Search results for: elementary mathematics

Authors: Preecha Yupapin And Somnath

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From the emptiness, the vibration induces the fractal, and the strings are formed. From which the first elementary particle groups, known as quarks, were established. The neutrino and electron are created by them. More elementary particles and life are formed by organic and inorganic substances. The universe is constructed, from which the multi-universe has formed in the same way. universe assumes that the intense energy has escaped from the singularity cone from the multi-universes. Initially, the single mass energy is confined, from which it is disturbed by the space-time distortion. It splits into the entangled pair, where the circular motion is established. It will consider one side of the entangled pair, where the fusion energy of the strong coupling force has formed. The growth of the fusion energy has the quantum physic phenomena, where the moving of the particle along the circumference with a speed faster than light. It introduces the wave-particle duality aspect, which will be saturated at the stopping point. It will be re-run again and again without limitation, which can say that the universe has been created and expanded. The Bose-Einstein condensate (BEC) is released through the singularity by the wormhole, which will be condensed to become a mass associated with the Sun's size. It will circulate(orbit) along the Sun. the consideration of the uncertainty principle is applied, from which the breath control is followed by the uncertainty condition ∆p∆x=∆E∆t~ℏ. The flowing in-out air into a body via a nose has applied momentum and energy control respecting the movement and time, in which the target is that the distortion of space-time will have vanished. Finally, the body is clean which can go to the next procedure, where the mind can escape from the body by the speed of light. However, the borderline between contemplation to being an Arahant is a vacuum, which will be explained.

Keywords: space-time, relativity, enlightenment, emptiness

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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: Kaine Gulozer

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A strong methodological conception in the practice of teaching, content, and language integrated learning (CLIL) is adapted to boost efficiency in the second language (L2) instruction with a range of proficiency levels. This study aims to investigate whether the incorporation of two different mediums of meaningful CLIL reading activities (in-school and out-of-school settings) influence L2 students’ development of comprehension skills differently. CLIL based instructional methodology was adopted and total of 50 preparatory year students (N=50, 25 students for each proficiency level) from two distinct language proficiency learners (elementary and intermediate) majoring in engineering faculties were recruited for the study. Both qualitative and quantitative methods through a post-test design were adopted. Data were collected through a questionnaire, a reading comprehension test and a semi-structured interview addressed to the two proficiency groups. The results show that both settings in relation to the development of reading comprehension are beneficial, whereas the impact of the reading activities conducted in school settings was higher at the elementary language level of students than that of the one conducted out-of-class settings based on the reported interview results. This study suggests that the incorporation of meaningful CLIL reading activities in both settings for both proficiency levels could create students’ self-awareness of their language learning process and the sense of ownership in successful improvements of field-specific reading comprehension. Further potential suggestions and implications of the study were discussed.

Keywords: content and language integrated learning, in-school setting, language proficiency, out-of-school setting, reading comprehension

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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: Sudhir Kumar Tewatia, Kanishck Tewatia, Anttriksh Tewatia

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Advancements in soil consolidation are discussed, and further improvements are proposed with particular reference to Tewatia’s Y-Y’ Approach, which is called the Settlement versus Rate of Settlement Approach in consolidation. A branch of calculus named Y-Y' (or y versus dy/dx) is suggested (as compared to the common X-Y', x versus dy/dx, dy/dx versus x or Newton-Leibniz branch) that solves some complicated/unsolved theoretical and practical problems in physical sciences (Physics, Chemistry, Mathematics, Biology, and allied sciences) and engineering in an amazingly simple and short manner, particularly when independent variable X is unknown and X-Y' Approach can’t be used. Complicated theoretical and practical problems in 1D, 2D, 3D Primary and Secondary consolidations with non-uniform gradual loading and irregularly shaped clays are solved with elementary school level Y-Y' Approach, and it is interesting to note that in X-Y' Approach, equations become more difficult while we move from one to three dimensions, but in Y-Y' Approach even 2D/3D equations are very simple to derive, solve, and use; rather easier sometimes. This branch of calculus will have a far-reaching impact on understanding and solving the problems in different fields of physical sciences and engineering that were hitherto unsolved or difficult to be solved by normal calculus/numerical/computer methods. Some particular cases from soil consolidation that basically creeps and diffusion equations in isolation and in combination with each other are taken for comparison with heat transfer. The Y-Y’ Approach can similarly be applied in wave equations and other fields wherever normal calculus works or fails. Soil mechanics uses mathematical analogies from other fields of physical sciences and engineering to solve theoretical and practical problems; for example, consolidation theory is a replica of the heat equation from thermodynamics with the addition of the effective stress principle. An attempt is made to give them mathematical analogies.

