Search results for: engineering mathematics

Authors: Jennifer Gallup, Beverly Ray, Esther Ntuli

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Many students such as students from linguistically or culturally diverse backgrounds and those with a disability remain chronically underrepresented in higher level science and mathematics disciplines as well as many hands-on-lab-based activities due to the need for remedial reading and mathematics instruction. Makerspace labs can be a conduit for supporting inclusive learning for these students through hands-on active learning strategies that support equitable access to STEM disciplines. Makerspace is a physical space where individuals gather to create, invent, innovate, and learn while using hands-on materials such as 2D and 3D printers, software programs, electronics, and other tools and supplies. Makerspaces are emerging across many P-12 settings; however, many teachers enter the field not prepared to harness the power inherent in a makerspace, especially for those with disabilities and differing needs. This paper offers suggestions on teaching pre-service teachers and practicing teachers how to incorporate a makerspace into their professional practice through guided instruction and hands-on practice. Recommendations for interested stakeholders are included as well.

Keywords: STEM learning, technology, autism, students with disabilities, makerspace

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Authors: M. Assaad, J. Mäkiö, T. Mäkelä, M. Kankaanranta, N. Fachantidis, V. Dagdilelis, A. Reid, C. R. del Rio, E. V. Pavlysh, S. V. Piashkun

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To bring science and society together in Europe, thus increasing the continent’s international competitiveness, STEM (science, technology, engineering and mathematics) education must be more relatable to European youths in their everyday life. STIMEY (Science, Technology, Innovation, Mathematics, Engineering for the Young) project researches and develops a hybrid educational environment with multi-level components that is being designed and developed based on a well-researched pedagogical framework, aiming to make STEM education more attractive to young people aged 10 to 18 years in this digital era. This environment combines social media components, robotic artefacts, and radio to educate, engage and increase students’ interest in STEM education and careers from a young age. Additionally, it offers educators the necessary modern tools to deliver STEM education in an attractive and engaging manner in or out of class. Moreover, it enables parents to keep track of their children’s education, and collaborate with their teachers on their development. Finally, the open platform allows businesses to invest in the growth of the youths’ talents and skills in line with the economic and labour market needs through entrepreneurial tools. Thus, universities, schools, teachers, students, parents, and businesses come together to complete a circle in which STEM becomes part of the daily life of youths through a hybrid educational environment that also prepares them for future careers.

Keywords: e-learning, entrepreneurship, pedagogy, robotics, serious gaming, social media, STEM education

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Authors: Lee Bih Ni, Nurul Asyikin Binti Hassan

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This paper discusses the use of mnemonic and mathematical methods in enhancing the understanding of history. Mnemonics can help students from all levels including high school and in various disciplines including language, math and history. At the secondary level, students are exposed to various courses that require them to remember many facts that can be mastered through the application of mnemonic techniques. Researchers use narrative literature studies to illustrate the current state of art and science in the field of research focused. Researchers used narrative literature reviews to build a scientific base of knowledge. Researchers gather all the key points in the discussion, and put it here by referring to the specific field where the paper is essentially based. The findings suggest that the use of mnemonic techniques can improve the individual's memory by adding little effort. In implementing mnemonic techniques, it is important to integrate mathematics and history in the course as both are interconnected as mathematics has shaped our history and vice versa. This study shows that memory skills can actually be improved; the human mind can remember something more than expected.

Keywords: cognitive strategy, mnemonic technique, secondary school level study, mathematical mnemonic

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Authors: Mohini Mohamed, Nurul Huda Mas’od

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This study was aimed at designing and developing an assistive mathematical teaching aid (courseware) in helping dyslexic students in learning multiplication. Computers and multimedia interactive courseware has benefits students in terms of increase learner’s motivation and engage them to stay on task in classroom. Most disability student has short attention span thus with the advantage offered by multimedia interactive courseware allows them to retain the learning process for longer period as compared to traditional chalk and talk method. This study was conducted in a public school at a primary level with the help of three special education teachers and six dyslexic students as participants. Qualitative methodology using interview with special education teachers and observations in classes were conducted. The development of the multimedia interactive courseware in this study was divided to three processes which were analysis and design, development and evaluation. The courseware was evaluated by using User Acceptance Survey Form and interview. Feedbacks from teachers were used to alter, correct and develop the application for a better multimedia interactive courseware.

Keywords: disability students, dyslexia, mathematics teaching aid, multimedia interactive courseware

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Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. Included is a close-up examination of a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two US states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data were collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used. The full paper will include the case study of Ana to illustrate the factors involved in what teachers take up and use from participating in the LTG PD.

