Search results for: playing with mathematics

Authors: Muktadir Ahmed, Sayed Akhlakur Rahaman, Mridha Shihab Mahmud

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The parents of Bangladesh have scarcity of knowledge about children play. Most of them do not know which toys are perfect for their children. Appropriate toys for playing is one of the most significant parts of children development from early age, besides for proper amelioration of children’s mental growth and brain capacities, toys play an emergent role. So selection of proper toy for children is very important. A toy forms the sagacity of a child and instructs child’s attitude. In this era of globalization to keep pace with everything children toys are also going forward but in a deleterious way. Maximum toys are now battery-driven and for this psychological developments of children are not increasing in effective way; therefore, pedagogical toys are proper selection. This type of toy inspires the wisdom and helps a child to reveal himself/herself. Pedagogical toys are attractive to children and help to stimulate their imagination. Pedagogical toys help them to build senso-motoric skills and hand-eye coordination. In this study, some children divided into two groups, one group played with pedagogical toys and another group played with conventional toys. This study is going to exhibit the difference between pedagogical and conventional toys for kids. The main aim of this study is to reveal the potency of pedagogical toy for children. To implement this study two Daycare Centers (DCC) Projapoti 1 & 3 of Mymensingh city had chosen. Every DCC having 1.5-6 years old children but for this study 2-5 years old children had been selected. The children of Projapoti-1 played with pedagogical toys and the children of Projapoti-2 played with conventional toys. After 6 weeks of study, the children of Projapoti-1 proved that they have improved their skills more than those children of Projapoti-3 who were playing with conventional toys. The children of Projapoti-1 have developed their touch sensation, muscular movement, imitation power, hand-eye coordination whereas the children of Projapoti-3 have only developed their muscular movement fairly (while running after battery driven toys) which is not better than those children of Projapoti-1. They cannot imitate like the children of Projapoti-1. They just had fun from playing virtual games, battery driven toys, watching cartoons etc. Actually, it is not possible to develop a child’s brain without pedagogical toy.

Keywords: brain development, mental growth, pedagogical toys, play for children

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Authors: R. M. Kashim

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

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

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Authors: Nazir Amir

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Teaching approaches to present science and mathematics content amongst academically-low-achieving students may need to be different than approaches that are adopted for the more academically-inclined students, primarily due to the different learning needs and learning styles of these students. In crafting out lessons to motivate and engage these students, teachers need to consider the backgrounds of these students and have a good understanding of their interests so that lessons can be presented in ways that appeal to them, and made relevant not just to the world around them, but also to their personal experiences. This presentation highlights how the author worked with a Professional Learning Community (PLC) of teachers in crafting out fun and feasible classroom teaching approaches to present science and mathematics content in ways that are made Relevant, Appealing, and Personal (RAP) to groups of academically-low-achieving students in Singapore. Feedback from the students and observations from their work suggest that they were engaged through the RAP-modes of instruction, and were able to appreciate the role of science and mathematics through a variety of low-cost design-based STEM (Science, Technology, Engineering, and Mathematics) activities. Such results imply that teachers teaching academically-low-achieving students, and those in under-resourced communities, could consider infusing RAP-infused instructions into their lessons in getting students develop positive attitudes towards STEM subjects.

Keywords: STEM Education, STEAM Education, Curriculum Instruction, Academically At-Risk Students, Singapore

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Authors: Guorong Sui, Xingwei Jia, Chenhui Yin, Xiumin Gao

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In the processing of camera-based high precision and non-contact measurement, the geometric-optical aberration is always inevitably disturbing the measuring system. Moreover, the aberration is different with the different focal length, which will increase the difficulties of the system’s calibration. Therefore, to understand the relationship between the focal length as a function of aberration properties is a very important issue to the calibration of the measuring systems. In this study, we propose a new mathematics model, which is based on the plane calibration method by Zhang Zhengyou, and establish a relationship between the focal length and aberration coefficient. By using the mathematics model and carefully modified compensation templates, the calibration precision of the system can be dramatically improved. The experiment results show that the relative error is less than 1%. It is important for optoelectronic imaging systems that apply to measure, track and position by changing the camera’s focal length.

