and university students, especially those who plan to study STEM (Science, Technology, Engineering and Mathematics). Most of them take College Algebra, and to continue their studies, they need to succeed in this course. Different pedagogical strategies are employed to promote the success of our students. There is, of course, the Traditional Method of teaching- lecture, examples, problems for students to solve. The Emporium Model, another pedagogical approach, replaces traditional lectures with a learning resource center model featuring interactive software and on-demand personalized assistance. This presentation will compare these two methods of pedagogy and the study done with its results on this comparison. Math is the foundation for science, technology, and engineering. Its work is generally used in STEM to find patterns in data. These patterns can be used to test relationships, draw general conclusions about data, and model the real world. In STEM, solutions to problems are analyzed, reasoned, and interpreted using math abilities in a assortment of real-world scenarios. This presentation will examine specific examples of how math is used in the different STEM disciplines. Math becomes practical in science when it is used to model natural and artificial experiments to identify a problem and develop a solution for it. As we analyze data, we are using math to find the statistical correlation between the cause of an effect. Scientists who use math include the following: data scientists, scientists, biologists and geologists. Without math, most technology would not be possible. Math is the basis of binary, and without programming, you just have the hardware. Addition, subtraction, multiplication, and division is also used in almost every program written. Mathematical algorithms are inherent in software as well. Mechanical engineers analyze scientific data to design robots by applying math and using the software. Electrical engineers use math to help design and test electrical equipment. They also use math when creating computer simulations and designing new products. Chemical engineers often use mathematics in the lab. Advanced computer software is used to aid in their research and production processes to model theoretical synthesis techniques and properties of chemical compounds. Mathematics mastery is crucial for success in the STEM disciplines. Pedagogical research on formative strategies and necessary topics to be covered are essential.

Keywords: emporium model, mathematics, pedagogy, STEM

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Authors: Aïda C. Terblanché-Greeff

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Afro-polychronism is a unique amalgamated cultural value of social self-construal and time orientation. As such, the construct Afro-polychronism is conceptually analysed by focusing on the aspects of Ubuntu as collectivism and African time as polychronism. It is argued that these cultural values have a reciprocal and thus inseparable relationship. As it is general practice to measure cultural values empirically, the author conducted empirically engaged philosophy and aimed to develop a scale to measure Afro-polychronism based on its two dimensions of Ubuntu as social self-construal and African time as time orientation. From the scale’s psychometric properties, it was determined that the scale was, in fact, not reliable and valid. It was found that the correlation between the Ubuntu dimension and the African time is moderate (albeit statistically significant). In conclusion, the author abduced why this cultural value cannot be empirically measured based on its theoretical definition and indicated which different path would be more promising.

Keywords: African time, Afro-polychronism, empirically engaged African philosophy, Ubuntu

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Authors: Manee Arpanantikul, Pennapa Unsanit, Dolrat Rujiwatthanakorn, Aporacha Lumdubwong

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In order to continuously perform self-care based on the sufficiency economy philosophy for the length of women’s lives is not easy. However, there are different ways that women can use to carry out self-care activities regularly. Some women individually perform self-care while others perform self-care in groups. Little is known about ways to sustaining self-care of women based on the fundamental principle of Thai culture. The purpose of this study was to investigate ways to sustaining self-care based on the sufficiency economy philosophy of Thai middle-aged women living in the community in order to achieve future healthy aging. This study employed a qualitative research design. Twenty women who were willing to participate in this study were recruited. Data collection were conducted through in-depth interviews with tape recording, doing field notes, and observation. All interviews were transcribed verbatim, and data were analyzed by using content analysis. The findings showed ways to sustaining self-care of Thai community women to achieve future healthy aging consisting of 7 themes: 1) having determination, 2) having a model, 3) developing a leader, 4) carrying on performing activities, 5) setting up rules, 6) building self-care culture, and 7) developing a self-care group/network. The findings of this study suggested that in order to achieve self-care sustainability women should get to know themselves, have intention and belief, together with having the power of community and support. Therefore, having self-care constantly will prevent disease and promote healthy in women’s lives.

