Search results for: computational mathematics

Authors: M. Rodionov, Z. Dedovets

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The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.

Keywords: teaching strategy, mathematics, motivation, student

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Authors: Asadullah Sheikh, Kerry Barnett, Paul Ayres

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Despite significant progress in access, equity and public examination success, poor student performance in mathematics in secondary schools has become a major concern in Bangladesh. A substantial body of research has emphasised the important contribution of teaching practices to student achievement. However, this has not been investigated in Bangladesh. Therefore, the study sought to find out the effectiveness of mathematics teaching practices as a means of improving secondary school mathematics in Dhaka Municipality City (DMC) area, Bangladesh. The purpose of this study was twofold, first, to identify the 20 highest performing secondary schools in mathematics in DMC, and second, to investigate the teaching practices of mathematics teachers in these schools. A two-phase mixed method approach was adopted. In the first phase, secondary source data were obtained from the Board of Intermediate and Secondary Education (BISE), Dhaka and value-added measures used to identify the 20 highest performing secondary schools in mathematics. In the second phase, a concurrent mixed method design, where qualitative methods were embedded within a dominant quantitative approach was utilised. A purposive sampling strategy was used to select fifteen teachers from the 20 highest performing secondary schools. The main sources of data were classroom teaching observations, and teacher interviews. The data from teacher observations were analysed with descriptive and nonparametric statistics. The interview data were analysed qualitatively. The main findings showed teachers adopt a direct teaching approach which incorporates orientation, structuring, modelling, practice, questioning and teacher-student interaction that creates an individualistic learning environment. The variation in developmental levels of teaching skill indicate that teachers do not necessarily use the qualitative (i.e., focus, stage, quality and differentiation) aspects of teaching behaviours effectively. This is the first study to investigate teaching behaviours of effective secondary mathematics teachers within Dhaka, Bangladesh. It contributes in an international dimension to the field of educational effectiveness and raise questions about existing constructivist approaches. Further, it contributes to important insights about teaching behaviours that can be used to inform the development of evidence-based policy and practice on quality teaching in Bangladesh.

Keywords: effective teaching, mathematics, secondary schools, student achievement, value-added measures

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Authors: Theresa Marie Miller, Ma. Nympha Joaquin

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The aim of this study was to check the predictive power of social-oriented and individual-oriented achievement motivation on student engagement and collaborative problem-solving skills in mathematics. A sample of 277 fourth year high school students from the Philippines were selected. Surveys and videos of collaborative problem solving activity were used to collect data from respondents. The mathematics teachers of the participants were interviewed to provide qualitative support on the data. Systemaitc correlation and regression analysis were employed. Results of the study showed that achievement motivations−SOAM and IOAM− linearly predicted student engagement but was not significantly associated to the collaborative problem-solving skills in mathematics. Student engagement correlated positively with collaborative problem-solving skills in mathematics. The results contribute to theorizing about the predictive power of achievement motivations, SOAM and IOAM on the realm of academic behaviors and outcomes as well as extend the understanding of collaborative problem-solving skills of 21st century learners.

Keywords: achievement motivation, collaborative problem-solving skills, individual-oriented achievement motivation, social-oriented achievement motivation, student engagement

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Authors: Ali Taher Othman Ali

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The aim of this research is to provide a draft proposal for the professional development of mathematics teachers in accordance with the orientation of science, technology, engineering and mathematics which is known by the abbreviation STEM, as a modern and contemporary orientation in the teaching and learning of mathematics and in order to achieve the objective of the research, the researcher used the theoretical descriptive method through the induction of the literature of education and the previous studies and experiments related to the topic. The researcher concluded by providing the proposal according to five basic axes, the first axe: professional development as a system, and its requirements include: development of educational systems, and allocate sufficient budgets to support the requirements of teaching STEM, identifying mechanisms for incentives and rewards for teachers attending professional development programs based on STEM; the second: development of in-depth knowledge content and its requirements include: basic sciences content development for STEM, linking the scientific understanding of teachers with real-world issues and problems, to provide the necessary resources to expand teachers' knowledge in this area; the third: the necessary pedagogical skills of teachers in the field of STEM, and its requirements include: identification of the required training and development needs and the mechanism of determining these needs, the types of professional development programs and the mechanism of designing it, the mechanisms and places of execution, evaluation and follow-up; the fourth: professional development strategies and mechanisms in the field of STEM, and its requirements include: using a variety of strategies to enable teachers to design and transfer effective educational experiences which reflect their scientific mastery in the fields of STEM, provide learning opportunities, and developing the skills of procedural research to generate new knowledge about the STEM; the fifth: to support professional development in the area of STEM, and its requirements include: support leadership within the school, provide a clear and appropriate opportunities for professional development for teachers within the school through professional learning communities, building partnerships between the Ministry of education and the local and international community institutions. The proposal includes other factors that should be considered when implementing professional development programs for mathematics teachers in the field of STEM.

