Search results for: mathematics competences

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: 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: Sabine A. Zauchner-Studnicka

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As the term indicates, reverse-mentoring flips the classical roles of mentoring: In school, students take over the role of mentors for adults, i.e. teachers or parents. Originally reverse-mentoring stems from US enterprises, which implemented this innovative method in order to benefit from the resources of skilled younger employees for the enhancement of IT competences of senior colleagues. However, reverse-mentoring in schools worldwide is rare. Based on empirical studies and theoretical approaches, in this article an implementation model for reverse-mentoring is developed in order to bring the significant potential reverse-mentoring has for education into practice.

Keywords: reverse-mentoring, innovation in education, implementation model, school education

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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: 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: T. Konst

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Most jobs include training and communication tasks, but often the people in these jobs lack pedagogical competences to plan, implement and assess learning. This paper aims to discuss how a learning approach called innovation pedagogy developed in higher education can be utilized for learning development in various organizations. The methods presented how to implement innovation pedagogy such as process consultation and train the trainer model can provide added value to develop pedagogical knowhow in organizations and thus support their internal learning and development.

Keywords: innovation pedagogy, learning, organizational development, process consultation

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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: 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: A. Vahanyan

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The paper touches upon the problem of revision and modernization of the current curriculum on translation studies at the Armenian Higher Education Institutions (HEIs). In the contemporary world where quality and speed of services provided are mostly valued, certain higher education centers in Armenia though do not demonstrate enough flexibility in terms of the revision and amendment of courses taught. This issue is present for various curricula at the university level and Translation Studies related curriculum, in particular. Technological innovations that are of great help for translators have been long ago smoothly implemented into the global Translation Industry. According to the European Master's in Translation (EMT) framework, translation service provision comprises linguistic, intercultural, information mining, thematic, and technological competencies. Therefore, to form the competencies mentioned above, the curriculum should be seriously restructured to meet the modern education and job market requirements, relevant courses should be proposed. New courses, in particular, should focus on the formation of technological competences. These suggestions have been made upon the author’s research of the problem across various HEIs in Armenia. The updated curricula should include courses aimed at familiarization with various computer-assisted translation (CAT) tools (MemoQ, Trados, OmegaT, Wordfast, etc.) in the translation process, creation of glossaries and termbases compatible with different platforms), which will ensure consistency in translation of similar texts and speeding up the translation process itself. Another aspect that may be strengthened via curriculum modification is the introduction of interdisciplinary and Project-Based Learning courses, which will enable info mining and thematic competences, which are of great importance as well. Of course, the amendment of the existing curriculum with the mentioned courses will require corresponding faculty development via training, workshops, and seminars. Finally, the provision of extensive internship with translation agencies is strongly recommended as it will ensure the synthesis of theoretical background and practical skills highly required for the specific area. Summing up, restructuring and modernization of the existing curricula on Translation Studies should focus on three major aspects, i.e., introduction of new courses that meet the global quality standards of education, professional development for faculty, and integration of extensive internship supervised by experts in the field.

Keywords: competencies, curriculum, modernization, technical literacy, translation studies

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Authors: Abdullah Abu-Tineh, Carol Murphy, Nigel Calder, Nasser Mansour

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This paper reports on an aspect of e-learning in developing inquiry-based learning (IBL). We present data on the views of teachers and students in Qatar following a professional development programme intended to help teachers implement IBL in their science and mathematics classrooms. Key to this programme was the use of WebQuests. Views of the teachers and students suggested that WebQuests helped students to develop technical skills, work collaboratively and become independent in their learning. The use of WebQuests also enabled a combination of digital and non-digital tools that helped students connect ideas and enhance their understanding of topics.

Keywords: digital technology, inquiry-based learning, mathematics and science education, professional development

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Authors: Tian Luo, Wing Mui Winnie So

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Gaining career awareness in STEM is an important educational outcome in STEM education. While many studies focused on students’ understanding of scientists and engineers, very few studies explore students’ perceptions of technologists as a group of STEM professionals. In this study, 300 valid surveys which include drawing task and follow-up questions about technologist were collected from 4th to 6th grade students. The results showed that 75.1% of the students draw a technologist as a male and 19.3% draw a technologist as a female. Most students believe that technologists use math, science or engineering in their work and can name a few categories of technologists. The drawings also showed that students tend to present technologists as people who work with a computer.