Keywords: qualitative research, sufficiency economy philosophy, Thai middle-aged women, ways to sustaining self-care

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Authors: Michael Granado

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The French philosopher Gaston Bachelard’s philosophy of time is articulated in his two works on the subject, the Intuition of the Instant (1932) and his The Dialectic of Duration (1936). Both works present a systematic methodology predicated upon the assumption that our understanding of time has radically changed as a result of Einstein and subsequently needs to be reimagined. Bachelard makes a major distinction in his discussion of time: 1. Time as it is (physical time), 2. Time as we experience it (phenomenological time). This paper will focus on the second distinction, phenomenological time, and explore the connections between Bachelard’s work and contemporary psychology. Several aspects of Bachelard’s philosophy of time nicely complement our current understanding of memory and self and clarify how the self relates to experienced time. Two points, in particular, stand out; the first is the relative nature of subjective time, and the second is the implications of subjective time in the formation of the narrative self. Bachelard introduces two philosophical concepts to explain these points: rhythmanalysis and reverie. By exploring these concepts, it will become apparent that there is an undeniable link between memory, self, and time. Through the use of narrative self, the individual connects and links memories and time together to form a sense of personal identity.

Keywords: Gaston Bachelard, memory, self, time

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Authors: Ovidiu Anemtoaicei

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This paper offers a possible answer to the question of what it means to think about men and masculinities through the philosophy of sexual difference as developed by Luce Irigaray, employing Gilles Deleuze’s concept of 'critique' and arguing, at the same time, for a concept of 'becoming-man' as an expression of this answer. First, while examining the nature of the role of male bodies underlying the theorizing of men and masculinities in the field of the Critical Studies of Men and Masculinities, the paper argues for a turn to sexual difference theory as an answer to the 'gap' between the representations on male bodies and their participation in thought and masculine subjective production. Secondly, sharing Luce Irigaray’s critique of Western thought, the paper explores alternative morphological bodily 'locations' for rethinking male imaginary in relation to male embodiments, on the one hand, and in relation to the maternal and the feminine, on the other hand. Thirdly, the paper develops the idea that a phenomenologically-influenced approach towards male bodies might be productive, especially when thought through Irigaray’s sexual difference as a relational and experiential ontology. Finally, while showing that Irigaray and Deleuze share a similar critique of Western philosophical thought and of the masculine historical subject, it proposes a rethinking of the concept of 'becoming-man' as an assemblage meeting between Irigaray’s theory of sexual difference and Deleuze and Guattari’s nomadologic project, as a possibility of thinking change in men’s masculine subjective constitution in relation to both women and other men. As far as the ethical implications of such rethinking are concerned, the paper urges for the cultivation of a masculine culture of stepping back and its constitutive political, social and cultural practices so as to make possible the construction of new spaces that would allow for the becoming of at least two subjects based on the respect for their differences.

Keywords: feminist philosophy, male bodies, masculinities, phenomenology, sexual difference

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Authors: Taik Kim

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Mathematics anxiety has an important consequence for teacher practices that influence students’ attitudes and achievement. Elementary prospective teachers have the highest levels of mathematics anxiety in comparison with other college majors. In his teaching practice, the researcher developed a highly successful teaching model to reduce pre-service teachers’ higher math anxiety and simultaneously to improve their pedagogical math content knowledge. There were eighty one participants from 2015 to 2018 who took the Mathematics for Elementary Teachers I and II. As the analysis data indicated, elementary prospective teachers’ math anxiety was greatly reduced with improving their math pedagogical knowledge. U.S encounters a critical shortage of well qualified educators. To solve the issue, it is essential to engage students in a long-term commitmentto shape better teachers, who will, in turn, produce k-12 school students that are better-prepared for college students. It is imperative that new instructional strategies are implemented to improve student learning and address declining interest, poor preparedness, a lack of diverse representation, and low persistence of students in mathematics. Many four year college students take math courses from the math department in the College of Arts& Science and then take methodology courses from the College of Education. Before taking pedagogy, many students struggle in learning mathematics and lose their confidence. Since the content course focus on college level math, instead of pre service teachers’ teaching area, per se elementary math, they do not have a chance to improve their teaching skills on topics which eventually they teach. The research, a joint appointment of math and math education, has been involved in teaching content and pedagogy. As the result indicated, participants were able to math content at the same time how to teach. In conclusion, the new initiative to use several teaching strategies was able not only to increase elementary prospective teachers’ mathematical skills and knowledge but also to improve their attitude toward mathematics. We need an innovative teaching strategy which implements evidence-based tactics in redesigning a education and math to improve pre service teachers’math skills and which can improve students’ attitude toward math and students’ logical and reasoning skills. Implementation of these best practices in the local school district is particularly important because K-8 teachers are not generally familiar with lab-based instruction. At the same time, local school teachers will learn a new way how to teach math. This study can be a vital teacher education model expanding throughout the State and nationwide. In summary, this study yields invaluable information how to improve teacher education in the elementary level and, eventually, how to enhance K-8 students’ math achievement.