Keywords: geometry, mathematics professional development, pedagogical content knowledge, teacher learning

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Authors: Verónica Díaz Quezada

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The importance given to the development of the problem solving skill and the requirement to solve problems framed in mathematical or real life contexts, in practice, they are not evidence in relation to the teaching of proportional variations. This qualitative and descriptive study aims to (1) to improve problem solving ability of high school students in Chile, (ii) to elaborate and describe a didactic intervention strategy based on learning situations in proportional variations, focused on solving types of routine problems of various contexts and non-routine problems. For this purpose, participant observation was conducted, test of mathematics problems and an opinion questionnaire to thirty-six high school students. Through the results, the highest academic performance is evidenced in the routine problems of purely mathematical context, realistic, fantasy context, and non-routine problems, except in the routine problems of real context and compound proportionality problems. The results highlight the need to consider in the curriculum different types of problems in the teaching of mathematics that relate the discipline to everyday life situations

Keywords: algebra, high school, proportion variations, nonroutine problem solving, routine problem solving

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Authors: Muhammad Akram, Qamar Naseem, Imtiaz Ahmad

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The purpose of this study was to correlate students’ perceptions of teacher effectiveness with their academic achievement in English and Mathematics at the secondary level (grade 9th) based on five national professional standards for teacher evaluation in Pakistan (subject matter knowledge, instructional planning and strategies, assessment, learning environment, effective communication. A Students’ Perceptions of Teacher Effectiveness Questionnaire (SPTEQ) was developed by the researchers to collect data from 2009 students from forty public girls and boys high/ higher secondary schools in district Khanewal, Pakistan. The overall reliability of the SPTEQ was α=.86. The study found a significant positive relationship among all the five factors of teacher effectiveness construct. The study also showed significant, positive relationship between teacher effectiveness factors and students’ achievement in English and mathematics. No significant differences were found between male and female students’ perceptions about their English teacher effectiveness. The implications include students’ personal attachments with their teachers that might convince them to overrate their teachers.

Keywords: communication, students’ achievement, teacher effectiveness, teaching strategies, teaching strategies

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Authors: Marie-Josée Morneau

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A literacy-based approach, centred on the use of the language of instruction as a cognitive tool, can increase the L2 communication skills of French immersion students. Academic subject areas such as science and mathematics offer an authentic language learning context where students can become more proficient speakers while using specific vocabulary and language structures to learn, interact and communicate their reasoning, when provided the opportunities and guidance to do so. In this Canadian quasi-experimental study, the effects of teaching specific language elements during mathematic classes through literacy-based activities in Early French Immersion programming were compared between two Grade 7/8 groups: the experimental group, which received literacy-based teaching for a 6-week period, and the control group, which received regular teaching instruction. The results showed that the participants from the experimental group made more progress in their mathematical communication skills, which suggests that targeting L2 language as a cognitive tool can be beneficial to immersion learners who learn mathematic concepts and remind us that all L2 teachers are language teachers.

Keywords: mathematics, French immersion, literacy-based, oral communication, L2

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Authors: Haofei Li

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To support academic growth and foster love of learning, MathMates has been introduced for grade 6-8 students at Andrew Hamilton public school in 2022. The program is targeted at students from diverse backgrounds, particularly those underperforming in Pennsylvania System of School Assessment (PSSA) exams. Then, this study aims to evaluate the efficacy of MathMates by comparing student performance on the PSSA test, before and after the intervention. Through a randomized control trial, the study will collect associated costs using the ingredients method and measure the effectiveness for cost-effectiveness analysis. Text messages will be sent to parents/guardians as a reminder of the program and to encourage student participation. The findings of this study will provide valuable insights for funding organizations seeking to understand the impact and costs of math tutoring interventions on student academic achievement, which also emphasizes the importance of the collaborative efforts between higher education and local public schools.

Keywords: mathematics education, mathematics tutoring, college-community initiative, middle schools, Philadelphia public schools, after-school program, PSSA

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Authors: Wajeeh Daher, Nimer Baya'a

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High Order Thinking Skills (HOTS) are suggested today as essential for the cognitive development of students and as preparing them for real life skills. Teachers are encouraged to use HOTS activities in the classroom to help their students develop higher order skills and deep thinking. So it is essential to prepare pre-service teachers to write and use HOTS activities for their students. This paper describes a model for integrating HOTS activities with GeoGebra in pre-service teachers’ preparation. This model describes four aspects of HOTS activities and working with them: Activity components, preparation procedure, strategies and processes used in writing a HOTS activity and types of the HOTS activities. In addition, the paper describes the pre-service teachers' difficulties in preparing and working with HOTS activities, as well as their perceptions regarding the use of these activities and GeoGebra in the mathematics classroom. The paper also describes the contribution of a HOTS activity to pupils' learning of mathematics, where this HOTS activity was prepared and taught by one pre-service teacher.