Keywords: STEM (Science, Technology, Engineering, and Mathematics) education, elementary students, technologist, STEM careers

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Authors: Denise Levy, Anna Lucia C. H. Villavicencio

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In a rapid-changing world, science teachers face considerable challenges. In addition to the basic curriculum, there must be included several transversal themes, which demand creative and innovative strategies to be arranged and integrated to traditional disciplines. In Brazil, nuclear science is still a controversial theme, and teachers themselves seem to be unaware of the issue, most often perpetuating prejudice, errors and misconceptions. This article presents the authors’ experience in the development of an interdisciplinary pedagogical proposal to include nuclear science in the basic curriculum, in a transversal and integrating way. The methodology applied was based on the analysis of several normative documents that define the requirements of essential learning, competences and skills of basic education for all schools in Brazil. The didactic materials and resources were developed according to the best practices to improve learning processes privileging constructivist educational techniques, with emphasis on active learning process, collaborative learning and learning through research. The material consists of an illustrated book for students, a book for teachers and a manual with activities that can articulate nuclear science to different disciplines: Portuguese, mathematics, science, art, English, history and geography. The content counts on high scientific rigor and articulate nuclear technology with topics of interest to society in the most diverse spheres, such as food supply, public health, food safety and foreign trade. Moreover, this pedagogical proposal takes advantage of the potential value of digital technologies, implementing QR codes that excite and challenge students of all ages, improving interaction and engagement. The expected results include the education of the educators for nuclear science communication in a transversal and integrating way, demystifying nuclear technology in a contextualized and significant approach. It is expected that the interdisciplinary pedagogical proposal contributes to improving attitudes towards knowledge construction, privileging reconstructive questioning, fostering a culture of systematic curiosity and encouraging critical thinking skills.

Keywords: science education, interdisciplinary learning, nuclear science, scientific literacy

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Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

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Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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Authors: Olga Shvetsova

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The research paper contains the different issues of competence management in innovation companies. The theoretical bases of human resources management and practical issues of innovative enterprises’ competitiveness are considered. The research is focused on the modern innovative enterprise management problems; it focuses on the effective management of the personnel of innovative enterprises on the basis of competence approach. The concept of core competence approach is discussed. The point of view, that the key competences of the company create the competitive advantages, support strategy development and protect business from external negative factors is considered. The used methodology is background research.

Keywords: competence model, competitiveness, innovation management, implementation

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Authors: Iryna Shevchenko

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The science of mathematics was originated at the order of count of objects and subsequently for the measurement of size and quality of objects using the logical or abstract means. The laws of mathematics are based on the study of absolute values. The number 0 or "nothing" is the purely logical (as the opposite to absolute) value as the "nothing" should always assume the space for the something that had existed there; otherwise the "something" would never come to existence. In this work we are going to prove that the number "0" is the abstract (logical) and not an absolute number and it has the absolute value of “∞” (infinity). Therefore, the number "0" might not stand in the row of numbers that symbolically represents the absolute values, as it would be the mathematically incorrect. The symbolical value of number "0" in the row of numbers could be represented with symbol "∞" (infinity). As a result, we have the mathematical row of numbers: epsilon, ...4, 3, 2, 1, ∞. As the conclusions of the theory of number “0” we presented the statements: multiplication and division by fractions of numbers is illegal operation and the mathematical division by number “0” is allowed.

Keywords: illegal operation of division and multiplication by fractions of number, infinity, mathematical row of numbers, theory of number “0”