Keywords: quality of education and improvement method, teacher education, innovative teaching and learning methodologies, math education

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Authors: Arpita Paul

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Wang Yang-ming introduced a revolutionary dimension to Japanese thought through his philosophy on intuitive moral consciousness. Post-Meiji Restoration,Emerson struck a chord with the Japanese due to the striking similarities his theories on transcendentalism had with doctrines of Wang Yang-ming'sschool of thought (Yōmeigaku), as pointed out by HomeiIwano (1873-1920). Wang's philosophy, chiefly anchored in the idea of the fundamental unity of thought and action, resembles the non-dualistic aspect of Brahman, a subject of Emerson's deep interest. Kitamura Tōkoku's (1868-1894) ardent reading of Emerson corroborated what he had learned in Wang Yang-ming's philosophy. This essay shall begin with a discussion on Emerson's discoveries of Vedanta that later, on a parallel ground with Yōmeigaku, significantly influenced Tōkoku. This essay will then demonstrate how Tōkokutransforms these philosophies to portray the advent of modern consciousness in Japan in his magnum opus"Naibuseimeiron." In his attempt to undo the blindfold of past feudalism,Tōkoku repeatedly championed the mental process of a self-reliant individual in his essays which showcase the metamorphosis of Japanese individualism in the final decades of the Meiji Period. In seeking to express Japan's budding intellectual enterprise,Tōkoku asserts securing one's vantage point in the world through an awakened consciousness. In his desire to articulate this, Tōkoku becomes, as argued in this paper's penultimate and final sections, a fascinating merging point of the philosophical doctrines of Vedanta, Yōmeigaku, and Emerson, a rare depiction in the existing scholarship.

Keywords: meiji intellengtsia, yomeigaku, vedanta, modern consciousness

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Authors: Veronica Diaz Quezada

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A study and its preliminary results are presented. The research is descriptive and exploratory and it is still in process. Its objective is to develop an assessment method in the field of fostering values using competence mathematics problem solving. This is part of a more extensive research that aims at contributing to educational integration in Latin America, particularly to the development of proposals to link education for citizenship and the mathematics lessons. This is being carried out by research teams of University of Barcelona-España; University Nacional of Costa Rica; University Autónoma of Querétaro-México; Pontificia University Católica of Perú, University Nacional of Villa María- Argentina and University of Los Lagos-Chile, in the context of Andrés Bello Chair for the Association of Latin American Universities. This research was developed and implemented in Chile in 2016, using mixed research methods. It included interviews and a problem-solving math test with ethical values that was administered to students of the secondary education of the regions of Los Ríos and of the Lakes of Chile. The results show the lack of integration between the teaching of values and science discipline.

Keywords: citizenchip, ethical values, mathematics, secondary school, solving problem

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Authors: Jian Wang

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Teachers’ lesson-based discussions presume central to their effective learning to teach. Whether and to what extent such discussions offer opportunities for teachers to learn to teach effectively is worth a careful empirical examination. This study examines this assumption by drawing on lesson-based discussions and relevant curriculum materials from Chinese teachers in three urban schools. Their lesson-based discussions consistently focused on pedagogical content knowledge and offered specific and reasoned suggestions for teachers to refine their teaching practices. The mandated curriculum and their working language-mediated their lesson-based discussions.

