Search results for: mathematics tutoring

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: Santiago Moll Lopez, Erica Vega Fleitas, Dolors Rosello Ferragud, Luis Manuel Sanchez Ruiz, Jose Antonio Moraño Fernandez

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Game-based learning (GBL) is becoming popular in education. Learning through games offers students a motivating experience related to the social aspect of games. Among the significant positive outcomes are promoting positive emotions and collaboration, improving the assimilation of concepts, and creating an attractive and dynamic environment standout. This work presents a study of the design and implementation of games created with RPG Maker MZ software with a Sci-Fi storytelling environment for developing specific and transversal skills in a Mathematics subject at the Beng in Aerospace Engineering. Games were applied during regular classes and as a part of a Flip-Teaching methodology to increase the motivation and the assimilation of mathematical concepts in an engaging way. The key features of the games were the introduction of avatar design and the promotion of collaboration among students. Students' opinions and grades obtained in the activities and exams showed increased motivation and a significant improvement in their performance compared with other groups or past students' performances.

Keywords: game-based learning, rol games, mathematics, science fiction

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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: Richard Harrison

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Developing competency in mathematics and related critical thinking skills is essential to the education of undergraduate students of Science, Technology, Engineering and Mathematics (STEM). Recently, the HE sector has been impacted by a seemingly widening disconnect between the mathematical competency of incoming first-year STEM students and their entrance qualification tariffs. Despite relatively high grades in A-Level Mathematics, students may initially lack fundamental skills in key areas such as algebraic manipulation and have limited capacity to apply problem solving strategies. Compounded by compensatory measures applied to entrance qualifications during the pandemic, there has been an associated decline in student performance on introductory university mathematics modules. In the UK, a number of online resources have been developed to help scaffold the transition to university mathematics. However, in general, these do not offer a structured learning journey focused on individual developmental needs, nor do they offer an experience coherent with the teaching and learning characteristics of the destination institution. In order to address some of these issues, a bespoke framework has been designed and implemented on our VLE in the Faculty of Engineering & Physical Sciences (FEPS) at the University of Surrey. Called the FEPS Maths Support Framework, it was conceived to scaffold the mathematical development of individuals prior to entering the university and during the early stages of their transition to undergraduate studies. More than 90% of our incoming STEM students voluntarily participate in the process. Students complete a set of initial diagnostic questions in the late summer. Based on their performance and feedback on these questions, they are subsequently guided to self-select specific mathematical topic areas for review using our proprietary resources. This further assists students in preparing for discipline related diagnostic tests. The framework helps to identify students who are mathematically weak and facilitates early intervention to support students according to their specific developmental needs. This paper presents a summary of results from a rich data set captured from the framework over a 3-year period. Quantitative data provides evidence that students have engaged and developed during the process. This is further supported by process evaluation feedback from the students. Ranked performance data associated with seven key mathematical topic areas and eight engineering and science discipline areas reveals interesting patterns which can be used to identify more generic relative capabilities of the discipline area cohorts. In turn, this facilitates evidence based management of the mathematical development of the new cohort, informing any associated adjustments to teaching and learning at a more holistic level. Evidence is presented establishing our framework as an effective early intervention strategy for addressing the sector-wide issue of supporting the mathematical development of STEM students transitioning to HE

Keywords: competency, development, intervention, scaffolding

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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: 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: Sibawu Witness Siyepu

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This study explores the effects of instructional design using blended learning in the learning of radian measures among Engineering students. Blended learning is an education programme that combines online digital media with traditional classroom methods. It requires the physical presence of both lecturer and student in a mathematics computer laboratory. Blended learning provides element of class control over time, place, path or pace. The focus was on the use of Khan Academy to supplement traditional classroom interactions. Khan Academy is a non-profit educational organisation created by educator Salman Khan with a goal of creating an accessible place for students to learn through watching videos in a computer assisted computer. The researcher who is an also lecturer in mathematics support programme collected data through instructing students to watch Khan Academy videos on radian measures, and by supplying students with traditional classroom activities. Classroom activities entails radian measure activities extracted from the Internet. Students were given an opportunity to engage in class discussions, social interactions and collaborations. These activities necessitated students to write formative assessments tests. The purpose of formative assessments tests was to find out about the students’ understanding of radian measures, including errors and misconceptions they displayed in their calculations. Identification of errors and misconceptions serve as pointers of students’ weaknesses and strengths in their learning of radian measures. At the end of data collection, semi-structure interviews were administered to a purposefully sampled group to explore their perceptions and feedback regarding the use of blended learning approach in teaching and learning of radian measures. The study employed Algebraic Insight Framework to analyse data collected. Algebraic Insight Framework is a subset of symbol sense which allows a student to correctly enter expressions into a computer assisted systems efficiently. This study offers students opportunities to enter topics and subtopics on radian measures into a computer through the lens of Khan Academy. Khan academy demonstrates procedures followed to reach solutions of mathematical problems. The researcher performed the task of explaining mathematical concepts and facilitated the process of reinvention of rules and formulae in the learning of radian measures. Lastly, activities that reinforce students’ understanding of radian were distributed. Results showed that this study enthused the students in their learning of radian measures. Learning through videos prompted the students to ask questions which brought about clarity and sense making to the classroom discussions. Data revealed that sense making through reinvention of rules and formulae assisted the students in enhancing their learning of radian measures. This study recommends the use of Khan Academy in blended learning to be introduced as a socialisation programme to all first year students. This will prepare students that are computer illiterate to become conversant with the use of Khan Academy as a powerful tool in the learning of mathematics. Khan Academy is a key technological tool that is pivotal for the development of students’ autonomy in the learning of mathematics and that promotes collaboration with lecturers and peers.