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: Jeansou Moun

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This study argues that constructivism and structuralism, which have been the two important schools of mathematical philosophy since the mid-19th century, can and should be synthesized into structure-constructivism. In fact, the philosophy of mathematics is divided into more than ten schools depending on the point of view. However, the biggest trend is Platonism which claims that mathematical objects are "abstract entities" that exists independently of the human mind and material objects. Its opposite is constructivism. According to the latter, mathematical objects are products of the construction of the human mind. However, whether the basis of the construction is a logical device, a symbolic system, or an empirical perception, it is subdivided into logicism, formalism, and intuitionism. However, these three schools themselves are further subdivided into various variants, and among them, structuralism, which emerged in the mid-20th century, is receiving the most attention. On the other hand, structuralism which emphasizes structure instead of individual objects, is divided into non-eliminative structuralism, which supports the a priori of structure, and non-eliminative structuralism, which rejects any abstract entity. In this context, it is believed that the structure itself is not an a priori entity but a result of the construction of the cognitive subject and that no object has ever been given to us in its full meaning from the outset. In other words, concepts are progressively structured through a dialectical cycle between sensory perception, imagination (abstraction), concepts, judgments, and reasoning. Symbols are needed for formal operation. However, without concrete manipulation, the formal operation cannot have any meaning. However, when formal structurization is achieved, the reality (object) itself is also newly structured. This is the "structure-constructivism".

Keywords: philosophy of mathematics, platonism, logicism, formalism, constructivism, structuralism, structure-constructivism

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Authors: Catarina Maria Neto Da Cruz, Ana Maria Reis D’Azevedo Breda

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The world is changing and, consequently, the young people need more sophisticated tools and skills to lead with the world’s complexity. The Organisation for Economic Co-operation and Development Learning Framework 2030 suggests an interdisciplinary knowledge as a principle for the future of education systems. In the curricular document Portuguese about the profile of students leaving compulsory education, the critical thinking and creative thinking are pointed out as skills to be developed, which imply the interconnection of different knowledge, applying it in different contexts and learning areas. Unlike primary school teachers, teachers specialized in a specific area lead to more difficulties in the implementation of interdisciplinary approaches in the classrooms and, despite the effort, the interdisciplinarity is not a common practice in schools. Statement like "Mathematics is everywhere" is unquestionable, however, many math teachers show difficulties in presenting such evidence in their classes. Mathematical modelling and problems in real contexts are promising in the development of interdisciplinary pedagogical practices and in Portugal there is a continuous training offer to contribute to the development of teachers in terms of their pedagogical approaches. But when teachers find themselves in the classroom, without a support, do they feel able to implement interdisciplinary practices? In this communication we will try to approach this issue through a case study involving a group of Mathematics teachers, who attended a training aimed at stimulating interdisciplinary practices in real contexts, namely related to the COVID-19 pandemic.

Keywords: education, mathematics, teacher training, interdisciplinarity

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Authors: Fahad Suleiman

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Agriculture has been the mainstay of the nation’s economy in Nigeria. It provides food for the ever rapidly increasing population and raw materials for the industries. People especially the rural dwellers are gainfully employed on their crop farms and small-scale livestock farms for income earning. In farming, availability of funds and time management are one of the major factors that influence the system of farming in Nigeria in which mathematical science knowledge was highly required in order for farms to be managed effectively. Farmers often applied mathematics, almost every day for a variety of tasks, ranging from measuring and weighing, to land marking. This paper, therefore, explores some of the ways math is used in farming. For instance, farmers use arithmetic variety of farm activities such as seed planting, harvesting crop, cultivation and mulching. It is also important in helping farmers to know how much their livestock weighs, how much milk their cows produce and crop yield per acres, among others.

Keywords: agriculture, application, economic, farming, mathematics

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Authors: Nasser Mansour, Ziad Said, Abdullah Abu-Tineh

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STEM teachers face the challenge of possessing expertise not only in their subject disciplines but also in the pedagogical knowledge required for integrated STEM lessons. However, research reveals a lack of pedagogical competencies related to project-based learning (PBL) in the STEM context. To bridge this gap, the study examines teachers' competencies and self-efficacy in TPACK (Technological Pedagogical Content Knowledge) and its specific integration with PBL and STEM content. Data from 245 specialized science and math teachers were collected using a questionnaire. The study emphasizes the importance of addressing gender disparities, supporting formal teacher education, and recognizing the expertise and experiences of STEM teachers in effective technology integration. The findings indicate that gender plays a role in self-efficacy beliefs, with females exhibiting higher confidence in pedagogical knowledge and males demonstrating higher confidence in technological knowledge. Teaching experience and workload factors have a limited impact on teachers' Technological Pedagogical Content Knowledge (TPACK). These findings enhance our understanding of contextual factors impacting science and math teachers' self-efficacy in utilizing TPACK for STEM and PBL. They inform the development of targeted interventions, professional development programs, and support systems to enhance teachers' competencies and self-efficacy in TPACK for teaching science and Mathematics through STEM and PBL.