Keywords: Chinese teachers, curriculum materials, lesson discussion, mathematics instruction

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Authors: Rex C. Apillanes, Ana Rubi L. Sereño, Ellen Joy L. Palangan

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The main objective of this action research is to know the effectiveness of the compendium on Contextualized Story Word Problem in Mathematics used as an intervention material to enhance the comprehension and problem-solving skills of Grade 4 pupils. This also addresses the competencies outlined in the curriculum guide while, at the same time, providing instructional material which the pupils can work on and practice solving word problems. The twelve randomly selected grade four pupils of Mantuyom Elementary School have been chosen as respondents for this action research in consideration of their consent and approval. A Pre-Test and a Post-test have been given to the pupils to determine their baseline proficiency level in four fundamental operations. The data has been statistically treated using a T-test to determine their difference. At a mean score of 13.42 and 16.83 for pre and post-tests, respectively, the p-value of 0.000620816 reflects a highly significant difference for the pre-test and post-test. This is lesser than the 0.05 level of significance (p≤0.05). Therefore, it is found that the compendium of contextualized story word problems is an efficient instructional material for Mathematics 4, yet; it is recommended that a Parents’ User Guide shall be developed to assist the parents in the conduct of the Remediation, Reinforcement and Enhancement (RRE).

Keywords: action research, compendium, contextualized, story, word problem, research, intervention

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Authors: Ovett Nwosimiri

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African tradition and what it entails are the content of African concepts of knowledge. The study of African concepts of knowledge is also known as African epistemology. In other words, African epistemology is a branch of African philosophy that deals with knowledge. This branch of African philosophy engages with the nature and concept of knowledge, the ways in which knowledge can be gained, the ways in which one can justify an epistemic claim or validate a knowledge claim and the limit of human knowledge, etc. The protagonists of African epistemology based their argument for a distinctive or unique African epistemology on the premise or proposition “that each race is endowed with a distinctive nature and embodies in its civilization a particular spirit”. All human beings share some certain basic values and perceptions irrespective of where you come from, and this idea actually fosters some forms of interaction between people from different nationality. Africans like other people share in some certain values, perceptions, and interaction with the rest of the world. These basic values, perceptions, and interaction that Africans share with the rest of the word prompted African people to attempt to “modernize” their societies or develop some forms of their tradition in harmony with the ethos of the contemporary world. Based on the above ideas, it would be interesting to investigate if such (African) epistemology is still unique. The advocates of African epistemology focus on the externalist notion of justification and neglect the idea that both the internalist and externalist notion of justification are needed in order to arrive at a coherent and well-founded account of epistemic justification. Thus, this paper will critically examine the claims that there is a unique African epistemology (a mode of knowing that is peculiar to Africans, and that African mode of knowing is social, monism and situated notion of knowledge), and the grounds for justifying beliefs and epistemic claims.

Keywords: internalist, externalist, knowledge, justification

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Authors: Nikoletta G. Karytsioti

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The European Union’s function and effectiveness are still an issue that minds, bringing about division even in the member-states interior. Recently, more serious issues have been added in the Union’s malfunction, which affects not only the Union’s function but also their residents’ safety. One of these issues is the migration crisis, which frustrates the European Union’s balances and the stability. The present paper’s aim to frame and interpret the Greek public opinion in basic migration matters, throughout the political philosophy and specifically via John Rawls ‘Theory of Justice’. The theory is deployed to examine if it may be used in a practical way, on a tangible issue and in a specific area. In order to obtain a real frame of the public opinion about the matter of migration, a questionnaire was addressed to Greek people. The sample was chosen for three main reasons: a) Greeks are experienced in the migration as they had migrated in the past, b) many young people migrated the recent years after the debt crisis, c) Greece is a reception state. Being based in the Theory of Justice and specifically in the ‘veil of ignorance’, is tried to overcome the obstacles of human nature’s subjectivity, while examining the variations in the responses per social group. The questionnaire will have demographic questions and special interest questions, related with the crisis, before and after ‘the veil of ignorance’. The paper’s originality comes from the fact that it is the first time that a philosophical theory is used to examine the migration issue in a practical manner. The main goals of the paper are three: - To examine the differences/similarities in the responses before and after the veil of ignorance, - to reveal opinions on migration crisis from E.U. citizens and - to confirm or not the practical usefulness of the Political Philosophy as a highlighting tool

Keywords: European Union, immigrants, migration crisis, political philosophy, theory of justice, veil of ignorance

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Authors: Peter Akayuure, Michael Johnson Nabie