Keywords: camera calibration, aberration coefficient, vision measurement, focal length, mathematics model

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Authors: Hector G. Perez-Gonzalez, Miriam Vazquez-Escalante, Sandra E. Nava-Muñoz, 
 Francisco E. Martinez-Perez, Alberto S. Nunez-Varela

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The software engineering teaching process has been the subject of many studies. To improve this process, researchers have proposed merely illustrative techniques in the classroom, such as topic presentations and dynamics between students on one side or attempts to involve students in real projects with companies and institutions to bring them to a real software development problem on the other hand. Simulators and serious games have been used as auxiliary tools to introduce students to topics that are too abstract when these are presented in the traditional way. Most of these tools cover a limited area of the huge software engineering scope. To address this problem, we have developed D6tions, an educational serious game that simulates the software engineering process and is designed to experiment the different stages a software engineer (playing roles as project leader or as a developer or designer) goes through, while participating in a software project. We describe previous approaches to this problem, how D6tions was designed, its rules, directions, and the results we obtained of the use of this game involving undergraduate students playing the game.

Keywords: serious games, software engineering, software engineering education, software engineering teaching process

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Authors: Eugenia Vomvoridi-Ivanovic

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

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

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Authors: Onesimus Bulus Shiaki

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The study investigated the effect of cooperative learning strategy on mathematics achievement and retention among senior secondary school students of different abilities in Taraba State Nigeria. Cooperative learning strategy could hopefully contribute to students’ achievement which will spur the teachers to develop strategies for better learning. The quasi-experimental of pretest, posttest and control group design was adopted in this study. A sample of one hundred and sixty-four (164) Senior Secondary Two (SS2) students were selected from a population of twelve thousand, eight hundred and seventy-three (12,873) SS2 Students in Taraba State. Two schools with equivalent mean scores in the pre-test were randomly assigned to experimental and control groups. The experimental group students were stratified according to ability levels of low, medium and high. The experimental group was guided by the research assistants using the cooperative learning instructional package. After six weeks post-test was administered to the two groups while the retention test was administered two weeks after the post-test. The researcher developed a 50-item Mathematics Achievement Test (MAT) which was validated by experts obtaining the reliability coefficient of 0.87. Mean scores and standard deviations were used to answer the research questions while the Analysis of Co-variance (ANCOVA) was used to test the hypotheses. Major findings from the statistical analysis showed that cooperative learning strategy has a significant effect on the mean achievement of students as well as retention among students of high, medium and low ability in mathematics. However, cooperative learning strategy has no effect on the interaction of ability level and retention. Based on the results obtained, it was therefore recommended that the adoption of the use of cooperative learning strategy in the teaching and learning of mathematics in senior secondary schools be initiated, maintained and sustained for the benefit of senior secondary school students in Taraba State. Periodic Government sponsored in-service training in form of long vacation training programme, workshops, conferences and seminars on the nature, scope, and use of cooperative learning strategy should be organized for senior secondary school mathematics teachers in Taraba state.

Keywords: ability level, cooperative learning, mathematics achievement, retention

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Authors: Cristina-Maria Păcurar

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The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

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Authors: Han Hyuk Cho, Hanik Jo

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In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

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Authors: Joanne Hardman

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

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

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

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

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

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Authors: Josephine Shamash, Stuart Smith

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We examine reasons for introducing definitions in teaching mathematics in a number of different cases. We try to determine if, where, and when to provide a definition, and which definition to choose. We characterize different types of definitions and the different purposes we may have for formulating them, and detail examples of each type. Giving a definition at a certain stage can sometimes be detrimental to the development of the concept image. In such a case, it is advisable to delay the precise definition to a later stage. We describe two models, the 'successive approximation model', and the 'model of the extending definition' that fit such situations. Detailed examples that fit the different models are given based on material taken from a number of textbooks, and analysis of the way the concept is introduced, and where and how its definition is given. Our conclusions, based on this analysis, is that some of the definitions given may cause discontinuities in the learning sequence and constitute obstacles and unnecessary cognitive conflicts in the formation of the concept definition. However, in other cases, the discontinuity in passing from definition to definition actually serves a didactic purpose, is unavoidable for the mathematical evolution of the concept image, and is essential for students to deepen their understanding.