Keywords: high order thinking skills, HOTS activities, pre-service teachers, professional development

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Authors: Z. Dedovets, M. Rodionov

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The goal of the modern education system is to prepare students to be able to adapt to ever-changing life situations. They must be able to acquire required knowledge independently; apply such knowledge in practice to solve various problems by using modern technologies; think critically and creatively; competently use information; be communicative, work in a team; and develop their own moral values, intellect and cultural awareness. As a result, the status of education significantly increases; new requirements to its quality have been formed. In recent years, the competency-based approach in education has become of significant interest. This approach is a strengthening of applied and practical characteristics of a school education and leads to the forming of the key students’ competencies which define their success in future life. In this article, the authors’ attention focuses on a range of key competencies, educational, informational and communicative and on the possibility to develop such competencies via STEM education. This research shows the change in students’ attitude towards scientific disciplines such as mathematics, general science, technology and engineering as a result of STEM education. Two-staged analyzes questionnaires completed by students of forms II to IV in the republic of Trinidad and Tobago allowed the authors to categorize students between two levels that represent students’ attitude to various disciplines. The significance of differences between selected levels was confirmed with the use of Pearsons’ chi-squared test. In summary, the analysis of obtained data makes it possible to conclude that STEM education has a great potential for development of core students’ competencies and encourages the development of positive student attitude towards the above mentioned above scientific disciplines.

Keywords: STEM, science, technology, engineering, mathematics, students’ competency, Pearson's chi-squared test

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Authors: Aida Nurul Safitri, Rosita Sari

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Physics is science, which in its learning there are some product such as theory, fact, concept, law and formula. So that to understand physics lesson students not only need a theory or concept but also mathematical calculation to solve physics problem through formula or equation. This is can be taken from mathematics lesson which obtained by students. This research is to know the influence of mathematics learning outcomes towards physics ability in Senior High School through authentic assessment system. Based on the researches have been discussed, is obtained that mathematic lesson have an important role in physics learning but it according to one aspect only, namely cognitive aspect. In Indonesia, curriculum of 2013 reinforces displacement in the assessment, from assessment through test (measuring the competence of knowledge based on the result) toward authentic assessment (measuring the competence of attitudes, skills, and knowledge based on the process and results). In other researches are mentioned that authentic assessment system give positive responses for students to improve their motivation and increase the physics learning in the school.

Keywords: authentic assessment, curriculum of 2013, mathematic, physics

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Authors: Ayoub Kafyulilo, Petra Fisser, Joke Voogt

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This study was conducted to assess the continuation of the use of technology in science and mathematics teaching of the pre-service and in-service teachers who attended the professional development programme. It also assessed professional development, personal, institutional, and technological factors contributing to the continuous use of technology in teaching. The study involved 42 teachers, thirteen pre-service teachers, and twenty-nine in-service teachers. A mixed-method research approach was used to collect data for this study. Findings showed that the continuous use of technology in teaching after the termination of the professional development arrangement was high among the pre-service teachers, and differed for the in-service teachers. The regression model showed that knowledge and skills, access to technology and ease of use were strong predictors (R2 = 55.3%) of the teachers’ continuous use of technology after the professional development arrangement. The professional development factor did not have a direct effect on the continuous use of technology, rather had an influence on personal factors (knowledge and skills). In turn, the personal factors had influence on the institutional factors (access to technology) and technological factors (ease of use), which together had an effect on the teachers’ continuous use of technology in teaching.

Keywords: technology, professional development, teachers, science and mathematics

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Authors: Mário Ernesto Sitoe, Orlando Zacarias

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University education is influenced by several factors that range from the adoption of strategies to strengthen the whole process to the academic performance improvement of the students themselves. This work uses data mining techniques to develop a predictive model to identify students with a tendency to evasion and retention. To this end, a database of real students’ data from the Department of University Admission (DAU) and the Department of Mathematics and Informatics (DMI) was used. The data comprised 388 undergraduate students admitted in the years 2009 to 2014. The Weka tool was used for model building, using three different techniques, namely: K-nearest neighbor, random forest, and logistic regression. To allow for training on multiple train-test splits, a cross-validation approach was employed with a varying number of folds. To reduce bias variance and improve the performance of the models, ensemble methods of Bagging and Stacking were used. After comparing the results obtained by the three classifiers, Logistic Regression using Bagging with seven folds obtained the best performance, showing results above 90% in all evaluated metrics: accuracy, rate of true positives, and precision. Retention is the most common tendency.