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Similar to many colonized nations in the world, one indelible mark left by colonial masters after Ghana’s independence in 1957 has been the fact that many contexts used to teach statistics and probability concepts are often alien and do not resonate with the social domain of our indigenous Ghanaian child. This has seriously limited the understanding, discoveries, and applications of mathematics for national developments. With the recent curriculum demands of making the Ghanaian child mathematically literate, this qualitative study involved video recordings and mathematical analysis of play sessions of an indigenous girl game called Ampe with the aim to demystify the concepts in probability theorem, which is applied in mathematics related fields of study. The mathematical analysis shows that the game of Ampe, which is widely played by school girls in Ghana, is suitable for learning concepts of the probability theorems. It was also revealed that as a girl game, the use of Ampe provides good lessons to educators, textbook writers, and teachers to rethink about the selection of mathematics tasks and learning contexts that are sensitive to gender. As we undertake to transform teacher education and student learning, the use of indigenous games should be critically revisited.

Keywords: Ampe, mathematical analysis, probability theorem, Ghanaian girl game

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Authors: E. Erdogan, H. A. Erdogan

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FengShui, an old Chinese discipline, dates back to more than 5000 years, is one of the design principles that aim at creating habitable and sustainable spaces in harmony with nature by systematizing data within its own structure. Having emerged from Chinese mysticism and embodying elements of faith in its principles, FengShui argues that the positive energy in the environment channels human behavior and psychology. This argument is supported with the thesis of quantum physics that ‘everything is made up of energy’ and gains an important place. In spaces where living and working take place with several principles and systematized rules, FengShui promises a happier, more peaceful and comfortable life by influencing human psychology, acts, and soul as well as the professional and social life of the individual. Observing these design properties in houses, workplaces, offices, the environment, and daily life as a design paradigm is significant. In this study, how FengShui, a Central Asian culture emanated from Chinese mysticism, shapes design and how it is used as an element of sustainable design will be explained.

Keywords: Feng Shui, design principle, sustainability, philosophy

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Authors: Geoffrey A. Wright

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In an attempt to address shortcomings revealed in international assessments and lamented in legislation, many schools are reducing or eliminating elective courses, applying the rationale that replacing "non-essential" subjects with core subjects, such as mathematics and language arts, will better position students in the global market. However, there is evidence that systematically pairing a core subject with another complementary subject may lead to greater overall learning in both subjects. In this paper, we outline the methods and preliminary findings from a study we conducted analyzing the influence learning programming has on student mathematical comprehension and ability. The purpose of this research is to demonstrate in what ways two subjects might complement each other, and to better understand the principles and conditions that encourage what we call lateral transfer, the synergistic effect that occurs when a learner studies two complementary subjects.

Keywords: programming, engineering, technology, complementary subjects

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Authors: E. Gouya Bozorg

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The issue of ranking of sports teams, in particular soccer teams is of primary importance in the professional sports. However, it is still based on classical statistics and models outside of area of mathematics. Rigorous mathematics and then statistics despite the expectation held of them have not been able to effectively engage in the issue of ranking. It is something that requires serious pathology. The purpose of this study is to change the approach to get closer to mathematics proper for using in the ranking. We recommend using theoretical mathematics as a good option because it can hermeneutically obtain the theoretical concepts and criteria needful for the ranking from everyday language of a League. We have proposed a framework that puts the issue of ranking into a new space that we have applied in soccer as a case study. This is an experimental and theoretical study on the issue of ranking in a professional soccer league based on theoretical mathematics, followed by theoretical statistics. First, we showed the theoretical definition of constant number Є = 1.33 or ‘golden number’ of a soccer league. Then, we have defined the ‘efficiency of a team’ by this number and formula of μ = (Pts / (k.Є)) – 1, in which Pts is a point obtained by a team in k number of games played. Moreover, K.Є index has been used to show the theoretical median line in the league table and to compare top teams and bottom teams. Theoretical coefficient of σ= 1 / (1+ (Ptx / Ptxn)) has also been defined that in every match between the teams x, xn, with respect to the ability of a team and the points of both of them Ptx, Ptxn, and it gives a performance point resulting in a special ranking for the League. And it has been useful particularly in evaluating the performance of weaker teams. The current theory has been examined for the statistical data of 4 major European Leagues during the period of 1998-2014. Results of this study showed that the issue of ranking is dependent on appropriate theoretical indicators of a League. These indicators allowed us to find different forms of ranking of teams in a league including the ‘special table’ of a league. Furthermore, on this basis the issue of a record of team has been revised and amended. In addition, the theory of ranking can be used to compare and classify the different leagues and tournaments. Experimental results obtained from archival statistics of major professional leagues in the world in the past two decades have confirmed the theory. This topic introduces a new theory for ranking of a soccer league. Moreover, this theory can be used to compare different leagues and tournaments.