Keywords: technological pedagogical content knowledge, TPACK, STEM, project-based learning, PBL, self-efficacy, mathematics, science

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Authors: J. Thiele

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Teachers working at vocational Colleges are often confronted with the problem, that many students graduated from different schools and therefore each had a different education. Especially in mathematics many students lack fundamentals or had different priorities at their previous schools. Furthermore, these vocational Colleges have to provide Graduations for many different working-fields, with different core themes. The Colleges are interested in measuring the different Education levels of their students and providing assistance for those who need to catch up. The Project mathe-meistern was initiated to remedy this problem at vocational Colleges. For this purpose, online-tests were developed. The aim of these tests is to evaluate basic mathematical abilities of the students. The tests are online Multiple-Choice-Tests with a total of 65 Items. They are accessed online with a unique Transaction-Number (TAN) for each participant. The content is divided in several Categories (Arithmetic, Algebra, Fractions, Geometry, etc.). After each test, the student gets a personalized summary depicting their strengths and weaknesses in mathematical Basics. Teachers can visit a special website to examine the results of their classes or single students. In total 5830 students did participate so far. For standardization and optimization purposes the tests are being evaluated, using the classic and probabilistic Test-Theory regarding Objectivity, Reliability and Validity, annually since 2015. This Paper is about the Optimization process considering the Rasch-scaling and Standardization of the tests. Additionally, current results using standardized tests will be discussed. To achieve this Competence levels and Types of errors of students attending vocational Colleges in Nordrheinwestfalen, Germany, were determined, using descriptive Data and Distractorevaluations.

Keywords: diagnostical tests in mathematics, distractor devaluation, test-optimization, test-theory

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Authors: Robert Vanderburg, Michael Cowling, Nicholas Gibson

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Mathematics is one of the core subjects taught in the Australian K-12 education system and is considered an important component for future studies in areas such as engineering and technology. In addition to this, Australia has been a world leader in distance education due to the vastness of its geographic landscape. Despite this, research is still needed on distance math instruction. Even though delivery of curriculum has given way to online studies, and there is a resultant push for computer-based (PC, tablet, smartphone) math instruction, much instruction still involves practice problems similar to those original curriculum packs, without the ability for students to self-regulate their learning using the full interactive capabilities of these devices. Given this need, this paper addresses issues students have during online instruction. This study consists of 32 students struggling with mathematics enrolled in a math tutorial conducted in an online setting. The study used a case study design to understand some of the blockades hindering the students’ success. Data was collected by tracking students practice and quizzes, tracking engagement of the site, recording one-on-one tutorials, and collecting data from interviews with the students. Results revealed that when students have cognitively straining tasks in an online instructional setting, the first thing to dissipate was their ability to self-regulate. The results also revealed that instructors could ameliorate the situation and provided useful data on strategies that could be used for designing future online tasks. Specifically, instructors could utilize cognitive dissonance strategies to reduce the cognitive drain of the tasks online. They could segment the instruction process to reduce the cognitive demands of the tasks and provide in-depth self-regulatory training, freeing mental capacity for the mathematics content. Finally, instructors could provide specific scheduling and assignment structure changes to reduce the amount of student centered self-regulatory tasks in the class. These findings will be discussed in more detail and summarized in a framework that can be used for future work.

Keywords: digital education, distance education, mathematics education, self-regulation

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Authors: Blanco T. F., Fernández-López A.