Keywords: evasion and retention, cross-validation, bagging, stacking

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Authors: Sarah Lister, Pauline Palmer

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Research findings presented within this paper form part of a larger scale collaboration between academics at Manchester Metropolitan University and a technology company. The overarching aims of this project focus on developing a series of game-based resources to promote the teaching of aspects of mathematics through a second language (L2) in primary schools. This study explores the potential of game-based learning (GBL) as a dynamic way to engage and motivate learners, making learning fun and purposeful. The research examines the capacity of GBL resources to provide a meaningful and purposeful context for CLIL. GBL is a powerful learning environment and acts as an effective vehicle to promote the learning of mathematics through an L2. The fun element of GBL can minimise stress and anxiety associated with mathematics and L2 learning that can create barriers. GBL provides one of the few safe domains where it is acceptable for learners to fail. Games can provide a life-enhancing experience for learners, revolutionizing the routinized ways of learning through fusing learning and play. This study argues that playing games requires learners to think creatively to solve mathematical problems, using the L2 in order to progress, which can be associated with the development of higher-order thinking skills and independent learning. GBL requires learners to engage appropriate cognitive processes with increased speed of processing, sensitivity to environmental inputs, or flexibility in allocating cognitive and perceptual resources. At surface level, GBL resources provide opportunities for learners to learn to do things. Games that fuse subject content and appropriate learning objectives have the potential to make learning academic subjects more learner-centered, promote learner autonomy, easier, more enjoyable, more stimulating and engaging and therefore, more effective. Data includes observations of the children playing the games and follow up group interviews. Given that learning as a cognitive event cannot be directly observed or measured. A Cognitive Discourse Functions (CDF) construct was used to frame the research, to map the development of learners’ conceptual understanding in an L2 context and as a framework to observe the discursive interactions that occur learner to learner and between learner and teacher. Cognitively, the children were required to engage with mathematical content, concepts and language to make decisions quickly, to engage with the gameplay to reason, solve and overcome problems and learn through experimentation. The visual elements of the games supported the learning of new concepts. Children recognised the value of the games to consolidate their mathematical thinking and develop their understanding of new ideas. The games afforded them time to think and reflect. The teachers affirmed that the games provided meaningful opportunities for the learners to practise the language. The findings of this research support the view that using the game-based resources supported children’s grasp of mathematical ideas and their confidence and ability to use the L2. Engaging with the content and language through the games led to deeper learning.

Keywords: CLIL, gaming, language, mathematics

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Fatimah Alsaleh, Glenda Anthony

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The practicum experience is a critical component of any initial teacher education (ITE) course. As well as providing a near authentic setting for pre-service teachers (PSTs) to practice in, it also plays a key role in shaping their perceptions and sense of preparedness. Nevertheless, merely including a practicum period as a compulsory part of ITE may not in itself be enough to induce feelings of preparedness and efficacy; the quality of the classroom experience must also be considered. Drawing on findings of a larger study of secondary and intermediate level mathematics PSTs’ sense of preparedness to teach, this paper examines the influence of the practicum experience in particular. The study sample comprised female mathematics PSTs who had almost completed their teaching methods course in their fourth year of ITE across 16 teacher education programs in Saudi Arabia. The impact of the practicum experience on PSTs’ sense of preparedness was investigated via a mixed-methods approach combining a survey (N = 105) and in-depth interviews with survey volunteers (N = 16). Statistical analysis in SPSS was used to explore the quantitative data, and thematic analysis was applied to the qualitative interviews data. The results revealed that the PSTs perceived the practicum experience to have played a dominant role in shaping their feelings of preparedness and efficacy. However, despite the generally positive influence of practicum, the PSTs also reported numerous challenges that lessened their feelings of preparedness. These challenges were often related to the classroom environment and the school culture. For example, about half of the PSTs indicated that the practicum schools did not have the resources available or the support necessary to help them learn the work of teaching. In particular, the PSTs expressed concerns about translating the theoretical knowledge learned at the university into practice in authentic classrooms. These challenges engendered PSTs feeling less prepared and suggest that more support from both the university and the school is needed to help PSTs develop a stronger sense of preparedness. The area in which PSTs felt least prepared was that of classroom and behavior management, although the results also indicated that PSTs only felt a moderate level of general teaching efficacy and were less confident about how to support students as learners. Again, feelings of lower efficacy were related to the dissonance between the theory presented at university and real-world classroom practice. In order to close this gap between theory and practice, PSTs expressed the wish to have more time in the practicum, and more accountability for support from school-based mentors. In highlighting the challenges of the practicum in shaping PSTs’ sense of preparedness and efficacy, the study argues that better communication between the ITE providers and the practicum schools is necessary in order to maximize the benefit of the practicum experience.