Keywords: efficiency of a team, ranking, special table, theoretical mathematic

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Authors: S. Goel

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In the current scenario, education should be realistic and nature-friendly. The earlier definition of education was restricted to the holistic development of the child which help them to increase their capacity and helps in social upliftment. But such definition gives a more individualistic aim of education. Due to that individualistic aim, we have become disconnected from nature. So, a school should be a place which provides students with an area to explore. They should get practical learning or learning from nature which is also propounded by Rousseau in the mid-eighteenth century. Integrating Sustainable development goals in the school curriculum will make it possible to connect the nature with the lives of the children in the classroom. Then, students will be more aware and sensitive towards their social and natural surroundings. The research attempts to examine the efficiency of project-based learning in mathematics to create awareness around sustainable development goals. The major finding of the research was that students are less aware of sustainable development goals, but when given time and an appropriate learning environment, students can be made aware of these goals. In this research, project-based learning was used to make students aware of sustainable development goals. Students were given pre test and post test which helped in analyzing their performance. After the intervention, post test result showed that mathematics projects can create an awareness of sustainable development goals.

Keywords: holistic development, natural learning, project based learning, sustainable development goals

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Authors: Evgeniia Surkova, Manal Assaad, Hleb Makeyeu, Juho Makio

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The main objective of STIMEY (Science, Technology, Innovation, Mathematics, Engineering for the Young) project is the delivery of a hybrid learning environment that combines multi-level components such as social media concepts, robotic artefacts, and radio, among others. It is based on a well-researched pedagogical framework to attract European youths to STEM (science, technology, engineering, and mathematics) education and careers. To develop and integrate these various components, STIMEY is executed in iterative research cycles leading to progressive improvements. Scrum was the development methodology of choice in the project, as studies indicated its benefits as an agile methodology in global software development, especially of e-learning and integrated learning projects. This paper describes the project partners’ experience with the Scrum framework, discussing the challenges faced in its implementation and the mitigation practices employed. The authors conclude with exploring user experience tools and principles for future research, as a novel direction in supporting the Scrum development team.

Keywords: e-learning, global software development, scrum, STEM education

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Authors: Emi̇ne Yuksel, Murat Kiliç, Onur Ülker

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Although minimalism has been coming into being in the field of interior design for a long time, it also brought a wide range of reaction. The more simple and feeling of emptiness usage of minimalism in space and furniture design has been found extremely boring so far, as a reaction to minimalism, a movement of maximalism was emerged. Thus more extravagant, splendid, magnificent and comfortable design approach was substituted by the greatest, largest and the extreme. Thus, the philosophy of “less is bore” of minimalism was replaced by “less is more” giving rise to a new interpretation in the field of interior design. While maximalism reminded us the Victorian, Rococo, Arts and Crafts and Neoclassic styles in interior design, it drew attention to the furniture designs that covered all areas of space all in one. In this study, we search the effect of maximalist approach which was born as a reaction to minimalism in furniture. Firstly, it is explained how did the maximalism emerge and its philosophy, a literature investigation was scanned and investigated. As a research method, it is concerned with the investigation of studies undertaken by the pioneers of interior space designers and architects. The findings of this study have been evaluated in the conclusion section.