Keywords: concept image, mathematical definitions, mathematics education, mathematics teaching

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Authors: Murray Olowa

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This article examines the studies investigating the Mathematical Knowledge for Teaching (MKT) of secondary preservice teachers in Papua New Guinea based on probabilities. This research was conducted due to the continuous issues faced in the country in both primary and secondary education, like changes in curriculum, emphasis on mathematics and science education, and a decline in mathematics performance. Moreover, the mathematics curriculum doesn’t capture Pedagogical Content Knowledge (PCK) or Subject Matter Knowledge (SMK). The two main domains that have been identified are SMK and PCK, which have been further sub-divided into Common Content Knowledge (CCK), Specialised Content Knowledge (SCK) and Horizon Content Knowledge (HCK), and Knowledge of Content and Students (KCS), Knowledge of Content and Teaching (KCT) and Knowledge of Content and Curriculum (KCC), respectively. The data collected from 15-_year-_ ones and 15-_year-_fours conducted at St Peter Chanel Secondary Teachers College revealed that there is no significant difference in subject matter knowledge between year one and year four since the P-value of 0.22>0.05. However, it was revealed that year fours have higher pedagogical content knowledge than year one since P-value was 0.007<0.05. Finally, the research has proven that year fours have higher MKT than year one. This difference occurred due to final year preservice teachers’ hard work and engagement in mathematics curriculum and teaching practice.

Keywords: mathematical knowledge for teaching, subject matter knowledge, pedagogical content knowledge, Papua New Guinea, preservice teachers, probability

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Authors: Farhaz Amyn Rajabali, Collins Odour

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Mathematics has been there for over 4000 years and has been one of the very first educational topics explored by human civilization. Throughout the years, it has become a complex study and has derived so many other subjects. With advancements in ICT, most of the computation in mathematics is done using powerful computers. In many different countries, the children in primary and secondary schools face difficulties in learning mathematics, and this has many reasons behind it, one being the students don’t engage much with the mathematical concepts hence failing to understand them deeply. The objective of this system is to help the students understand this mathematical concept interactively, which in return will encourage the love for learning and increase thorough understanding of many concepts. Research was conducted among a group of samples and about 50% of respondents replied that they had never used an augmented reality application before. This means that the chances for this system to be accepted in the market are high due to its innovative idea. Around 60% of people did recommend the use of this system to learn mathematics. The study also showed several challenges in an educational system, including but not limited to lack of resources which was chosen by 30% of respondents, the challenge to read from textbooks (34.6%) and how hard it is to visualize concepts (46.2%). The survey question asked what benefits the users see using augmented reality to learn mathematics. The responses that were picked the most were increased student engagement and using real-world examples to understand concepts, both being 65.4% and followed by easy access to learning material at 61.5%, and increased knowledge retention at 50%. This shows that there are plenty of issues with an education system that can be addressed by software applications; now that the newer generation is so enthusiastic about electronic devices, it can actually be used to deliver good knowledge and skills to the upcoming students and mitigate most of the challenges faced currently. The study concludes that the implementation of the system is a best practice for the educational system especially leveraging a new technology that has the ability to attract the attention of many young students and use it to deliver information. It will also give rise to awareness of new technology and on multiple ways it can be implemented. Addressing the educational sector in developing countries using information technology is an imperative task since these kids studying now is the future of the country and will use what they learn and understand during their childhood will help them to make decisions about their lives in the future which will not only affect them personally but also affect the whole society in general.

Keywords: AR, mathematics, system development, augmented reality

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Authors: Melaku Takele Abate, Abbi Lemma Wodajo, Adula Bekele Hunde

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This study aimed at exploring mathematics teachers' reactions, learning, school leaders’ support, and use of the Lesson Study for Transformative Assessment (LSforTA) program ideas in practice. The LSforTA program was new, and therefore, a local and grounded approach was needed to examine teachers’ knowledge and skills acquired using LSforTA. So, a design-based research approach was selected to evaluate and refine the LSforTA approach. The results showed that LSforTA increased teachers' knowledge and use of different levels of mathematics assessment tasks. The program positively affected teachers' practices of transformative assessment and enhanced their knowledge and skills in assessing students in a transformative way. The paper concludes how the LSforTA procedures were adapted in response to this evaluation and provides suggestions for future development and research.