Keywords: algebraic insight framework, blended learning, Khan Academy, radian measures

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Authors: Sereen Itani

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As the world aspires for technological innovation, Innovative Robotics Technology-Supported Pedagogic Models in STEAM Education (Science, Technology, Engineering, Arts, and Mathematics) are critical in our global education system to build and enhance the next generation 21st century skills. Thus, diverse international schools endeavor in attempts to construct an integrated robotics and technology enhanced curriculum based on interdisciplinary subjects. Accordingly, it is vital that the globe remains resilient in STEAM fields by equipping the future learners and educators with Innovative Technology Experiences through robotics to support such fields. A variety of advanced teaching methods is employed to learn about Robotics Technology-integrated pedagogic models. Therefore, it is only when STEAM and innovations in Robotic Technology becomes integrated with real-world applications that transformational learning can occur. Robotics STEAM education implementation faces major challenges globally. Moreover, STEAM skills and concepts are communicated in separation from the real world. Instilling the passion for robotics and STEAM subjects and educators’ preparation could lead to the students’ majoring in such fields by acquiring enough knowledge to make vital contributions to the global STEAM industries. Thus, this necessitates the establishment of Pedagogic models such as Innovative Robotics Technologies to enhance STEAM education and develop students’ 21st-century skills. Moreover, an ICT innovative supported robotics classroom will help educators empower and assess students academically. Globally, the Robotics Design System and platforms are developing in schools and university labs creating a suitable environment for the robotics cross-discipline STEAM learning. Accordingly, the research aims at raising awareness about the importance of robotics design systems and methodologies of effective employment of robotics innovative technology-supported pedagogic models to enhance and develop (STEAM) education globally and enhance the next generation 21st century skills.

Keywords: education, robotics, STEAM (Science, Technology, Engineering, Arts and Mathematics Education), challenges

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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: 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: 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 defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both 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 double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: Jessica Chakowa

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Learning a foreign language requires practice that needs to be undertaken beyond the classroom. Nowadays, learners can find a lot of resources online, but it can be challenging for them to find suitable material, receive timely and effective feedback on their progress, and, more importantly practice the target language with native speakers. This paper focuses on the development of interactive activities combined with online tutoring sessions to consolidate and enhance the learning experience of beginner students of French at * University. This project is based on collaboration with four pre-service teachers from a French university. It calls for authentic language learning material, real-life situations, cultural awareness, and aims for the sustainability of learning and teaching. The paper will first present the design of the project as part of a holistic approach. It will then provide some examples of activities before commenting on the learners and the teachers’ experiences based on quantitative and qualitative data obtained through activity reports, surveys and focus groups. The main findings of the study lie in the tension between the willingness to achieve pedagogical goals and to be involved in authentic interactions, highlighting the complementary between the role of the learner and the role of teacher. The paper will conclude on benefits, challenges and recommendations when implementing such educational projects.