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Nowadays, education, motivated by the new demands of the 21st century, acquires a dimension that converts the skills that new generations may need into a huge and uncertain set of knowledge too broad to be entirety covered. Within this set, and as tools to reach them, we find Learning and Knowledge Technologies (LKT). Thus, in order to prepare students for an everchanging society in which the technological boom involves everything, it is essential to develop digital competence. Nevertheless LKT seems not to have found their place in the educational system. This work is aimed to go a step further in the research of the most appropriate procedures and resources for technological integration in the classroom. The main objective of this exploratory study is to analyze the didactic suitability (epistemic, cognitive, affective, interactional, mediational and ecological) for teaching and learning processes of mathematics with robotics and 3D printing. The analysis carried out is drawn from a STEAM (Science, Technology, Engineering, Art and Mathematics) project that has the Pilgrimage way to Santiago de Compostela as a common thread. The sample is made up of 25 Primary Education students (10 and 11 years old). A qualitative design research methodology has been followed, the sessions have been distributed according to the type of technology applied. Robotics has been focused towards learning two-dimensional mathematical notions while 3D design and printing have been oriented towards three-dimensional concepts. The data collection instruments used are evaluation rubrics, recordings, field notebooks and participant observation. Indicators of didactic suitability proposed by Godino (2013) have been used for the analysis of the data. In general, the results show a medium-high level of didactic suitability. Above these, a high mediational and cognitive suitability stands out, which led to a better understanding of the positions and relationships of three-dimensional bodies in space and the concept of angle. With regard to the other indicators of the didactic suitability, it should be noted that the interactional suitability would require more attention and the affective suitability a deeper study. In conclusion, the research has revealed great expectations around the combination of teaching-learning processes of mathematics and LKT. Although there is still a long way to go in terms of the provision of means and teacher training.

Keywords: 3D printing, didactic suitability, educational design, robotics

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Authors: Giovanna Bimonte, Luigi Senatore, Francesco Saverio Tortoriello, Ilaria Veronesi

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The education process considers capabilities not only to be seen as a means to a certain end but rather as an effective purpose. Sen's capability approach challenges human capital theory, which sees education as an ordinary investment undertaken by individuals. A complex reality requires complex thinking capable of interpreting the dynamics of society's changes to be able to make decisions that can be rational for private, ethical and social contexts. Education is not something removed from the cultural and social context; it exists and is structured within it. In Italy, the "Mathematical High School Project" is a didactic research project is based on additional laboratory courses in extracurricular hours where mathematics intends to bring itself in a dialectical relationship with other disciplines as a cultural bridge between the two cultures, the humanistic and the scientific ones, with interdisciplinary educational modules on themes of strong impact in younger life. This interdisciplinary mathematics presents topics related to the most advanced technologies and contemporary socio-economic frameworks to demonstrate how mathematics is not only a key to reading but also a key to resolving complex problems. The recent developments in mathematics provide the potential for profound and highly beneficial changes in mathematics education at all levels, such as in socio-economic decisions. The research project is built to investigate whether repeated interactions can successfully promote cooperation among students as rational choice and if the skill, the context and the school background can influence the strategies choice and the rationality. A Laboratory on Game Theory as mathematical theory was conducted in the 4th year of the Mathematical High Schools and in an ordinary scientific high school of the Scientific degree program. Students played two simultaneous games of repeated Prisoner's Dilemma with an indefinite horizon, with two different competitors in each round; even though the competitors in each round will remain the same for the duration of the game. The results highlight that most of the students in the two classes used the two games with an immunization strategy against the risk of losing: in one of the games, they started by playing Cooperate, and in the other by the strategy of Compete. In the literature, theoretical models and experiments show that in the case of repeated interactions with the same adversary, the optimal cooperation strategy can be achieved by tit-for-tat mechanisms. In higher education, individual capacities cannot be examined independently, as conceptual framework presupposes a social construction of individuals interacting and competing, making individual and collective choices. The paper will outline all the results of the experimentation and the future development of the research.

Keywords: game theory, interdisciplinarity, mathematics education, mathematical high school

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

Procedia PDF Downloads 259

Authors: Anita Kéri

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With the outbreak of the global pandemic of COVID-19, online education characterizes today’s higher education. For some higher education institutions (HEIs), the shift from classroom education to online solutions was swift and smooth, and students are continuously asked about their experience regarding online education. Therefore, there is a growing emphasis on student satisfaction with online education, a field that had emerged previously, but has become the center of higher education and research interest today. The aim of the current paper is to give a brief overview of the tools used in the online education of marketing-related classes at the examined university and to investigate student satisfaction with the applied teaching methodologies with the tool of a questionnaire. Results show that students are most satisfied with their teachers’ competences and preparedness, while they are least satisfied with online class quality, where it seems that further steps are needed to be taken.

Keywords: netnography, online teaching, pandemic, satisfaction

Procedia PDF Downloads 143