Keywords: classroom assessment, feedback practices, lesson study, mathematics, design-based research

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Authors: Zhidong Zhang, Amanda Resendez

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This study is to examine how teachers’ perspective on education technology use in their class influence their students’ achievement. The authors hypothesized that teachers’ perspective can directly or indirectly influence students’ learning, performance, and achievements. In this study, a questionnaire entitled, Teacher’s Perspective on Educational Technology, was delivered to 63 teachers and 1268 students’ mathematics and reading achievement records were collected. The questionnaire consists of four parts: a) demographic variables, b) attitudes on technology integration, c) outside factor affecting technology integration, and d) technology use in the classroom. Kruskal-Wallis and hierarchical regression analysis techniques were used to examine: 1) the relationship between the demographic variables and teachers’ perspectives on educational technology, and 2) how the demographic variables were causally related to students’ mathematics and reading achievements. The study found that teacher demographics were significantly related to the teachers’ perspective on educational technology with p < 0.05 and p < 0.01 separately. These teacher demographical variables included the school district, age, gender, the grade currently teach, teaching experience, and proficiency using new technology. Further, these variables significantly predicted students’ mathematics and reading achievements with p < 0.05 and p < 0.01 separately. The variations of R² are between 0.176 and 0.467. That means 46.7% of the variance of a given analysis can be explained by the model.

Keywords: teacher's perception of technology use, mathematics achievement, reading achievement, Kruskal-Wallis test, hierarchical regression analysis

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Authors: Stephen O. Amaraihu

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This research investigated the effect of Computer Based Instruction on Students’ interest, achievement, and retention in Algebra in Abia State College of Education (Technical), Arochukwu. Three research questions and two hypotheses guided the study. Two instruments, Maths Achievement Test (MAT) and Maths Interest Inventory were employed, to test a population of three hundred and sixteen (316) NCE 1 students in algebra. It is expected that this research will lead to the improvement of students’ performance and enhance their interest and retention of basic algebraic concept. It was found that the majority of students in the college are not proficient in the use of ICT as a result of a lack of trained personnel. It was concluded that the state government was not ready to implement the usage of mathematics in Abia State College of Education. The paper recommends, amongst others, the employment of mathematics Lectures with competent skills in ICT and the training of lecturers of mathematics.

Keywords: achievement, computer based instruction, interest, retention

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Authors: Eva Nolan, Timothy Mcnichols

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Gamers spend over 3 billion hours collectively playing video games a week, which is arguably not nearly enough time to indulge in the many benefits gaming has to offer. Much of the previous research on video gaming is centered on the effects of playing violent video games and the negative impacts they have on the individual. However, there is a dearth of research in the area of non-violent video games, specifically the emotional and cognitive benefits playing non-violent games can offer individuals. Current research in the area of video game play suggests there are many benefits to playing for an individual, such as decreasing symptoms of depression, decreasing stress, increasing positive emotions, inducing relaxation, decreasing anxiety, and particularly improving mood. One suggestion as to why video games may offer such benefits is that they possess ideal characteristics to create and maintain flow experiences, which in turn, is the subjective experience where an individual obtains a heightened and improved state of mind while they are engaged in a task where a balance of challenge and skill is found. Many video games offer a platform for collaborative gameplay, which can enhance the emotional experience of gaming through the feeling of social support and social inclusion. The present study was designed to examine the effects of collaborative gameplay and flow experience on participants’ perceived mood. To investigate this phenomenon, an in-between subjects design involving forty participants were randomly divided into two groups where they engaged in solo or collaborative gameplay. Each group represented an even number of frequent gamers and non-frequent gamers. Each participant played ‘The Lego Movie Videogame’ on the Playstation 4 console. The participant’s levels of flow experience and perceived mood were measured by the Flow State Scale (FSS) and the Positive and Negative Affect Schedule (PANAS). The following research hypotheses were investigated: (i.) participants in the collaborative gameplay condition will experience higher levels of flow experience and higher levels of mood than those in the solo gameplay condition; (ii.) participants who are frequent gamers will experience higher levels of flow experience and higher levels of mood than non-frequent gamers; and (iii.) there will be a significant positive relationship between flow experience and mood. If the estimated findings are supported, this suggests that engaging in collaborative gameplay can be beneficial for an individual’s mood and that experiencing a state of flow can also enhance an individual’s mood. Hence, collaborative gaming can be beneficial to promote positive emotions (higher levels of mood) through engaging an individual’s flow state.

Keywords: collaborative gameplay, flow experience, mood, games, positive emotions

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Authors: Edwin Christmann, John Hicks

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This meta-analysis compared the mathematics achievement of students who received either traditional instruction or traditional instruction supplemented with computer-assisted instruction (CAI). From the 27 conclusions, an overall mean effect size of 0.236 was calculated, indicating that, on average, students receiving traditional instruction supplemented with CAI attained higher mathematics achievement than did 59.48 percent of those receiving traditional instruction per se.