Keywords: impact, mathematics, practicum experience, pre-service teachers, sense of preparedness

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Authors: Olteanu Constanta, Olteanu Lucian

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Researchers note that algebraic reasoning and sense making is essential for building conceptual knowledge in school mathematics. Consequently, pre-service teachers’ own reasoning and sense making are useful in fostering and developing students’ algebraic reasoning and sense making. This article explores the forms of reasoning and sense making that pre-service mathematics teachers exhibit and use in the process of analysing problem-posing tasks with a focus on first-degree equations. Our research question concerns the characteristics of the problem-posing tasks used for reasoning and sense making of first-degree equations as well as the characteristics of pre-service teachers’ reasoning and sense making in problem-posing tasks. The analyses are grounded in a post-structuralist philosophical perspective and variation theory. Sixty-six pre-service primary teachers participated in the study. The results show that the characteristics of reasoning in problem-posing tasks and of pre-service teachers are selecting, exploring, reconfiguring, encoding, abstracting and connecting. The characteristics of sense making in problem-posing tasks and of pre-service teachers are recognition, relationships, profiling, comparing, laddering and verifying. Beside this, the connection between reasoning and sense making is rich in line of flight in problem-posing tasks, while the connection is rich in line of rupture for pre-service teachers.

Keywords: first-degree equations, problem posing, reasoning, rhizomatic assemblage, sense-making, variation theory

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Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Sevket Ceyhun Cetin, Mehmet Oren

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According to existing educational research studies, students learn better with high teacher quality. Therefore, professional development has become a crucial way of increasing the quality of novices and veteran in-service teachers by providing support regarding content and pedagogy. To answer what makes PD effective, researchers have studied different PD models and revealed some critical elements that need to be considered, such as duration of a PD and the manner of delivery (e.g., lecture vs. engaging). Also, it has been pointed out that if PDs are prepared as one-size-fits-all, they most likely be ineffective in addressing teachers’ needs toward improving instructional quality. Instead, teachers’ voices need to be heard, and the foci of PDs should be determined based on their specific needs. Thus, this study was conducted to identify professional development needs of middle school mathematics teachers based on their self-evaluation of their performances in light of teaching standards. This study also aimed to explore whether the PD needs with respect to years of teaching experience (novice vs. veteran). These teachers had participated in a federally-funded research grant, which aimed to improve the competencies of 6-9 grade-level mathematics teachers in pedagogy and content areas. In the research project, the participants had consistently videoed their lessons throughout a school year and reflected on their performances, using Teacher Advanced Program (TAPTM) rubric, which was based on the best practices of teaching. Particularly, they scored their performances in the following areas and provided evidence as the justifications of their scores: Standards and Objectives, Presenting Instructional Content, Lesson Structure and Pacing, Activities and Materials, Academic Feedback, Grouping Students, and Questioning. The rating scale of the rubric is 1 through 5 (i.e., 1=Unsatisfactory [performance], 3=Proficient, and 5=Exemplary). For each area mentioned above, the numerical scores of 77 written reports (for 77 videoed lessons) of 24 teachers (nnovices=12 and nveteran=12) were averaged. Overall, the average score of each area was below 3 (ranging between 2.43 and 2.86); in other words, teachers judged their performances incompetent across the seven areas. In the second step of the data analysis, the lowest three areas in which novice and veteran teachers performed poorly were selected for further qualitative analysis. According to the preliminary results, the lowest three areas for the novice teachers were: Questioning, Grouping Students, and Academic Feedback. Grouping Students was also one of the lowest areas of the veteran teachers, but the other two areas for this group were: Lesson Structure & Pacing, and Standards & Objectives. Identifying in-service teachers’ needs based on their reflective practitioner experiences provides educators very crucial information that can be used to create more effective PD that improves teacher quality.

Keywords: mathematics teacher, professional development, self-reflection, video data

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Authors: Zahra Alikhani Koopaei

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In the fifth lesson of the third-grade mathematics book, students are introduced to the concept of multiplication. However, some students showed a lack of interest in learning this topic. To address this, a simple electronic multiplication table was designed with the aim of making the concept of multiplication entertaining and engaging for students. It provides them with moments of excitement during the learning process. To achieve this goal, a device was created that produced a bell sound when two wire ends were connected. Each wire end was connected to a specific number in the multiplication table, and the other end was linked to the corresponding answer. Consequently, if the answer is correct, the bell will ring. This study employs interactive and engaging methods to teach mathematics, particularly to students who have previously shown little interest in the subject. By integrating game-based learning and critical thinking, we observed an increase in understanding and interest in learning multiplication compared to before using this method. This further motivated the students. As a result, the intelligent multiplication table was successfully designed. Students, under the instructor's supervision, could easily construct the device during the lesson. Through the implementation of these operations, the concept of multiplication was firmly established in the students' minds. Engaging multiple intelligences in each student enhances a more stable and improved understanding of the concept of multiplication.