Keywords: calculus, clay, consolidation, creep, diffusion, heat, settlement

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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: Jerickson Abbie Flores, Jana Fragante, Jan Paolo Dipasupil, Jan Jorge Francisco

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Malnutrition is one of the rapidly growing health problems affecting the world at present. Children affected are not only at risk for significant health problems, but are also faced with psychological and social consequences, including low self-esteem. School-age children are specifically vulnerable to develop poor self-esteem especially when their peers find them physically unattractive. Thus, malnutrition, whether obesity or undernourishment, contributes a significant role to a developing child’s health and behavior. This research aims to determine if there is a significant difference on the level of self-esteem among Filipino children ages 9-12 years old with abnormal body mass index (BMI) and those children with desirable BMI. Using a cross-sectional study design, the correlation between body mass index (BMI) and self-esteem was observed among children ages 9-12 years old. Participants took the Hare self esteem questionnaire, which is specifically designed to measure self-esteem in school age children. The lowest possible score is 15 and the highest possible score is 45. A total of 1140 students with ages 9-12 years old from Cembo Elementary School (public school) participated in the study. Among the participants, 239 out of the 1140 have desirable body mass index, 878 are underweight, and 23 are overweight. Using the test questionnaire, the computed mean scores were 36.599, 36.045 and 36.583 for normal, underweight and overweight categories respectively. Using Pearson’s Correlation Test and Spearman’s Correlation Coefficient Test, the study showed positive correlation (p value of 0.047 and 0.004 respectively) between BMI and Self-esteem scores which indicates that the higher the BMI, the higher the self-esteem of the participants.

Keywords: body mass index, malnutrition, school-age children, self-esteem

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Authors: Yuliana Wahyu, Ambros Leonangung Edu

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The learning praxis that is proposed by 2013 Curriculum (K-13) is no longer school-oriented as a supply-driven, but now a demand-driven provider. This vision is connected with Jokowi-Kalla Nawacita program to create a competitive nation in the global era. Competition is a social fact that must be faced. Therefore the curriculum will design a process to be the innovators and entrepreneurs.To get this goal, K-13 implements the character education. This aims at creating the innovators and entrepreneurs from an early age (primary school). One part of strengthening it is literacy formations (reading, numeracy, science, ICT, finance, and culture). Thus, science literacy is an integral part of character education. The above outputs are only formed through the innovative process through intra-curricular (blended learning), co-curriculer (hands-on learning) and extra-curricular (personalized learning). Unlike the curriculums before that child cram with the theories dominating the intellectual process, new breakthroughs make natural, social, and cultural phenomena as learning sources. For example, Science in primary schoolsplaceBiology as the platform. And Science places natural, social, and cultural phenomena as a learning field so that students can learn, discover, solve concrete problems, and the prospects of development and application in their everyday lives. Science education not only learns about facts collection or natural phenomena but also methods and scientific attitudes. In turn, Science will form the science literacy. Science literacy have critical, creative, logical, and initiative competences in responding to the issues of culture, science and technology. This is linked with science nature which includes hands-on and minds-on. To sustain the effectiveness of science learning, K-13 opens a new way of viewing a contextual learning model in which facts or natural phenomena are drawn closer to the child's learning environment to be studied and analyzed scientifically. Thus, the topic of elementary science discussion is the practical and contextual things that students encounter. This research is about to contextualize Science in primary schools at Manggarai, NTT, by placing local wisdom as a learning source and media to form the science literacy. Explicitly, this study discovers the concept of science and mathematics in Mbaru Niang. Mbaru Niang is a forgotten potentials of the centralistic-theoretical mainstream curriculum so far. In fact, the traditional Manggarai community stores and inherits much of the science-mathematical indigenous sciences. In the traditional house structures are full of science and mathematics knowledge. Every details have style, sound and mathematical symbols. Learning this, students are able to collaborate and synergize the content and learning resources in student learning activities. This is constructivist contextual learning that will be applied in meaningful learning. Meaningful learning allows students to learn by doing. Students then connect topics to the context, and science literacy is constructed from their factual experiences. The research location will be conducted in Manggarai through observation, interview, and literature study.