Keywords: CAI, science, meta-analysis, traditional

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Authors: Vojo George Fasinu, Nadaraj Govender, Predeep Kumar

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An Antenna, which remains the hub of technological development in Africa had been found to be a course that is been taught and designed in an abstract manner in some universities. One of the reasons attached to this is that the appropriate approach of teaching antenna design is not yet understood by many engineering academics in some universities in South Africa. Also, another problem reported is the main difficulty encountered when interpreting and applying some of the mathematical concepts learned into their practical antenna design course. As a result of this, some engineering experts classified antenna as a mysterious technology that could not be described by anybody using mathematical concepts. In view of this, this paper takes it as its point of departure in explaining what an antenna is all about with a strong emphasis on its mathematical modelling. It also argues that the place of modelling mathematical concepts into the teaching of engineering design cannot be overemphasized. Therefore, it explains the mathematical concepts adopted during the teaching of an antenna design course, the Strategies of modelling those mathematics concepts, the behavior of antennas, and their mathematics usage were equally discussed. More so, the paper also sheds more light on mathematical modelling in South Africa context, and also comparative analysis of mathematics concepts taught in mathematics class and mathematics concepts taught in engineering courses. This paper focuses on engineering academics teaching selected topics in electronic engineering (Antenna design), with special attention on the mathematical concepts they teach and how they teach them when teaching the course. A qualitative approach was adopted as a means of collecting data in order to report the naturalistic views of the engineering academics teaching Antenna design. The findings of the study confirmed that some mathematical concepts are being modeled into the teaching of an antenna design with the adoption of some teaching approaches. Furthermore, the paper reports a didactical-realistic mathematical model as a conceptual framework used by the researchers in describing how academics teach mathematical concepts during their teaching of antenna design. Finally, the paper concludes with the importance of mathematical modelling to the engineering academics and recommendations for further researchers.

Keywords: modelling, mathematical concepts, engineering, didactical, realistic model

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Authors: Silvia Benvenuti, Alessandra Cardinali

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In recent years, for instance, in relation to the Covid 19 pandemic and the evidence of climate change, it is becoming quite clear that the development of a young kid into an adult citizen requires a solid scientific background. Citizens are required to exert logical thinking and know the methods of science in order to adapt, understand, and develop as persons. Mathematics sits at the core of these required skills: learning the axiomatic method is fundamental to understand how hard sciences work and helps in consolidating logical thinking, which will be useful for the entire life of a student. At the same time, research shows that the axiomatic study of geometry is a problematic topic for students, even for those with interest in mathematics. With this in mind, the main goals of the research work we will describe are: (1) to show whether non-Euclidean geometries can be a tool to allow students to consolidate the knowledge of Euclidean geometries by developing it in a critical way; (2) to promote the understanding of the modern axiomatic method in geometry; (3) to give students a new perspective on mathematics so that they can see it as a creative activity and a widely discussed topic with a historical background. One of the main issues related to the state-of-the-art in this topic is the shortage of experimental studies with students. For this reason, our aim is to show further experimental evidence of the potential benefits of teaching non-Euclidean geometries at high school, based on data collected from a study started in 2005 in the frame of the Italian National Piano Lauree Scientifiche, continued by a teacher training organized in September 2018, perfected in a pilot study that involved 77 high school students during the school years 2018-2019 and 2019-2020. and finally implemented through an experimental study conducted in 2020-21 with 87 high school students. Our study shows that there is potential for further research to challenge current conceptions of the school mathematics curriculum and of the capabilities of high school mathematics students.

Keywords: Non-Euclidean geometries, beliefs about mathematics, questionnaires, modern axiomatic method

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Authors: Beruk Berhanu Desalegn, Tona Diddana, Alemneh Daba