Keywords: intelligent multiplication table, design, construction, education, increased interest, students

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Authors: Faiza Abdul Latip

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One of the ultimate goals of any nation is to produce competitive manpower and this includes Philippines. Inclination in the field of Mathematics has a significant role in achieving this goal. However, Mathematics, as considered by most people, is the most difficult subject matter along with its topics to learn. This could be manifested from the low performance of students in national and international assessments. Educators have been widely using learning style models in identifying the way students learn. Moreover, it could be the frontline in knowing the difficulties held by each learner in a particular topic specifically concepts pertaining to fractions. However, as what many educators observed, students show difficulties in doing mathematical tasks and in great degree in dealing with fractions most specifically in the district of Datu Odin Sinsuat, Maguindanao. This study focused on the Datu Odin Sinsuat district grade six pupils’ learning styles along with their achievements and difficulties in learning concepts on fractions. Five hundred thirty-two pupils from ten different public elementary schools of the Datu Odin Sinsuat districts were purposively used as the respondents of the study. A descriptive research using the survey method was employed in this study. Quantitative analysis on the pupils’ learning styles on the Kolb’s Learning Style Inventory (KLSI) and scores on the mathematics diagnostic test on fraction concepts were made using this method. The simple frequency and percentage counts were used to analyze the pupils’ learning styles and their achievements on fractions. To determine the pupils’ difficulties in fractions, the index of difficulty on every item was determined. Lastly, the Kruskal-Wallis Test was used in determining the significant difference in the pupils’ achievements on fractions classified by their learning styles. This test was set at 0.05 level of significance. The minimum H-Value of 7.82 was used to determine the significance of the test. The results revealed that the pupils of Datu Odin Sinsuat districts learn fractions in varied ways as they are of different learning styles. However, their achievements in fractions are low regardless of their learning styles. Difficulties in learning fractions were found most in the area of Estimation, Comparing/Ordering, and Division Interpretation of Fractions. Most of the pupils find it very difficult to use fraction as a measure, compare or arrange series of fractions and use the concept of fraction as a quotient.

Keywords: difficulties in fraction, fraction, Kolb's model, learning styles

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Authors: Verónica Arredondo, Miguel Martínez-Panero, Teresa Peña, Victoriano Ramírez

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The Mexican Chamber of Deputies is composed of 500 representatives: 300 of them elected by relative majority and another 200 ones elected through proportional representation in five electoral clusters (constituencies) with 40 representatives each. In this mixed-member electoral system, the seats distribution of proportional representation is not independent of the election by relative majority, as it attempts to correct representation imbalances produced in single-member districts. This two-fold structure has been maintained in the successive electoral reforms carried out along the last three decades (eight from 1986 to 2014). In all of them, the election process of 200 seats becomes complex: Formulas in the Law are difficult to understand and to be interpreted. This paper analyzes the Mexican electoral system after the electoral reform of 2014, which was applied for the first time in 2015. The research focuses on contradictions and issues of applicability, in particular situations where seats allocation is affected by ambiguity in the law and where asymmetrical treatment of political parties arises. Due to these facts, a proposal of electoral reform will be presented. It is intended to be simpler, clearer, and more enduring than the current system. Furthermore, this model is more suitable for producing electoral outcomes free of contradictions and paradoxes. This approach would allow a fair treatment of political parties and as a result an improved opportunity to exercise democracy.

Keywords: electoral mathematics, electoral reform, Mexican electoral system, political asymmetry, proportional representation

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Authors: Noa Shriki, Atara Shriki

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Lifelong learning is considered as essential for teacher's professional development, which in turn has implications for the improvement of the entire education system. In recent years, many programs designed to support teachers' professional development are criticized for not achieving their goal. A variety of reasons have been proposed for the purpose of explaining the causes of the ineffectiveness of such programs. In this study, we put to test the possibility that teachers do not change as a result of their participation in professional programs due to a gap between the contents and approaches included in them and teacher's beliefs about teaching and learning. Eighteen elementary school mathematics teachers participated in the study. These teachers were involved in collaborating with their students in inquiring mathematical ideas, while implementing action research. Employing educational theories, the results indicated that this experience had a positive effect on teacher's professional development. In particular, there was an evident change in their beliefs regarding their role as mathematics teachers. However, while employing a different perspective for analyzing the data, the lens of Kurt Lewin's theory of re-education, we realized that this change of beliefs must be questioned. Therefore, it is suggested that analysis of educational processes should be carried out not only through common educational theories, but also on the basis of social and organizational theories. It is assumed that both the field of education and the fields of social studies and organizational consulting will benefit from the multifocal viewpoint