Keywords: professional development, mathematics teachers, the orientation of science, technology, engineering and mathematics (STEM)

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Authors: Juanita Morris

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The purpose of this study will examine the mediating relationships between the theories of intelligence, mathematics anxiety, gender stereotype threat, meta-cognition and math performance through the use of eye tracking technology, affecting student perception and problem-solving abilities. The participants will consist of (N=80) female graduate students. Test administered were the Abbreviated Math Anxiety Scale, Tobii Eye Tracking software, gender stereotype threat through Google images, and they will be asked to describe their problem-solving approach allowed to measure metacognition. Participants will be administered mathematics problems while having gender stereotype threat shown to them through online images while being directed to look at the eye tracking software Tobii. We will explore this by asking ‘Is mathematics anxiety associated with the theories of intelligence and gender stereotype threat and how does metacognition and math performance place a role in mediating those perspectives?’. It is hypothesized that math-anxious students are more likely affected by the gender stereotype threat and that may play a role in their performance? Furthermore, we also want to explore whether math anxious students are more likely to be an entity theorist than incremental theorist and whether those who are math anxious will be more likely to be fixated on variables associated with coefficients? Path analysis and independent samples t-test will be used to generate results for this study. We hope to conclude that both the theories of intelligence and metacognition mediate the relationship between mathematics anxiety and gender stereotype threat.

Keywords: math anxiety, emotions, affective domains fo learning, cognitive underlinings

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Authors: Ezeamagu M.U, Madu B.C

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This study was designed to investigate the efficacy of 5Es constructivist-based instructional model on students’ retention in primary Mathematics. 5Es stands for Engagement, Exploration, Explanation, Elaboration and Evaluation. The study adopted the pre test post test non-equivalent control group quasi-experimental research design. The sample size for the study was one hundred and thirty four pupils (134), seventy six male (76) and fifty eight female (58) from two primary schools in Nsukka education zone. Two intact classes in each of the sampled schools comprising all the primary four pupils were used. Each of the schools was given the opportunity of being assigned randomly to either experimental or control group. The Experimental group was taught using 5Es model while the control group was taught using the conventional method. Two research questions were formulated to guide the study and three hypotheses were tested at p ≤ 0. 05. A Fraction Achievement Test (FAT) of ten (10) questions were used to obtain data on pupils’ retention. Research questions were answered using mean and standard deviation while hypotheses were tested using analysis of covariance (ANCOVA). The result revealed that the 5Es model was more effective than the conventional method of teaching in enhancing pupils’ performance and retention in mathematics, secondly there is no significant difference in the mean retention scores of male and female students taught using 5Es instructional model. Based on the findings, it was recommended among other things, that the 5Es instructional model should be adopted in the teaching of mathematics in primary level of the educational system. Seminar, workshops and conferences should be mounted by professional bodies, federal and state ministries of education on the use of 5Es model. This will enable the mathematics educator, serving teachers, students and all to benefit from the approach.

Keywords: constructivist, education, mathematics, primary, retention

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Authors: Early Sol A. Gadong, Lourdes C. Zamora, Jonny B. Pornel, Aurora Fe C. Bautista

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Various research has shown that writing allows students to engage in metacognition and provides them with a venue to communicate their disposition towards what they are learning. However, few studies have explored students’ feelings about the incorporation of such writing activities in their mathematics classes. Through reflection sheets, group discussions, and interviews, this mixed-methods study explored students’ perceptions and insights on supplementary writing activities in their Elementary Algebra class. Findings revealed that while students generally have a positive regard for writing activities, they have conflicting views about how writing activities can help them in their learning. A big majority contend that writing activities can enhance the learning of mathematical content and attitudes towards mathematics if they allow students to explore and synthesize what they have learned and reflected on their emotional disposition towards mathematics. Also, gender does not appear to play a significant role in students’ reactions to writing activities.