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Objective: The aim of this study was to assess the magnitude and determinants of overnutrition among school going adolescents from Dale District of Ethiopia. Methods: An institution-based cross-sectional study was done between November and December 2020. A total of 333 school going adolescents aged 10-19 years were participated. Socio-demographic, lifestyle, physical activity level, an estimated individual dietary energy intake; and height and weight data were collected. Body Mass Index for age (BAZ) was computed. Results: The magnitude of over-nutrition was 7.2% (10.8% in urban vs. 3.6% in rural). Lack of adequate playing area (AOR=2.53, 95% CI:1.02, 6.26), being an urban resident (AOR=3.05, 95% CI:1.12, 8.29), having more energy intake than expenditure (AOR=9.47, 95% CI:1.58, 56.80), ever consumed fast foods a month before the survey (AOR=2.60, 95% CI:1.93, 6.83), having moderate physical activity (PA) (AOR =9.28, 95% CI: 6.70, 71.63), low PA (AOR=7.95, 95% CI:1.12, 56.72), and having snack between meals (AOR=3.32, 95% CI:1.15, 9.58) were positively associated with over-nutrition. Conclusion: The magnitude of over-nutrition among school going adolescents was lower compared to previous reports in Ethiopia. Sedentary lifestyles, excess calorie intake, not having adequate playing areas in the schools, and having snacks between meals were statistically predicted determinants for over-nutrition in the study area.

Keywords: adolescent, over-nutrition, school, Ethiopia

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Authors: Nadeesha Sewwandi, Dilini Shashikala, R. Kanapathy, S. Viyasan, R. M. S. Kumara, Duminda Guruge

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Early childhood development is important to the emotional, social, and physical development of young children and it has a direct effect on their overall development and on the adult they become. Play is so important to optimal child developments including skill development, social development, imagination, creativity and it fulfills a baby’s inborn need to learn. So, health promotion approach empowers people about the development of early childhood. Play area is a new concept and this study focus how this play areas helps to the development of early childhood of children in rural villages in Sri Lanka. This study was conducted with a children society in a rural village called Welankulama in Sri Lanka. Survey was conducted with children society about emotional, social and physical development of young children (Under age eight) in this village using questionnaires. It described most children under eight years age have poor level of emotional, social and physical development in this village. Then children society wanted to find determinants for this problem and among them they prioritized determinants like parental interactions, learning environment and social interaction and address them using an innovative concept called play area. In this village there is a common place as play area under a big tamarind tree. It consists of a playhouse, innovative playing toys, mobile library, etc. Twice a week children, parents, grandparents gather to this nice place. Collective feeding takes place in this area once a week and it was conducted by several mothers groups in this village. Mostly grandparents taught about handicrafts and this is a very nice place to share their experiences with all. Healthy competitions were conducted in this place through playing to motivate the children. Happy calendar (mood of the children) was marked by children before and after coming to the play area. In terms of results qualitative changes got significant place in this study. By learning about colors and counting through playing the thinking and reasoning skills got developed among children. Children were widening their imagination by means of storytelling. We observed there were good developments of fine and gross motor skills of two differently abled children in this village. Children learn to empathize with other people, sharing, collaboration, team work and following of rules. And also children gain knowledge about fairness, through role playing, obtained insight on the right ways of displaying emotions such as stress, fear, anger, frustration, and develops knowledge of how they can manage their feelings. The reading and writing ability of the children got improved by 83% because of the mobile library. The weight of children got increased by 81% in the village. Happiness was increased by 76% among children in the society. Playing is very important for learning during early childhood period of a person. Health promotion interventions play a major role to the development of early childhood and it help children to adjust to the school setting and even to enhance children’s learning readiness, learning behaviors and problem solving skills.

Keywords: early childhood development, health promotion approach, play and learning, working with children

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Authors: Wern Lin Yeo, Choo Kim Tan, Sook Ling Lew

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Mathematics anxiety refers to the feeling of anxious when one having difficulties in solving mathematical problem. Mathematics anxiety is the most common type of anxiety among other types of anxiety which occurs among the students. However, level of anxiety among males and females are different. There were few past study were conducted to determine the relationship of anxiety and gender but there were still did not have an exact results. Hence, the purpose of this study is to determine the relationship of anxiety level between male and female undergraduates at a private university in Malaysia. Convenient sampling method used in this study in which the students were selected based on the grouping assigned by the faculty. There were 214 undergraduates who registered the probability courses had participated in this study. Mathematics Anxiety Rating Scale (MARS) was the instrument used in study which used to determine students’ anxiety level towards probability. Reliability and validity of instrument was done before the major study was conducted. In the major study, students were given briefing about the study conducted. Participation of this study were voluntary. Students were given consent form to determine whether they agree to participate in the study. Duration of two weeks were given for students to complete the given online questionnaire. The data collected will be analyzed using Statistical Package for the Social Sciences (SPSS) to determine the level of anxiety. There were three anxiety level, i.e., low, average and high. Students’ anxiety level were determined based on their scores obtained compared with the mean and standard deviation. If the scores obtained were below mean and standard deviation, the anxiety level was low. If the scores were at below and above the mean and between one standard deviation, the anxiety level was average. If the scores were above the mean and greater than one standard deviation, the anxiety level was high. Results showed that both of the gender were having average anxiety level. Males having high frequency of three anxiety level which were low, average and high anxiety level as compared to females. Hence, the mean values obtained for males (M = 3.62) was higher than females (M = 3.42). In order to be significant of anxiety level among the gender, the p-value should be less than .05. The p-value obtained in this study was .117. However, this value was greater than .05. Thus, there was no significant difference of anxiety level among the gender. In other words, there was no relationship of anxiety level with the gender.