Keywords: indigenous science, Mbaru Niang, science literacy, science

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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: Abrar Ajmal

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This quantitative study explored elementary school teachers' pedagogical content knowledge and effects on grade 8 students' achievement in Punjab, Pakistan. A teacher sample (N=100) rated competencies across inquiry-focused teaching, conceptual building, interaction practices and peer collaboration promotion. A student sample (N=120) self-reported academic abilities, intrinsic motivation, help-seeking and accountability. Findings reveal teachers highly endorse learner-centric strategies, although peer interaction promotion seems less common currently. Meanwhile, significant gender disparities in self-perceived expertise emerge, favouring female over male educators across all facets measured. Additionally, teachers' knowledge positively—and significantly—correlates with student achievement overall and for both genders, highlighting the importance of professional enrichment. However, female pupils demonstrate greater confidence, drive, utilization of academic support, and ownership over learning than male counterparts. Recommendations include ongoing teacher training, targeted competency building for male students and teachers, leveraging gender peer collaboration similarities, and holistic female support amid widening divides. Sustaining instructional quality through empowering, equitable practices that nurture disadvantaged and gifted learners alike can spur systemic improvements. Ultimately, the fire line confirms the interrelations between teachers' multifaceted knowledge and student success.

Keywords: pedagogical knowledge, academic achievement, teacher gender differences, student gender differences, empowering instruction

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Authors: Shukran M. Dadayev

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To author's best knowledge, in this paper, the Basic Properties and Research methods of a Fundamental Particle is studied for the first time. That's to say, Fundamental Particle has not been discovered in the Nature yet. Because Fundamental Particle consists of specific Physical, Geometrical and Internal bases. Geometrical and Internal characteristics that are considered significant for the elementary and fundamental particles aren’t basic properties, characteristics or criteria of a Fundamental Particle. Of course, completely new Physical and Visual experimental methods of Quantum mechanics and Behavioral-Physical investigations of Particles are needed to study and discover the Fundamental Particle. These are new Physical, Visual and Behavioral-Physical experimental methods for describing and discovering the Fundamental Particle in the Nature and Microworld. Fundamental Particle consists of the same Energy-Mass-Motion system and a symmetry of Energy-Mass-Motion. Fundamental Particle supplies each of the elementary particles with the same Energy-Mass-Motion system at the same time and regulates each of the particles. Fundamental Particle gives Energy, Mass and Motion to each particles at the same time, each of the Particles consists of acquired Energy-Mass-Motion system and symmetry. Energy, Mass, Motion given by the Fundamental Particle to the particles are Symmetrical Equivalent and they remain in their primary shapes in all cases. Fundamental Particle gives Energy-Mass-Motion system and symmetry consisting of different measures and functions to each of the particles. The Motion given by the Fundamental Particle to the particles is Gravitation, Gravitational Interaction not only gives Motion, but also cause Motion by attracting. All Substances, Fields and Cosmic objects consist of Energy-Mass-Motion. The Field also includes specific Mass. They are always Energetic, Massive and Active. Fundamental Particle establishes the bases of the Nature. Supplement and Regulating of all the particles existing in the Nature belongs to Fundamental Particle.