Keywords: furniture design, maximalism, minimalism, texture

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Authors: Isaac Benning

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Using technology to expand the learning space is critical for a productive mathematical discourse. This is a case study of two teachers who developed and enacted GeoGebra-based mathematics lessons following their engagement in a two-year professional development. The didactical and semiotic affordance of GeoGebra in widening the learning space for a productive mathematical discourse was explored. The approach of thematic analysis was used for lesson artefact, lesson observation, and interview data. The results indicated that constructing tools in GeoGebra provided a didactical milieu where students used them to explore mathematical concepts with little or no support from their teacher. The prompt feedback from the GeoGebra motivated students to practice mathematical concepts repeatedly in which they privately rethink their solutions before comparing their answers with that of their colleagues. The constructing tools enhanced self-discovery, team spirit, and dialogue among students. With regards to the semiotic construct, the tools widened the physical and psychological atmosphere of the classroom by providing animations that served as virtual concrete to enhance the recording, manipulation, testing of a mathematical idea, construction, and interpretation of geometric objects. These findings advance the discussion of widening the classroom for a productive mathematical discourse within the context of the mathematics curriculum of Ghana and similar Sub-Saharan African countries.

Keywords: GeoGebra, theory of didactical situation, semiotic mediation, mathematics laboratory, mathematical discussion

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Authors: Nessa-Amie T. Peñaflor, Antonio Cinto

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

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

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Authors: Sam Solaimani, Jack A. A. van der Veen, Mehdi Latifi

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Considering the increasingly VUCA (Volatile, Uncertain, Complex, Ambiguous) business market, innovation is the name of the game in contemporary business. Innovation is not solely created within the organization itself; its 'network environment' appears to be equally important for innovation. There are, at least, two streams of literature that emphasize the idea of using the extended organization to foster innovation capability, namely, Supply Chain Collaboration (SCC) (also rooted in the Lean philosophy) and Open Innovation (OI). Remarkably, these two concepts are still considered as being totally different in the sense that these appear in different streams of literature and applying different concepts in pursuing the same purposes. This paper explores the commonalities between the two concepts in order to conceptually further our understanding of how OI can effectively be applied in Supply Chain networks. Drawing on available literature in OI, SCC and Lean, the paper concludes with five principles that help firms to contextualize the implementation of OI to the peculiar setting of SC. Theoretically, the present paper aims at contributing to the relatively under-researched theme of Supply Chain Innovation. More in practical terms, the paper provides OI and SCC communities with a workable know-how to seize on and sustain OI initiatives.

Keywords: lean philosophy, open innovation, supply chain collaboration, supply chain management

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Authors: Pi-Hsia Hung

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The development of mathematical competency has individual benefits as well as benefits to the wider society. Children who begin school behind their peers in their understanding of number, counting, and simple arithmetic are at high risk of staying behind throughout their schooling. The development of effective strategies for improving the educational trajectory of these individuals will be contingent on identifying areas of early quantitative knowledge that influence later mathematics achievement. A computer-based quantity assessment was developed in this study to investigate the characteristics of 2nd and 3rd grade slow learners in quantity. The concept of quantification involves understanding measurements, counts, magnitudes, units, indicators, relative size, and numerical trends and patterns. Fifty-five tasks of quantitative reasoning—such as number sense, mental calculation, estimation and assessment of reasonableness of results—are included as quantity problem solving. Thus, quantity is defined in this study as applying knowledge of number and number operations in a wide variety of authentic settings. Around 1000 students were tested and categorized into 4 different performance levels. Students’ quantity ability correlated higher with their school math grade than other subjects. Around 20% students are below basic level. The intervention design implications of the preliminary item map constructed are discussed.

Keywords: mathematics assessment, mathematical cognition, quantity, number sense, validity

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Authors: Shubham Arora

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This paper illustrates a relationship between the Dvaitādvaita (dualistic non-dualistic) doctrine of Nimbārka school of Vedānta and philosophy of Indian classical dance, through the Rasa theory. There would be a separate focus on the philosophies of both the disciplines and then analyzing Rasa theory as a connexion between them. The paper presents ideas regarding the similarity between the Brahman and the dancer, manifestation of enacting character and the Jīva (soul), the existence of the phenomenal world and the imaginary world classification of rasa on the basis of three modes of nature, and the feelings and expressions depicting the Dvaita and Advaita. The reason behind choosing such a topic is an intention to explore the relativity of the Vedantic philosophy of this school in real manner. It is really important to study the practical implications and relevance of the doctrine with other disciplines for perceiving it cogently. In our daily lives, we use various forms of facial expressions and bodily gestures in order to communicate, along with the oral and written means of communication. What if, when gestures and expressions mingle with the music beats, in order to present an idea? Indian Classical dance is highly rich in expressing the emotions using extraordinary expressions, unconventional bodily gestures and mesmerizing music beats. Ancient scriptures like Nāṭyaśāstra of Bharata Muni and Abhinava Bhārati by Abhinavaguptā recount aesthetics in a well-defined and structured way of acting and dancing and also reveal the grammar of rasa theory. Indian Classical dance is not only for entertainment but it is deeply in contact with divinity. During the period of Bhakti movement in India, this art form was used as a means to narrate the vignettes from epics like Rāmāyana and Mahābhārata and Purānas. Even in present era, this art has a deep rooted philosophy within.