Keywords: writing in math, metacognition, affective factors in learning, elementary algebra classroom

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Authors: Ali Rashash Alzahrani, Elizabeth Stojanovski

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Data on various aspects of education are collected at the institutional and government level regularly. In Australia, for example, students at various levels of schooling undertake examinations in numeracy and literacy as part of NAPLAN testing, enabling longitudinal assessment of such data as well as comparisons between schools and states within Australia. Another source of educational data collected internationally is via the PISA study which collects data from several countries when students are approximately 15 years of age and enables comparisons in the performance of science, mathematics and English between countries as well as ranking of countries based on performance in these standardised tests. As well as student and school outcomes based on the tests taken as part of the PISA study, there is a wealth of other data collected in the study including parental demographics data and data related to teaching strategies used by educators. Overall, an abundance of educational data is available which has the potential to be used to help improve educational attainment and teaching of content in order to improve learning outcomes. A multivariate assessment of such data enables multiple variables to be considered simultaneously and will be used in the present study to help develop profiles of students based on performance in mathematics using data obtained from the PISA study.

Keywords: cluster analysis, education, mathematics, profiles

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Authors: Emmanuel Iyamuremye, Irenee Ndayambaje

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This study investigated the influence of Concrete Pictorial Abstract (CPA) teaching approach on mathematics achievement based on a sample of eighth-grade students (N = 10,345) from the Rwandan Lower Secondary School quasi-experimental study with pre-test and post-test control group of 2019 (RLSQES19). Key aspects studied included mathematics concept understanding and mathematics concept retention and how these are influenced by teacher's teaching approach. Specifically, the study aimed to a.) investigate students' concept understanding and concept retention in mathematics when exposed to CPA approach and to those exposed to non-CPA approach before and after the intervention, and b.) ascertain the significant difference between the performance of the students exposed to CPA approach and those exposed to non-CPA approach in terms of post-test scores and retention test scores. Two groups (control and experimental) undergone pre-test, post-test, and retention test. The assignment of control and experimental group among senior two classes from 10 schools was done randomly. The materials used to determine the performance of the students is a teacher-made test. Descriptive statistics and ANCOVA were used for the analysis of the study. For determining the improvement in concept understanding of mathematics, Hakes methods of calculating gain were used to analyze the pre-test and post test score. The level of performance of the two groups in the pre-test is below average level. During the post-test and retention test, the performance of students in non-CPA group is on average level, and students in CPA group are on above average level. Hakes methods of calculating gain revealed higher significant performance in the post-test and retention test of CPA group of students than non-CPA group of students.

Keywords: concept understanding, concept retention, performance, teaching approach

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Authors: Carol Okigbo

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Mathematical problem solving has long been accorded an important place in mathematics curricula at every education level in both advanced and emerging economies. Its classroom approaches have varied, such as teaching for problem-solving, teaching about problem-solving, and teaching mathematics through problem-solving. It requires engaging in tasks for which the solution methods are not eminent, making sense of problems and persevering in solving them by exhibiting processes, strategies, appropriate attitude, and adequate exposure. Teachers play important roles in helping students acquire competency in problem-solving; thus, they are expected to be good problem-solvers and have proper conceptions of problem-solving. Studies show that teachers’ conceptions influence their decisions about what to teach and how to teach. Therefore, how teachers view their roles in teaching problem-solving will depend on their pedagogical conceptions of problem-solving. If teaching problem-solving is a major component of secondary school mathematics instruction, as recommended by researchers and mathematics educators, then it is necessary to establish teachers’ conceptions, what they do, and how they approach problem-solving. This study is designed to determine secondary school teachers’ conceptions regarding mathematical problem solving, its current situation, how teachers’ conceptions relate to their demographics, as well as the interaction patterns in the mathematics classroom. There have been many studies of mathematics problem solving, some of which addressed teachers’ conceptions using single-method approaches, thereby presenting only limited views of this important phenomenon. To address the problem more holistically, this study adopted an integrated mixed methods approach which involved a quantitative survey, qualitative analysis of open-ended responses, and ethnographic observations of teachers in class. Data for the analysis came from a random sample of 327 secondary school mathematics teachers in two Nigerian states - Anambra State and Enugu State who completed a 45-item questionnaire. Ten of the items elicited demographic information, 11 items were open-ended questions, and 25 items were Likert-type questions. Of the 327 teachers who responded to the questionnaires, 37 were randomly selected and observed in their classes. Data analysis using ANOVA, t-tests, chi-square tests, and open coding showed that the teachers had different conceptions about problem-solving, which fall into three main themes: practice on exercises and word application problems, a process of solving mathematical problems, and a way of teaching mathematics. Teachers reported that no period is set aside for problem-solving; typically, teachers solve problems on the board, teach problem-solving strategies, and allow students time to struggle with problems on their own. The result shows a significant difference between male and female teachers’ conception of problems solving, a significant relationship among teachers’ conceptions and academic qualifications, and teachers who have spent ten years or more teaching mathematics were significantly different from the group with seven to nine years of experience in terms of their conceptions of problem-solving.