Keywords: basic properties of a fundamental particle, behavioral-physical and visual methods, energy-mass-motion system and symmetrical equivalence, fundamental particle

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Authors: Aline Giardin, Maria Rosa Chitolina

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Our research conducted in 8 different schools in the city of Rio Grande do Sul, Brazil, we can clearly see that, even in modern times, where the search for equality between men and women is already over 60 years of struggle in this world where you show Much more than two genres and in this world that is proving that sex is not just biological, are confronted with sexist and phallocentric situations in our Schools, and among our students. The sample consisted of 503 students with a mean age between 13 and 21 years. 107 students identified themselves as gay, lesbian, bisexual or transgender. The remainder was identified as heterosexual or none at all. Compared to LGBT students, transgender students faced the school's more hostile climates, while non-transgender female students were less likely to experience anti-LGBT victimization. In addition, transgender students experienced more negative experiences at school compared to students whose gender expression adhered to traditional gender norms. Transgender students were more likely to feel insecure at school, with 80.0% of transgender students reporting that they felt insecure at school because of their gender identity. Female students in our research reported lower frequencies of victimization based on sexual orientation and gender identity and were less likely to feel insecure at school. In all indicators of discrimination in school, high school students have outperformed elementary school students and have had fewer resources and supports related to LGBT. High school students reported higher rates of victimization on sexual orientation and gender expression than elementary school students. For example, about one-third (35.5%) of high school students suffered regular physical Very often) based on their sexual orientation, compared to less than a quarter (21.4%) of primary school students. The whole premise here is to perceive the phallocentrism and sexism hidden in our schools. Opposition between the sexes is not reflexive or articulates a biological fact, but a social construction.

Keywords: transgender students, school, psychological implications, discrimination

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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: Mardianto

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Education and learning are now grown rapidly. Synergy of techonology especially instructional technology in the learning activities are very big influence on the effectiveness of learning and creativity to achieve optimal results. But on the other hand there is a education value that is difficult to be articulated through character-forming technology such as honesty, discipline, hard work, heroism, and so forth. Learning strategy and storytelling from the past until today is still an option for teachers to convey the message of character values. With the material was loaded from the local culture (stories folklore), the combination of learning objectives (build character child) strategy, and traditional methods (storytelling and story), and the preservation of local culture (dig tale folklore) is critical to maintaining the nation's culture. In the context of maintaining the nation's culture, then since the age of the child at the level of government elementary school a necessity. Globalization, the internet and technology sometimes feel can displace the role of the teacher in the learning activities. To the oral tradition is a mainstay of storytelling should be maintained and preserved. This research was conducted at the elementary school in the city of Medan, North Sumatra Indonesia, with a random sampling technique, the 27 class teachers were respondents who were randomly assigned to the Madrasah Ibtdaiyah (Islamic Elementary School) both public and private. Research conducted at the beginning of 2014 refers to a curriculum that is being transformed in the environment ministry Republic Religion Indonesia. The results of this study indicate that; the declining skills of teachers to develop storytelling this can be seen from; 74.07% of teachers have never attended a special training storytelling, 85.19% no longer nasakah new stories, only 22.22% are teachers who incorporate methods of stories in the learning plan. Most teachers are no longer concerned with storytelling, among those experiencing difficulty in developing methods because the story; 66.67% of children are more interested in children's cartoons like Bobo boy, Angrybirds and others, 59.26 children prefer other activities than listening to a story. The teachers hope, folklore books should be preserved, storytelling training should be provided by the government through the ministry of religion, race or competition of storytelling should be scheduled, writing a new script-based populist storytelling should be provided immediately. The teachers’ hope certainly not excessive, by realizing the story method becomes articulation as the efforts of child character development based populist, therefore the local knowledge can be a strong fortress facing society in the era of progress as at present, and future.