Keywords: Advaita, Brahman, Dvaita, Jiva, Nimbarka, Rasa, Vedanta

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Authors: Qiao Mao

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There is a growing number of studies concerning STEM (Science, Technology, Engineering, and Mathematics) and STEAM (Science, Technology, Engineering, Arts, and Mathematics). However, the research is little on STEAM competitions from Arts' perspective. This study takes the annual PowerTech STEAM competition in Taiwan as an example. In this activity, students are asked to make wooden bionic mechanical beasts on the spot and participate in a model and speed competition. This study aims to explore how Arts influences STEM after it involves in the making of mechanical beasts. A case study method is adopted. Through expert sampling, five prize winners in the PowerTech Youth Science and Technology Creation Competition and their supervisors are taken as the research subjects. Relevant data which are collected, sorted out, analyzed and interpreted afterwards, derive from observations, interview and document analyses, etc. The results of the study show that in the PowerTech Youth Science and Technology Creation Competition, when Arts involves in STEM, (1) it has an impact on the athletic performance, balance, stability and symmetry of mechanical beasts; (2) students become more interested and more creative in making STEAM mechanical beasts, which can promote students' learning of STEM; (3) students encounter more difficulties and problems when making STEAM mechanical beasts, and need to have more systematic thinking and design thinking to solve problems.

Keywords: PowerTech, STEAM contest, mechanical beast, arts' role

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Authors: Jutharat Sunprasert, Ekapong Hirunsirisawat, Narongrit Waraporn, Somporn Peansukmanee

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Metal Ship and Robotic Car is one of the hands-on activities in the course, the Fundamental of Engineering that can be divided into three parts. The first part, the metal ships, was made by using engineering drawings, physics and mathematics knowledge. The second part is where the students learned how to construct a robotic car and control it using computer programming. In the last part, the students had to combine the workings of these two objects in the final testing. This aim of study was to investigate the effectiveness of hands-on activity by integrating Science, Technology, Engineering and Mathematics (STEM) concepts to develop scientific and engineering skills. The results showed that the majority of students felt this hands-on activity lead to an increased confidence level in the integration of STEM. Moreover, 48% of all students engaged well with the STEM concepts. Students could obtain the knowledge of STEM through hands-on activities with the topics science and mathematics, engineering drawing, engineering workshop and computer programming; most students agree and strongly agree with this learning process. This indicated that the hands-on activity: “Metal Ship and Robotic Car” is a useful tool to integrate each aspect of STEM. Furthermore, hands-on activities positively influence a student’s interest which leads to increased learning achievement and also in developing scientific and engineering skills.

Keywords: hands-on activity, STEM education, computer programming, metal work

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Authors: Sunandapriya Bhikkhu, Shimo Sraman

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The main objective of this research is to analytically study the concept of Lyotard’s different that rejects the monopoly criteria and single rule with the incommensurable, which can explain about conceptual problems of beauty in the philosophy of contemporary art. In Lyotard’s idea that basic value judgment of human should be a value like a phrase that is a small unit and an individual such as the aesthetic value that to explain the art world. From the concept of the anti-war artist that rejects the concept of the traditional aesthetic which cannot be able to explain the changing in contemporary society but emphasizes the meaning of individual beauty that is at the beginning of contemporary art today. In the analysis of the problem, the researcher supports the concept of Lyotard’s different that emphasizes the artistic expression which opens the space of perception and beyond the limitations of language process. Art is like phrase or small units that can convey a sense of humanity through the aesthetic value of the individual, not social criteria or universal. The concept of Lyotard’s different awakens and challenge us to the rejection of the single rule that is not open the social space to minorities by not accepting the monopoly criteria.

Keywords: difference, Jean-Francois Lyotard, postmodern, beauty, contemporary art

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