Keywords: educational theories, professional development, re-education, teachers' beliefs

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Authors: Roselyn Alejandro-Ymana

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The study was an attempt to assess the MTAP Saturday Class Program along its eight components namely, modules, instructional materials, scheduling, trainer-teachers, supervisory support, administrative support, financial support and educational facilities, the results of which served as bases in developing policy guidelines to enhance the MTAP Saturday Class Program. Using a descriptive development method of research, this study involved the participation of twenty-eight (28) schools with MTAP Saturday Class Program in the Division of Dasmarinas City where twenty-eight school heads, one hundred twenty-five (125) teacher-trainer, one hundred twenty-five (125) pupil program participants, and their corresponding one hundred twenty-five (125) parents were purposively drawn to constitute the study’s respondent. A self-made validated survey questionnaire together with Pre and Post-Test Assessment Test in Mathematics for pupils participating in the program, and an unstructured interview guide was used to gather the data needed in the study. Data obtained from the instruments administered was organized and analyzed through the use of statistical tools that included the Mean, Weighted Mean, Relative Frequency, Standard Deviation, F-Test or One-Way ANOVA and the T-Test. Results of the study revealed that all the eight domains involved in the MTAP Saturday Class Program were practiced with the areas of 'trainer-teachers', 'educational facilities', and 'supervisory support' identified as the program’s strongest components while the areas of 'financial support', 'modules' and 'scheduling' as being the weakest program’s components. Moreover, the study revealed based on F-Test, that there was a significant difference in the assessment made by the respondents in each of the eight (8) domains. It was found out that the parents deviated significantly from the assessment of either the school heads or the teachers on the indicators of the program. There is much to be desired when it comes to the quality of the implementation of the MTAP Saturday Class Program. With most of the indicators of each component of the program, having received overall average ratings that were at least 0.5 point away from the ideal rating 5 for total quality, school heads, teachers, and supervisors need to work harder for total quality of the implementation of the MTAP Saturday Class Program in the division.

Keywords: mathematics achievement, MTAP program, policy guidelines, program assessment

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Authors: Irena Smetackova

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The important part of school mathematics are word problems which represent the connection between school knowledge and life reality. To find the reasons why students consider word problems to be difficult, it is necessary to take into consideration the motivational settings, besides mathematical knowledge and reading skills. Our goal is to identify whether the familiar or unfamiliar context of math word problem influences solving success rate and if so, whether the reasons are motivational or cognitive. For this purpose, we conducted three steps study in group of fifty pupils 9-10 years old. In the first step, we asked pupils to create ‘the best’ word problems for entered numerical formula. The set of 19 word problems with different contexts were selected. In the second step, pupils were asked to evaluate (without solving) how they like each item and how easy it is for them. The 6 word problems with low preference and low estimated success rate were selected and combined with other 6 problems with high preference and success rate. In the third step, the same pupils were asked to solve the word problems. The analysis showed that pupils attitudes and solving toward word problems varied by the context. The strong gender patterns both in preferred contexts and in estimated success rates were identified however the real success rate did not differ so strongly. The success gap between word problems with and without preferred contexts were stronger than the gap between problems with and without real experience with the context. The hypothesis that motivational factors are more important than cognitive factors was confirmed.

Keywords: mathematics, context of reality, motivation, cognition, word problems

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Authors: Bijan Gillani, Roya Gillani

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The purpose of this paper is to propose a pedagogical model where engineering provides the interconnection to integrate the other topics of science, technology, engineering, and mathematics. The author(s) will first present a brief discussion of cognitive theory and then derive an integrated pedagogy to use engineering and technology, such as drones, sensors, camera, iPhone, radio waves as the nexus to an integrated curriculum development for the other topics of STEM. Based on this pedagogy, one example developed by the author(s) called “Drones and Environmental Science,” will be presented that uses a drone and related technology as an appropriate instructional delivery medium to apply Piaget’s cognitive theory to create environments that promote the integration of different STEM subjects that relate to environmental science.