Keywords: authenticity, language teaching and learning, online interaction, sustainability

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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: Naomi Weiner-Levy

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The Mofet Institute of Research, established a School of Professional Development, the only one of its kind in Israel and throughout the world. It offers specialized programs for teacher educators, providing them with the professional knowledge and skills. The studies aim at updating teachers about rapidly changing knowledge and skills. Teacher educators are conceptualized as shifting from first order practitioners (school teachers) to second order practitioners. Those who train teachers are referred to as third order practitioners. The instructors in the School of Professional Development are third-order practitioners – teacher educators specializing in teaching their colleagues. Collegial guidance by teachers’ college staff members is no simple task: Tutors must be expert in their field of specialization, as well as in instruction. Moreover, although colleagues, they have to position themselves within the group as authoritative figures in terms of instruction and knowledge. To date, the role and professional identity of these third-order practitioners, has not been studied. To understand the nature and development of professional identity, a qualitative study was conducted in which 12 tutors of various subjects were interviewed. These were analyzed by categorical content analysis. The findings, assessed professional identity through a post-modern prism, while examining the interplay among events that tutors experienced, the knowledge they acquired and the structuring of their professional identity. The Tutors’ identity transformed through negotiating with ‘self’ and ‘other’ in the class, and constructed by their mutual experiences as tutors and learners. Understanding the function and identity of tutors facilitates comprehension of this unique training process for teacher educators.

Keywords: professional development, professional identity, teacher education, tutoring

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Authors: J. R. Bhalla, Gautam, Gurcharan Singh, Sanjeev Naval

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Mathematics is everywhere behind the every things on the earth as well as in the universe. Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. Now a day’s we can made and apply an equation on a complex geometry through applied mathematics. Here we work and focus on to create a formula which apply in the field of civil engineering in new concrete technology. In this paper our target is to make a formula which is applied on “BAUT” Metal Aggregate. In this paper our approach is to make formulation and equation on special “BAUT” Metal Aggregate by Applied Mathematical Study Case 1. BASIC PHYSICAL FORMULATION 2. ADVANCE EQUATION which shows the mechanical performance of special metal aggregates for concrete technology. In case 1. Basic physical formulation shows the surface area and volume manually and in case 2. Advance equation shows the mechanical performance has been discussed, the metal aggregates which had outstandingly qualities to resist shear, tension and compression forces. In this paper coarse metal aggregates is 20 mm which used for making high performance concrete (H.P.C).

Keywords: applied mathematical study case, special metal aggregates, concrete technology, basic physical formulation, advance equation

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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: Hatice Yildirim

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This study is an investigation into ‘The role of teaching assistants (TAs) for deaf pupils in an English primary school’, in order not only to contribute to the education of deaf pupils but also contribute to the literature, in which there has been a lack of attention paid to the role of TAs for deaf pupils. With this in mind, the research design was planned based on using a case study as a qualitative research approach in order to have a deep and first-hand understanding of the case for ‘the role of TAs for deaf pupils’ in a real-life context. 12 semi-structured classroom observations and six semi-structured interviews were carried out with four TAs and two teachers in one English mainstream primary school. The data analysis followed a thematic analysis framework. The results indicated that TAs are utilised based on a one-on-one support model and are deployed under the class teacher in the classroom. Out of the classroom activities are carried out in small groups with the agreement of the TAs and the class teacher, as per the policy of the school. Due to the one-on-one TA support model, the study pointed out the seven different roles carried out by TAs in the education of deaf pupils in an English mainstream primary school. While supporting deaf pupils academically and socially are the main roles of TAs, they also support deaf pupils by recording their progress, communicating with their parents, taking on a pastoral care role, tutoring them in additional support lessons, and raising awareness of deaf pupils’ issues.

Keywords: deaf, mainstream, teaching assistant, teaching assistant's roles

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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: Varda Gil, Ella Shoval, Tussia Mira

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Teacher mentoring is a complex practical profession whose unique characteristic is the teacher-mentors' commitment to helping teachers link theory with teaching practice in the process of decision-making and in their reflections on teaching. The aim of this research is to examine the way practicing teacher-mentors participating in a teacher mentoring course made the connection between theory and practice. The researchers analyzed 20 final papers submitted by participants in a course to train teacher mentors. The participants were all veteran high-school teachers. The course comprised 112 in-class hours in addition to mentoring novices in the field. The course covered the following topics: The teacher-mentors' perception of their role; formative and summative evaluation of the novices; tutoring strategies and tools; types of learners; and ways of communicating and dealing with novice teachers' resistance to counseling. The course participants were required to write a 4-5 page reflective summary of their field mentoring practice. In addition, they were required to link theories explicitly learned in the course to their practice in the field. A qualitative analysis of the papers led to the creation of the taxonomy of the link between theory and practice relating to four topics: The kinds of links made between theory and practice, the quality of these links, the links made between private teaching theories and official teaching theory, and the qualities of these links. This taxonomy may prove to be a useful tool in the teacher-mentor training processes.

Keywords: taxonomy, teacher-mentors, theory, practice, teacher-mentor training

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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 107