Keywords: conceptions, education, mathematics, problem solving, teacher

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Authors: Ayşegül Çabuk, Mine Işıksal

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Mathematics is a sense-making activity so that it requires meaningful learning. Hence based on this idea, meaningful mathematical connections are necessary to learn mathematics. At that point, the major question has become that which educational methods can provide opportunities to provide mathematical connections and to understand mathematics. The amalgam of reasoning and proof can be the one of the methods that creates opportunities to learn mathematics in a meaningful way. However, even if reasoning and proof should be included from prekindergarten to grade 12, studies in literature generally include secondary school students and pre-service mathematics teachers. With the light of the idea that the amalgam of reasoning and proof has significant effect on middle school students' mathematical learning, this study aims to investigate middle grade students' tendencies while reasoning the correctness of statements related to numbers. The sample included 272 middle grade students, specifically 69 of them were sixth grade students (25.4%), 101 of them were seventh grade students (37.1%) and 102 of them were eighth grade students (37.5%). Data was gathered through an achievement test including 2 essay types of problems about algebra. The answers of two items were analyzed both quantitatively and qualitatively in terms of students' solutions strategies while reasoning the correctness of the statements. Similar on the findings in the literature, most of the students, in all grade levels, used numerical examples to judge the statements. Moreover the results also showed that the majority of these students appear to believe that providing one or more selected examples is sufficient to show the correctness of the statement. Hence based on the findings of the study, even students in earlier ages have proving and reasoning abilities their reasoning's generally based on the empirical evidences. Therefore, it is suggested that examples and example-based reasoning can be a fundamental role on to generate systematical reasoning and proof insight in earlier ages.

Keywords: reasoning, mathematics learning, middle grade students

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Authors: Zahid Ullah, Atlas Khan

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In today's data-driven world, the role of mathematics in bridging the gap between theory and applications is becoming increasingly vital. This abstract highlights the significance of mathematics as a powerful tool for analyzing, interpreting, and extracting meaningful insights from vast amounts of data. By integrating mathematical principles with real-world applications, researchers can unlock the full potential of data-driven decision-making processes. This abstract delves into the various ways mathematics acts as a bridge connecting theoretical frameworks to practical applications. It explores the utilization of mathematical models, algorithms, and statistical techniques to uncover hidden patterns, trends, and correlations within complex datasets. Furthermore, it investigates the role of mathematics in enhancing predictive modeling, optimization, and risk assessment methodologies for improved decision-making in diverse fields such as finance, healthcare, engineering, and social sciences. The abstract also emphasizes the need for interdisciplinary collaboration between mathematicians, statisticians, computer scientists, and domain experts to tackle the challenges posed by the data-driven landscape. By fostering synergies between these disciplines, novel approaches can be developed to address complex problems and make data-driven insights accessible and actionable. Moreover, this abstract underscores the importance of robust mathematical foundations for ensuring the reliability and validity of data analysis. Rigorous mathematical frameworks not only provide a solid basis for understanding and interpreting results but also contribute to the development of innovative methodologies and techniques. In summary, this abstract advocates for the pivotal role of mathematics in bridging theory and applications in a data-driven world. By harnessing mathematical principles, researchers can unlock the transformative potential of data analysis, paving the way for evidence-based decision-making, optimized processes, and innovative solutions to the challenges of our rapidly evolving society.

