Search results for: playing with mathematics

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: Young Ik Suh, Sanghak Lee, Tywan G. Martin

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An increasing number of athletes, across all sports, are moving from their home countries to play in foreign countries. The migration of athletes, coaches, managers, and administrators within and between nations is an important aspect of the social and cultural changes taking place in modern, global sports. It is especially important to understand the context of these migrations as they are critical factors in the successful development of sports policies. In previous decades, efforts have been made to understand the motives of migrating athletes from a variety of sports, including rugby, cricket, baseball, and soccer. These studies focused on the athletes’ motivations, experiences as migrants, and recruit process. However, few studies have been conducted in order to understand athletes’ constraints of migration. The concept of constraints in leisure studies refers to the barriers that exist between an individual’s desire for participation and an individual’s real participation. The study of constraints is not a new topic in the fields of sports and recreation. In addition to understanding the motives that drive athletes to work or play in foreign countries, it is also important to recognize that negative dimensions exist that stop some athletes from migrating. Furthermore, little research has explored what makes athletes consider playing in small and unknown volleyball markets, such as the Korean Volleyball League (V-League). The V-League is a professional men’s and women’s volleyball league, started in 2005. It consists of seven men’s clubs, and six women’s clubs and each team has one foreign player. In addition, several limitations are placed on the foreign players, such as on height, position, and salary to play in the V-League. Thus, the main focus of the present research is to understand why foreign athletes (e.g., European, American, Brazil, etc.) are attracted to the V-League, which has a smaller market compared to its neighbors (i.e., China, Japan, and The Philippines). In addition, the current study seeks to identify the negative factors that prevent athletes from playing in the V-League. The participants for this study will be foreign volleyball players participating in the V-League. The investigators will provide a brief introduction to this study and inform the potential participants that they can choose whether to participate in this study. In terms of theoretical saturation, at least 12 participants are generally an adequate number to reach saturation, if they belong to a relatively homogenous group based on culture and ethnicity. This study utilizes a qualitative approach in order to understand the migration experiences foreign volleyball athletes playing in the V-League. The proposed study represents ongoing research to support work conducted by the investigators to understand the possible motivations and constraints for foreign volleyball players playing in the V-League. In addition, significant contributions to scholarship in the field of sports, psychology, and coaching studies will be an outcome of this study along with additions to the body of knowledge in several disciplines, including psychology, sociology, and social work.

Keywords: athletes’ migration, motivation, constraints, volleyball

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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: Maja Ruzic-Baf, Mirjana Radetic-Paic

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The use of computers by children has many positive aspects, including the development of memory, learning methods, problem-solving skills and the feeling of one’s own competence and self-confidence. Playing on line video games can encourage hanging out with peers having similar interests as well as communication; it develops coordination, spatial relations and presentation. On the other hand, the Internet enables quick access to different information and the exchange of experiences. How kids use computers and what the negative effects of this can be depends on various factors. ICT has improved and become easy to get for everyone. In the past 12 years so many video games has been made even to that level that some of them are free to play. Young people, even some adults, had simply start to forget about the real outside world because in that other, digital world, they have found something that makes them feal more worthy as a man. This article present the use of ICT, forms of behavior and addictions to on line video games. The use of computers by children has many positive aspects, including the development of memory, learning methods, problem-solving skills and the feeling of one’s own competence and self-confidence. Playing on line video games can encourage hanging out with peers having similar interests as well as communication; it develops coordination, spatial relations and presentation. On the other hand, the Internet enables quick access to different information and the exchange of experiences. How kids use computers and what the negative effects of this can be depends on various factors. ICT has improved and become easy to get for everyone. In the past 12 years so many video games has been made even to that level that some of them are free to play. Young people, even some adults, had simply start to forget about the real outside world because in that other, digital world, they have found something that makes them feal more worthy as a man. This article present the use of ICT, forms of behavior and addictions to on line video games.

Keywords: addiction to video games, behaviour, ICT, young people

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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: 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: 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: 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: Prerna Mohan Saxena, Avni Joshi, Raju K Parasher

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Disability is a state of decreased functioning associated with disease, disorder, injury, or other health condition, which in the context of one’s environment is experienced as an impairment, activity limitation, or participation restriction. With the concept of disability evolving over the years, the current ICF model of disability has integrated this concept into a comprehensive whole of multiple dimensions of human functioning, including biological, psychological, social, and environmental aspects. Wheelchair basketball is one of the greatest examples of adapted sports for the disabled. Through this study, we aim to evaluate the functional performance and self-esteem levels in differently-abled pediatric wheelchair basketball players, providing an insight on their abilities and deficits and how they can be worked on at a larger level to improve overall performance. The study was conducted on 9 pediatric wheelchair basketball players at Amar Jyoti school for inclusive education Delhi their physical performance was assessed using a battery of tests, and physical self esteem was assessed using the Physical self-description instrument (PSDQ-S). Results showed that 9 participants age ranged between 10-21 years, mostly males with BMI ranging between 16.7 to 28.9 kg/m2 most of them had the experience of 5 to 6 years of playing the sport. The data showed physical performance in accordance to years of experience of playing, physical self esteem showed a different perspective, with experience players scoring less on it. This study supports a multidimensional construct of physical performance and physical self-esteem, suggesting that both may be applied on the wheelchair basketball players at competitive levels.