Keywords: story telling, local wisdom, education, technology development

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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: Reiko Yamamoto

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This paper reports on how synchrony occurs between children and their teacher, and what prevents or facilitates synchrony. The aim of the experiment conducted in this study was to precisely analyze their movements and synchrony and reveal the process of synchrony in a real-world classroom. Specifically, the experiment was conducted for around 20 minutes during an English as a foreign language (EFL) lesson. The participants were 11 fourth-grade school children and their classroom teacher in a public elementary school in Japan. Previous researchers assert that synchrony causes the state of flow in a class. For checking the level of flow, Short Flow State Scale (SFSS) was adopted. The experimental procedure had four steps: 1) The teacher read aloud the first half of an English storybook to the children. Both the teacher and the children were at their own desks. 2) The children were subjected to an SFSS check. 3) The teacher read aloud the remaining half of the storybook to the children. She made the children remove their desks before reading. 4) The children were again subjected to an SFSS check. The movements of all participants were recorded with a video camera. From the movement analysis, it was found that the children synchronized better with the teacher in Step 3 than in Step 1, and that the teacher’s movement became free and outstanding without a desk. This implies that the desk acted as a barrier between the children and the teacher. Removal of this barrier resulted in the children’s reactions becoming synchronized with those of the teacher. The SFSS results proved that the children experienced more flow without a barrier than with a barrier. Apparently, synchrony is what caused flow or social emotions in the classroom. The main conclusion is that synchrony leads to cognitive outcomes such as children’s academic performance in EFL learning.

Keywords: engagement in a class, English as a foreign language (EFL) learning, interactional synchrony, social emotions

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Authors: Pál Iván Szontagh

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We suppose that today, the motivation for the career of a pedagogue (including its existential, organizational and infrastructural conditions) is different from the level of commitment to the profession of an educator (which can be experienced informally, or outside of the public education system). In our research, we made efforts to address the widest possible range of student elementary teachers, and to interpret their responses using different filters. In the first phase of our study, we analyzed first-year kindergarten teacher students’ career motivation and commitment to the profession, and in the second phase, that of final-year kindergarten teacher candidates. In the third phase, we conducted surveys to explore students’ motivation for the profession and the career path of a pedagogue in four countries of the Carpathian Basin (Hungary, Slovakia, Romania and Serbia). The surveys were conducted in 17 campuses of 11 Hungarian teacher’s training colleges and universities. Finally, we extended the survey to practicing graduates preparing for their on-the-job rating examination. Based on our results, in all breakdowns, regardless of age group, training institute or - in part - geographical location and nationality, it is proven that lack of social- and financial esteem of the profession poses serious risks for recruitment and retention of teachers. As a summary, we searched for significant differences between the professional- and career motivations of the three respondent groups (kindergarten teacher students, elementary teacher students and practicing teachers), i.e. the motivation factors that change the most with education and/or with the time spent on the job. Based on our results, in all breakdowns, regardless of age group, training institute or - in part - geographical location and nationality, it is proven that lack of social- and financial esteem of the profession poses serious risks for recruitment and retention of teachers.

Keywords: career motivation, career socialization, professional motivation, teacher training

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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

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Authors: Peter Akayuure

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Geometry is considered an important strand in mathematics due to its wide-ranging utilitarian value and because it serves as a building block for understanding other aspects of undergraduate mathematics, including algebra and calculus. Matters regarding students’ geometric thinking have therefore long been pursued by mathematics researchers and educators globally via different theoretical lenses, curriculum reform efforts, and innovative instructional practices. However, so far, studies remain inconclusive about the instructional platforms that effectively promote geometric thinking. At the University of Education, Winneba, an undergraduate geometry course was designed and delivered on UEW Learning Management System (LMS) using Moodle platform. This study utilizes van Hiele’s theoretical lens to examine the entry and exit’s geometric thinking behaviours of prospective teachers who took the undergraduate geometry course in the LMS platform. The study was a descriptive survey that involved an intact class of 280 first-year students enrolled to pursue a bachelor's in mathematics education at the university. The van Hiele’s Geometric thinking test was used to assess participants’ entry and exit behaviours, while semi-structured interviews were used to obtain data for triangulation. Data were analysed descriptively and displayed in tables and charts. An Independent t-test was used to test for significant differences in geometric thinking behaviours between those who entered the university with a diploma certificate and with senior high certificate. The results show that on entry, more than 70% of the prospective teachers operated within the visualization level of van Hiele’s geometric thinking. Less than 20% reached analysis and abstraction levels, and no participant reached deduction and rigor levels. On exit, participants’ geometric thinking levels increased markedly across levels, but the difference from entry was not significant and might have occurred by chance. The geometric thinking behaviours of those enrolled with diploma certificates did not differ significant from those enrolled directly from senior high school. The study recommends that the design principles and delivery of undergraduate geometry course via LMS should be structured and tackled using van Hiele’s geometric thinking levels to serve as means of bridging the existing learning gaps of undergraduate students.