Keywords: mathematics, bridging theory and applications, data-driven world, mathematical models

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Authors: Ahmet Erdoğan, Şahin Kesici, Mustafa Baloğlu

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Information technologies have lead to changes in the areas of communication, learning, and teaching. Besides offering many opportunities to the learners, these technologies have changed the teaching methods and beliefs of teachers. What the Technological Pedagogical Content Knowledge (TPACK) means to the teachers is considerably important to integrate technology successfully into teaching processes. It is necessary to understand how to plan and apply teacher training programs in order to balance students’ pedagogical and technological knowledge. Because of many inefficient teacher training programs, teachers have difficulties in relating technology, pedagogy and content knowledge each other. While providing an efficient training supported with technology, understanding the three main components (technology, pedagogy and content knowledge) and their relationship are very crucial. The purpose of this study is to determine whether motivational beliefs and self-regulated learning strategies are significant predictors of mathematics teacher candidates' TPACK perceptions. A hundred seventy five Turkish mathematics teachers candidates responded to the Motivated Strategies for Learning Questionnaire (MSLQ) and the Technological Pedagogical And Content Knowledge (TPACK) Scale. Of the group, 129 (73.7%) were women and 46 (26.3%) were men. Participants' ages ranged from 20 to 31 years with a mean of 23.04 years (SD = 2.001). In this study, a multiple linear regression analysis was used. In multiple linear regression analysis, the relationship between the predictor variables, mathematics teacher candidates' motivational beliefs, and self-regulated learning strategies, and the dependent variable, TPACK perceptions, were tested. It was determined that self-efficacy for learning and performance and intrinsic goal orientation are significant predictors of mathematics teacher candidates' TPACK perceptions. Additionally, mathematics teacher candidates' critical thinking, metacognitive self-regulation, organisation, time and study environment management, and help-seeking were found to be significant predictors for their TPACK perceptions.

Keywords: candidate mathematics teachers, motivational beliefs, self-regulated learning strategies, technological and pedagogical knowledge, content knowledge

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Authors: S. Rawashdi, D. Bshouty

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This paper aimed at discussing how to urge middle and high school Arab students in Israel to be aware of the importance of and investing in learning mathematics. In the first phase of the study, three questionnaires were passed to two nine-grade classes, one on Awareness, one on Awakeness and one on Learning. One of the two classes was an outstanding class from a public school (PUBS) of 31 students, and the other a heterogeneous class from a private school (PRIS) with 31 students. The Learning questionnaire which was administrated to the Awareness and Awareness topics was passed to PRIS and the Awareness and Awareness Questionnaires were passed to the PUBS class After two months we passed the post-questionnaire to both classes to validate the long-term impact of the study. The findings of the study show that awakeness and awareness processes have an effect on the math learning process, on its context in students' daily lives and their growing interest in learning math.

Keywords: awakeness, awareness, learning mathematics, pupils

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Authors: Jay-R. Hosana Leonidas, Jayson A. Lucilo

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The K-12 Curriculum in the Philippines shed light to mathematics education as it recognizes the use of smartphones/mobile phones as appropriate tools necessary in teaching mathematics. However, there were limited pieces of evidence on the use of these devices in teaching and learning process. This descriptive study developed lessons integrating the use of mobile phone applications with basis on low-level competencies of students in Precalculus and determined its effects on students’ conceptual understanding, procedural skills, and attitudes towards Precalculus. Employing Bring Your Own Device (BYOD) scheme in the study, lessons developed were conducted among Grade 11 Science, Technology, Engineering, and Mathematics (STEM) students at Central Bicol State University of Agriculture for the academic year 2018-2019. This study found that there is a significant difference between the competency levels of students along conceptual understanding and procedural skills prior to and after the conduct of lessons developed. Also, it disclosed that the use of mobile phone applications had positive effects on students’ attitudes towards Precalculus. Thus, the use of mobile phone applications in teaching Precalculus can enrich students’ understanding of concepts and procedural skills (solving and graphing skills) and can increase students’ motivation, self-confidence, and enjoyment in dealing with Precalculus.

Keywords: bring your own device, mathematics education, mobile phone applications, senior high school

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Authors: A. Giannakopoulos, S. B. Buckley