Keywords: ase series, physical performance, physical self-esteem, wheelchair basketball

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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: Sujay Bisht

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The purpose of the study was to assess and examines the pattern of injury among the field hockey players at different field position during practice & game. It was hypothesized that the backfield might have the height rate of injury, followed by midfield. Methods: university level and national level male field hockey (N=60) are selected as a subject and requested to respond an anon questionnaire. Personal characteristics of each and individual players were also collected like (age, height, weight); field hockey professional information (level of play, year of experience, playing surface); players injury history (site, types, cause etc). The rates of injury per athlete per year were also calculated. Result: Around half of the injury occurred were to the lower limbs (49%) followed by head and face (30%), upper limbs (19%) and torso region (2%). Injuries included concussion, wounds, broken nose, ligament sprain, dislocation, fracture, and muscles strain and knee injury. The ligament sprain is the highest rate (40%) among the other types of injuries. After investigation and evaluation backfield players had the highest rate of risk of injury (1.10 injury/athletes-year) followed by midfield players (0.70 injury/athlete-year), forward players (0.45 injury/athlete-year) & goalkeeper was (0.37 injury/athlete-year). Conclusion: Due to the different field position the pattern & rate of injury were different. After evaluation, lower limbs had the highest rate of injury followed by head and face, upper limbs and torso respectively. It also revealed that not only there is a difference in the rate of injury between playing the position, but also in the types of injury sustain at a different position.

Keywords: trauma, sprain, strain, astroturf, acute injury

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Authors: Susan Lee

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Situated learning principles are adopted in the design of the module, professional communication, in its iteration of tasks and assignments to create a learning environment that simulates workplace reality. The success of situated learning is met when students are able to transfer and apply their skills beyond the classroom, in their personal life, and workplace. The learning process should help students recognize the relevance and opportunities for application. In the module’s learning component on negotiation, cases are created based on scenarios inspired by industry practices. The cases simulate scenarios that students on the course may encounter when they enter the workforce when they take on executive roles in the real estate sector. Engaging in the cases has enhanced students’ learning experience as they apply interpersonal communication skills in negotiation contexts of executives. Through the process of case analysis, role-playing, and peer feedback, students are placed in an experiential learning space to think and act in a deliberate manner not only as students but as professionals they will graduate to be. The immersive skills practices enable students to continuously apply a range of verbal and non-verbal communication skills purposefully as they stage their negotiations. The theme in students' feedback resonates with their awareness of the authentic and workplace experiences offered through visceral role-playing. Students also note relevant opportunities for the future transfer of the skills acquired. This indicates that students recognize the possibility of encountering similar negotiation episodes in the real world and realize they possess the negotiation tools and communication skills to deliberately apply them when these opportunities arise outside the classroom.

Keywords: deliberate practice, interpersonal communication skills, role-play, situated learning

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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: 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: Haif Alharthy, Samar Altarteer

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Blind and sighted teenagers might find it challenging to communicate and have fun interaction with each other. The previous studies emphasize the importance of the interactive communication of the blind with the sighted people in developing the interpersonal and social skills of the blind people . Playing games is one of the effective ways used to engage the blind with the sighted people and help in enhancing their social skills. However, it is difficult to find a fun game that is designed to encourage interaction between blind and sighted teenagers in which the blind can play it independently without help and that the sighted find its design attractive and satisfying. The aim of this paper is to examine how challenging is to have fun interaction between blind and sighted people and offer interactive tabletop game solution in which both of them can independently participate and enjoy. The paper discusses the importance and the impact of the interactive fun communication between blind and sighted people and how to get them involved with each other through games. The paper investigates several approaches to design a universal game. A survey was conducted for blind teenager’s family members to discover what difficulties they face while playing and communicating with their blind family member and to identify the blind’s needs and interests in games. The study reveals that although families like to play tabletop games with their blind member, they find difficulties in finding universal games that is interesting and adequate for both. Also, qualitative interviews were conducted with blind teenager shows the sufficiency in tabletop games that do not require help from another family member to play the game. The results suggested that an effective approach is to develop an interactive tabletop game embedded with audio and tactile techniques. The findings of the pilot study highlighted the necessary information such as tools, visuals, and game concepts that should be considered in developing interactive card game for blind and sighted teenagers.

Keywords: Blind, card game, communication, interaction, play, tabletop game, teenager

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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: Crista Arangala

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Light switching games are both popular and well studied. This paper introduces a cellular automata called Langton’s turmite to several different light switching scenarios and discusses when Langton’s turmite can solve these games.

Keywords: cellular automata, lights out, alien tiles, chaos, Langton's Turmite

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Authors: Fiona Armstrong, David Gaul, Michael Barrett, Lorraine D'Arcy

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Playing is an instinctive and universal human behavior, is a child’s way of learning and an outlet for their innate need of activity. Risky play can be defined as any play that is thrilling or exciting involving the risk of injury. The benefits of risky play have been acknowledged as helping children to explore and conquer fears, develop confidence, reduce anxiety, and develop risk-management skills. Studies indicate that children learn sound judgment by assessing and confronting risks in relation to their own capabilities through exposure to carefully managed play experiences. Risky play has been associated with danger and increased risk of injury, with families focusing on risk aversion and protecting children from the risks inherent in the modern world. Despite children needing cultural, social, emotional, physical, and geographical space to play, the opportunity for children to play is diminishing. Aim: This study explores play behaviors and risky play in an Irish context by investigating parental attitudes to risky play. Methodology: This is a mixed methods study involving the State of Play survey and semi-structured interviews exploring parental attitudes to risky play. Data will be quantitatively analyzed using descriptive and inferential statistics using IBM SPSS and qualitatively analyzed via thematic analysis using NVivo. Conclusion: The information gathered could advise stakeholders regarding the creation and provision of developmentally appropriate, challenging, stimulating, adaptable, accessible, and safe as necessary outdoor play areas. This research can inform parents, planners, architects, and authorities involved in creating environments for play and contribute to policy development.

Keywords: child development, parental attitudes, play opportunities, risky play

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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

Procedia PDF Downloads 96