Keywords: cogntive theories, drone, environmental science, pedagogy

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Authors: Daniela Velichová

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Plenty of ideas on how to adopt active learning methods in education are available nowadays. Mathematics is a subject where the active involvement of students is required in particular in order to achieve desirable results regarding sustainable knowledge and deep understanding. The present article is based on the outcomes of an Erasmus+ project DrIVE-MATH, that was aimed at developing a novel and integrated framework to teach maths classes in engineering courses at the university level. It is fundamental for students from the early years of their academic life to have agile minds. They must be prepared to adapt to their future working environments, where enterprises’ views are always evolving, where all collaborate in teams, and relations between peers are thought for the well-being of the whole - workers and company profit. This reality imposes new requirements on higher education in terms of adaptation of different pedagogical methods, such as project-based and active-learning methods used within the course curricula. Active learning methodologies are regarded as an effective way to prepare students to meet the challenges posed by enterprises and to help them in building critical thinking, analytic reasoning, and insight to the solved complex problems from different perspectives. Fostering learning-by-doing activities in the pedagogical process can help students to achieve learning independence, as they could acquire deeper conceptual understanding by experimenting with the abstract concept in a more interesting, useful, and meaningful way. Clear information about learning outcomes and goals might help students to take more responsibility for their learning results. Active learning methods implemented by the project team members in their teaching practice, eduScrum and Jigsaw in particular, proved to provide better scientific and soft skills support to students than classical teaching methods. EduScrum method enables teachers to generate a working environment that stimulates students' working habits and self-initiative as they become aware of their responsibilities within the team, their own acquired knowledge, and their abilities to solve problems independently, though in collaboration with other team members. This method enhances collaborative learning, as students are working in teams towards a common goal - knowledge acquisition, while they are interacting with each other and evaluated individually. Teams consisting of 4-5 students work together on a list of problems - sprint; each member is responsible for solving one of them, while the group leader – a master, is responsible for the whole team. A similar principle is behind the Jigsaw technique, where the classroom activity makes students dependent on each other to succeed. Students are divided into groups, and assignments are split into pieces, which need to be assembled by the whole group to complete the (Jigsaw) puzzle. In this paper, analysis of students’ perceptions concerning the achievement of deeper conceptual understanding in mathematics and the development of soft skills, such as self-motivation, critical thinking, flexibility, leadership, responsibility, teamwork, negotiation, and conflict management, is presented. Some new challenges are discussed as brought by introducing active learning methods in the basic mathematics courses. A few examples of sprints developed and used in teaching basic maths courses at technical universities are presented in addition.

Keywords: active learning methods, collaborative learning, conceptual understanding, eduScrum, Jigsaw, soft skills

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Authors: Ana Hol

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We live in a constantly changing environment where technology has become an integral component of our day to day life. We rely heavily on mobile devices, we search for data via web, we utilise smart home sensors to create the most suited ambiences and we utilise applications to shop, research, communicate and share data. Heavy reliance on technology therefore is creating new connections between STEM (Science, Technology, Engineering and Mathematics) fields which in turn rises a question of what the STEM education of the future should be like? This study was based on the reviews of the six Australian Information Systems students who undertook an international study tour to India where they were given an opportunity to network, communicate and meet local students, staff and business representatives and from them learn about the local business implementations, local customs and regulations. Research identifies that if we are to continue to implement and utilise electronic devices on the global scale, such as for example implement smart cars that can smoothly cross borders, we will need the workforce that will have the knowledge about the cars themselves, their parts, roads and transport networks, road rules, road sensors, road monitoring technologies, graphical user interfaces, movement detection systems as well as day to day operations, legal rules and regulations of each region and country, insurance policies, policing and processes so that the wide array of sensors can be controlled across country’s borders. In conclusion, it can be noted that allowing students to learn about the local conditions, roads, operations, business processes, customs and values in different countries is giving students a cutting edge advantage as such knowledge cannot be transferred via electronic sources alone. However once understanding of each problem or project is established, multidisciplinary innovative STEM projects can be smoothly conducted.

Keywords: STEM, curiosity, innovation, advancements

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Authors: M. Tomaschko

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The integration of technology in educational settings has gained a lot of interest. Especially the use of mobile devices and accompanying mobile applications can offer great potentials to complement traditional education with new technologies and enrich students’ learning in various ways. Nevertheless, the usability of the deployed mathematics application is an indicative factor to exploit the full potential of technology enhanced learning because directing cognitive load toward using an application will likely inhibit effective learning. For this reason, the purpose of this research study is the identification of possible usability issues of the mobile GeoGebra Graphing Calculator application. Therefore, eye tracking in combination with task scenarios, think aloud method, and a SUS questionnaire were used. Based on the revealed usability issues, the mobile application was iteratively redesigned and assessed in order to verify the success of the usability improvements. In this paper, the identified usability issues are presented, and recommendations on how to overcome these concerns are provided. The main findings relate to the conception of a mathematics keyboard and the interaction design in relation to an equation editor, as well as the representation of geometrical construction tools. In total, 12 recommendations were formed to improve the usability of a mobile graphing calculator application. The benefit to be gained from this research study is not only the improvement of the usability of the existing GeoGebra Graphing Calculator application but also to provide helpful hints that could be considered from designers and developers of mobile math applications.

Keywords: GeoGebra, graphing calculator, math education, smartphone, usability

Procedia PDF Downloads 113