Keywords: anxiety level, gender, mathematics anxiety, probability and statistics

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Authors: Muhammet Şahal, Oğuz Köklü

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As statistical thinking and problem-solving processes have become increasingly important, teachers need to be more rigorously prepared with statistical knowledge to teach their students effectively. This study examined preservice mathematics teachers' development of statistical investigation projects using data and exploratory data analysis tools, following a design-based research perspective and statistical investigation cycle. A total of 26 pre-service senior mathematics teachers from a public university in Turkiye participated in the study. They formed groups of 3-4 members voluntarily and worked on their statistical investigation projects for six weeks. The data sources were audio recordings of pre-service teachers' group discussions while working on their projects in class, whole-class video recordings, and each group’s weekly and final reports. As part of the study, we reviewed weekly reports, provided timely feedback specific to each group, and revised the following week's class work based on the groups’ needs and development in their project. We used content analysis to analyze groups’ audio and classroom video recordings. The participants encountered several difficulties, which included formulating a meaningful statistical question in the early phase of the investigation, securing the most suitable data collection strategy, and deciding on the data analysis method appropriate for their statistical questions. The data collection and organization processes were challenging for some groups and revealed the importance of comprehensive planning. Overall, preservice senior mathematics teachers were able to work on a statistical project that contained the formulation of a statistical question, planning, data collection, analysis, and reaching a conclusion holistically, even though they faced challenges because of their lack of experience. The study suggests that preservice senior mathematics teachers have the potential to apply statistical knowledge and techniques in a real-world context, and they could proceed with the project with the support of the researchers. We provided implications for the statistical education of teachers and future research.

Keywords: design-based study, pre-service mathematics teachers, statistical investigation projects, statistical model

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Authors: M. Rodionov, N. Sharapova, Z. Dedovets

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The article describes methods of preparation of future teachers that includes the entire diversity of traditional and computer-oriented methodological approaches. The authors reveal how, in the specific educational environment, a teacher can choose the most effective combination of educational technologies based on the nature of the learning task. The key conditions that determine such a choice are that the methodological approach corresponds to the specificity of the problem being solved and that it is also responsive to the individual characteristics of the students. The article refers to the training of students in the proper use of mathematical electronic tools for educational purposes. The preparation of future mathematics teachers should be a step-by-step process, building on specific examples. At the first stage, students optimally solve problems aided by electronic means of teaching. At the second stage, the main emphasis is on modeling lessons. At the third stage, students develop and implement strategies in the study of one of the topics within a school mathematics curriculum. The article also recommended the implementation of this strategy in preparation of future teachers and stated the possible benefits.

Keywords: education, methodological approaches, teacher, secondary school

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Authors: Abubakar Sadiq Mensah, Hassan Usman

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The study compared the effectiveness of Audition, Multiplication, subtraction and Division (AMSD) and Addition, subtraction, Multiplication and Division (ASMD), sequence of teaching these four basic operations in mathematics to primary one pupil’s in Katsina Local Government, Katsina State. The study determined the sequence that was more effective and mostly adopted by teachers of the operations. One hundred (100) teachers and sixty pupils (60) from primary one were used for the study. The pupils were divided into two equal groups. The researcher taught these operations to each group separately for four weeks (4 weeks). Group one was taught using the ASMD sequence, while group two was taught using ASMD sequence. In order to generate the needed data for the study, questionnaires and tests were administered on the samples. Data collected were analyzed and major findings were arrived at: (i) Two primary mathematics text books were used in all the primary schools in the area; (ii) Each of the textbooks contained the ASMD sequence; (iii) 73% of the teachers sampled adopted the ASMD sequence of teaching these operations; and (iv) Group one of the pupils (taught using AMSD sequence) performed significantly better than their counter parts in group two (taught using AMSD sequence). On the basis of this, the researcher concluded that the AMSD sequence was more effective in teaching the operations than the ASMD sequence. Consequently, the researcher concluded that primary schools teachers, authors of primary mathematics textbooks, and curriculum planner should adopt the AMSD sequence of teaching these operations.