Keywords: geometric thinking, van Hiele’s, UEW learning management system, undergraduate geometry

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Authors: Bernardita Tornero

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Cognitive Acceleration in Mathematics Education (CAME) programmes have been used successfully for promoting the development of thinking skills in school students for the last 30 years. Given that the approach has had a tremendous impact on the thinking capabilities of participating students, this study explored the experience of using the programme with prospective primary teachers in Chile. Therefore, this study not only looked at the experience of prospective primary teachers during the CAME course as learners, but also examined how they perceived the approach from their perspective as future teachers, as well as how they could transfer the teaching strategies they observed to their future classrooms. Given the complexity of the phenomenon under study, this research used a mixed methods approach. For this reason, the impact that the CAME course had on prospective teachers’ thinking skills was not only approached by using a test that assessed the participants’ improvements in these skills, but their learning and teaching experiences were also recorded through qualitative research tools (learning journals, interviews and field notes). The main findings indicate that, at the end of the CAME course, prospective teachers not only demonstrated higher thinking levels, but also showed positive attitudinal changes towards teaching and learning in general, and towards mathematics in particular. The participants also had increased confidence in their ability to teach mathematics and to promote thinking skills in their students. In terms of the CAME methodology, prospective teachers not only found it novel and motivating, but also commented that dealing with the thinking skills topic during a university course was both unusual and very important for their professional development. This study also showed that, at the end of the CAME course, prospective teachers felt they had developed strategies that could be used in their classrooms in the future. In this context, the relevance of the study is not only that it described the impact and the positive results of the first experience of using a CAME approach with prospective teachers, but also that some of the conclusions have significant implications for the teaching of thinking skills and the training of primary school teachers.

Keywords: cognitive acceleration, formal reasoning, prospective teachers, initial teacher training

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Authors: Hong Lu, Xin Chen, Zhengcheng Fan

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Prior research has claimed a close association between handwriting and mathematics attainment with the help of spatial cognition. However, the exact mechanism behind this relationship remains un-investigated. Focusing on visual-motor integration (VMI), one critical spatial skill, this meta-analysis aims to estimate the size of the handwriting- visual-motor integration relationship and examine the moderating effect of handwriting dimensions on the link. With a random effect model, a medium relation (r=.26, 95%CI [.22, .30]) between handwriting and VMI was summarized in 38 studies with 55 unique samples and 141 effect sizes. Findings suggested handwriting dimensions significantly moderated the handwriting- VMI relationship, with handwriting legibility showing a substantial correlation with VMI, but neither handwriting speed nor pressure. Identifying the essential relationship between handwriting legibility and VMI, this study adds to the literature about the key cognitive processing needs underlying handwriting, and spatial cognition thus highlights the cognitive mechanism regarding handwriting, spatial cognition, and mathematics performances.

Keywords: handwriting, visual-motor integration, legibility, meta-analysis

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Authors: Dairo Jose Hernandez Paez

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The quantum theory of atoms in molecules (QTAIM) allows us to obtain topological information on electronic density in quantum mechanical systems. The QTAIM starts by considering the electron density as a continuous mathematical object. On the other hand, the discretization of electron density is also a mathematical object, which, from discrete mathematics, would allow a new approach to its topological study. From this point of view, it is necessary to develop a series of steps that provide the theoretical support that guarantees its application. Some of the steps that we consider most important are mentioned below: (1) obtain good representations of the electron density through computational calculations, (2) design a methodology for the discretization of electron density, and construct the simplicial complex. (3) Make an analysis of the discrete vector field associating the simplicial complex. (4) Finally, in this research, we propose to use the discrete Morse theory as a mathematical tool to carry out studies of electron density topology.

Keywords: discrete mathematics, Discrete Morse theory, electronic density, computational calculations

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Authors: M. Richichi

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Evidencing the learning and developmental needs of students in specific educational institutions is central to determining the type of whole school pedagogical shift required. Initiating this transition by designing and implementing STEAM (Science, technology, engineering, art, and mathematics) project-based learning opportunities, in collaboration with industry, exposes teachers to new pedagogical and assessment practices. This experience instills confidence and a renewed sense of energy, which contributes to greater efficacy. Championing teachers in such learning environments leads to “bleeding” of inventive pedagogical understanding and skills as well as motivation. This contributes positively to collective teacher efficacy and the transition towards more cross-disciplinary initiatives and opportunities, and hence an innovative pedagogical shift. Evidence of skill and knowledge development in students, combined with greater confidence, work ethic and interest in STEAM areas, are further indicators of the success of the transitioning process.

Keywords: efficacy, pedagogy, transition, STEAM

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Authors: Komon Paisal

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The purposes of this research were (1) to create a learning activity for constructivism, (2) study the Mathematical Analysis courses learning achievement, and (3) study students’ attitude toward the learning activity for constructivism. The samples in this study were divided into 2 parts including 3 Mathematical Analysis courses instructors of Suan Sunandha Rajabhat University who provided basic information and attended the seminar and 17 Mathematical Analysis courses students who were studying in the academic and engaging in the learning activity for constructivism. The research instruments were lesson plans constructivism, subjective Mathematical Analysis courses achievement test with reliability index of 0.8119, and an attitude test concerning the students’ attitude toward the Mathematical Analysis courses learning activity for constructivism. The result of the research show that the efficiency of the Mathematical Analysis courses learning activity for constructivism is 73.05/72.16, which is more than expected criteria of 70/70. The research additionally find that the average score of learning achievement of students who engaged in the learning activities for constructivism are equal to 70% and the students’ attitude toward the learning activity for constructivism are at the medium level.

Keywords: constructivism, learning management, mathematics analysis courses, learning activity

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Authors: Jitendra Sharma

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Here a Homogeneous Charge is used as in a spark-ignited engine, but the charge is compressed to auto ignition as in a diesel. The main difference compared with the Spark Ignition (SI) engine is the lack of flame propagation and hence the independence from turbulence. Compared with the diesel engine. HCCI has a homogeneous charge and have no problems associated with soot and Nox but HC and CO were higher than in SI mode. It was not possible to achieve high IMEP (Indicated Mean Effective Pressure) values with HCCI. The Homogeneous charge compression ignition (HCCI) is an attractive technology because of its high efficiency and low emissions. However, HCCI lakes a direct combustion trigger making control of combustion timing challenging, especially during transients. To aid in HCCI engine control we present a simple model of the HCCI combustion process valid over a range of intake pressures, intake temperatures, equivalence ratios and engine speeds. HCCI a new combustion technology that may develop as an alternative to diesel engines with high efficiency and low Knox and particulate matter emissions. The homogenous charge compression ignition (HCCI) is a promising new engine technology that combines elements of the diesel and gasoline engine operating cycles. HCCI as a way to increase the efficiency of the gasoline engine. The attractive properties are increased fuel efficiency due to reduced throttling losses, increased expansion ratio and higher thermodynamic efficiency. With the advantages there are some mechanical limitations to the operation of the HCCI engine. The implementation of homogenous charge compression ignition (HCCI) to gasoline engines is constrained by many factors. The main drawback of HCCI is the absence of direct combustion timing control. Therefore all the right conditions for auto ignition have to be set before combustion starts. This paper describes the past and current research done on HCCI engine. Many research got considerable success in doing detailed modeling of HCCI combustion. This paper aims at studying the fundamentals of HCCI combustion, the strategy to control the limitation of HCCI engine.

Keywords: HCCI, diesel engine, combustion, elementary investigation

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