Keywords: matematic, high school, four basic operations, effectiveness of teaching

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Authors: Luis Miguel Méndez Díaz

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In this article, a mathematics teaching-learning strategy will be presented, specifically differential calculus in one variable, in a fun and competitive space in which the action on the part of the student is manifested and not only the repetition of information on the part of the teacher. Said action refers to motivating, problematizing, summarizing, and coordinating a game of dominoes whose thematic cards are designed around the basic and main contents of differential calculus. The strategies for teaching this area are diverse and precisely the game of dominoes is one of the most used strategies in the practice of mathematics because it stimulates logical reasoning and mental abilities. The objective on this investigation is to identify the way in which the game of dominoes affects the learning and understanding of fundamentals concepts of differential calculus in one variable through experimentation carried out on students of the first semester of the School of Engineering and Sciences of the Technological Institute of Monterrey Campus Querétaro. Finally, the results of this study will be presented and the use of this strategy in other topics around mathematics will be recommended to facilitate logical and meaningful learning in students.

Keywords: collaborative learning, logical-mathematical intelligence, mathematical games, multiple intelligences

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Authors: Myla Zenaida Cabrillas-Torio, Von Anthony G. Torio

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Homework is defined as an additional task that a student does outside of the school. This added activity is in recognition of the necessity to spend additional time for subjects such as Mathematics. The dilemma comes in the form of the advantages and disadvantages that can be derived from homework. Studies have revealed varying effects to students on academic and non-academic areas. Teachers are at the forefront of the decision towards the giving or not of homework. Pre-service teachers at the elementary level represent the future leaders of the educational system and should be acquainted and involved at the onset of the dilemma. The main objective of this study is to determine the perspective of pre-service elementary teachers towards homework. The anatomy of their belief can be key towards addressing the issue via teacher training. Salient results revealed that the subjects favor the giving homework on the following grounds: it helps add knowledge and confidence. Those who do not favor homework find it as an additional burden. Difficulties in complying with homework are usually associated with lack of references and performance of other household chores. Students usually spend late nights to comply with homework and are unable to perform at the best of their potentials.

Keywords: attitude, homework, pre-service teachers, mathematics education, Philippines

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Authors: Viktor Müller, Ulman Lindenberger

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Neurophysiological evidence suggests that the physiological states of the system are characterized by specific network structures and network topology dynamics, demonstrating a robust interplay between network topology and function. It is also evident that interpersonal action coordination or social interaction (e.g., playing music in duets or groups) requires strong intra- and interbrain synchronization resulting in a specific hyper brain network activity across two or more brains to support such coordination or interaction. Such complex hyper brain networks can be described as multiplex or multilayer networks that have a specific multidimensional or multilayer network organization characteristic for superordinate systems and their constituents. The aim of the study was to describe multilayer hyper brain networks and synchronization patterns of guitarists playing guitar in a quartet by using electroencephalography (EEG) hyper scanning (simultaneous EEG recording from multiple brains) and following time-frequency decomposition and multilayer network construction, where within-frequency coupling (WFC) represents communication within different layers, and cross-frequency coupling (CFC) depicts communication between these layers. Results indicate that communication or coupling dynamics, both within and between the layers across the brains of the guitarists, play an essential role in action coordination and are particularly enhanced during periods of high demands on musical coordination. Moreover, multilayer hyper brain network topology and dynamical structure of guitar sounds showed specific guitar-guitar, brain-brain, and guitar-brain causal associations, indicating multilevel dynamics with upward and downward causation, contributing to the superordinate system dynamics and hyper brain functioning. It is concluded that the neuronal dynamics during interpersonal interaction are brain-wide and frequency-specific with the fine-tuned balance between WFC and CFC and can best be described in terms of multilayer multi-brain networks with specific network topology and connectivity strengths. Further sophisticated research is needed to deepen our understanding of these highly interesting and complex phenomena.

Keywords: EEG hyper scanning, intra- and interbrain coupling, multilayer hyper brain networks, social interaction, within- and cross-frequency coupling

Procedia PDF Downloads 47