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Problem solving in any field is recognised as a prerequisite for any advancement in knowledge. For example in South Africa it is one of the seven critical outcomes of education together with critical thinking. As a systematic way to problem solving was initiated in mathematics by the great mathematician George Polya (the father of problem solving), more detailed and comprehensive ways in problem solving have been developed. This paper is based on the findings by the author and subsequent recommendations for further research in problem solving and critical thinking. Although the study was done in mathematics, there is no doubt by now in almost anyone’s mind that mathematics is involved to a greater or a lesser extent in all fields, from symbols, to variables, to equations, to logic, to critical thinking. Therefore it stands to reason that mathematical principles and learning cannot be divorced from any field. In management of knowledge situations, the types of problems are similar to mathematics problems varying from simple to analogical to complex; from well-structured to ill-structured problems. While simple problems could be solved by employees by adhering to prescribed sequential steps (the process), analogical and complex problems cannot be proceduralised and that diminishes the capacity of the organisation of knowledge creation and innovation. The low efficiency in some organisations and the low pass rates in mathematics prompted the author to view problem solving as a product. The authors argue that using mathematical approaches to knowledge management problem solving and treating problem solving as a product will empower the employee through further training to tackle analogical and complex problems. The question the authors asked was: If it is true that problem solving and critical thinking are indeed basic skills necessary for advancement of knowledge why is there so little literature of knowledge management (KM) about them and how they are connected and advance KM?This paper concludes with a conceptual model which is based on general accepted principles of knowledge acquisition (developing a learning organisation), knowledge creation, sharing, disseminating and storing thereof, the five pillars of knowledge management (KM). This model, also expands on Gray’s framework on KM practices and problem solving and opens the doors to a new approach to training employees in general and domain specific areas problems which can be adapted in any type of organisation.

Keywords: critical thinking, knowledge management, mathematics, problem solving

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Authors: Idha Novianti, Suci Nurhayati, Puryati, Elang Krisnadi

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Community service activities are activities of the academic community in practicing and cultivating science, knowledge, and technology to advance the general welfare and educate the nation's life as described in the Higher Education Law. Training activities on the use of GeoGebra software are an option because GeoGebra software is software that is easy to operate and complete in the presentation of graphic design. The training activity was held for 3 hours online via teams and 3 hours offline. Involving 15 junior high school mathematics teachers located around south Tangerang. As a result, all teachers were satisfied with the activity, and they had additional new knowledge and skills to teach mathematics in the topic of geometry and algebra. The existence of new knowledge made the participants increase their confidence in developing mathematical science for students at school.

Keywords: geogebra, Ms. teams, junior high school teacher, mathematics

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Authors: J. Shamash

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The high-school curriculum in algebra deals mainly with the solution of different types of equations. However, modern algebra has a completely different viewpoint and is concerned with algebraic structures and operations. A question then arises: What might be the relevance and contribution of an abstract algebra course for developing expertise and mathematical perspective in secondary school mathematics instruction? This is the focus of this paper. The course Algebra: From Equations to Structures is a carefully designed abstract algebra course for Israeli secondary school mathematics teachers. The course provides an introduction to algebraic structures and modern abstract algebra, and links abstract algebra to the high-school curriculum in algebra. It follows the historical attempts of mathematicians to solve polynomial equations of higher degrees, attempts which resulted in the development of group theory and field theory by Galois and Abel. In other words, algebraic structures grew out of a need to solve certain problems, and proved to be a much more fruitful way of viewing them. This theorems in both group theory and field theory. Along the historical ‘journey’, many other major results in algebra in the past 150 years are introduced, and recent directions that current research in algebra is taking are highlighted. This course is part of a unique master’s program – the Rothschild-Weizmann Program – offered by the Weizmann Institute of Science, especially designed for practicing Israeli secondary school teachers. A major component of the program comprises mathematical studies tailored for the students at the program. The rationale and structure of the course Algebra: From Equations to Structures are described, and its relevance to teaching school algebra is examined by analyzing three kinds of data sources. The first are position papers written by the participating teachers regarding the relevance of advanced mathematics studies to expertise in classroom instruction. The second data source are didactic materials designed by the participating teachers in which they connected the mathematics learned in the mathematics courses to the school curriculum and teaching. The third date source are final projects carried out by the teachers based on material learned in the course.

Keywords: abstract algebra , linking abstract algebra and school mathematics, school algebra, secondary school mathematics, teacher professional development

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Authors: Itumeleng Phage

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Students’ comprehension of graphs may be affected by the characteristics of the discipline in which the graph is used, the type of the task as well as the background of the students who are the readers or interpreters of the graph. This research study investigated these aspects of the graph comprehension of 152 first-year undergraduate physics students by comparing their responses to corresponding tasks in the mathematics and physics disciplines. The discipline characteristics were analysed for four task-related constructs namely coordinates, representations, area and slope. Students’ responses to corresponding visual decoding and judgement tasks set in mathematics and kinematics contexts were statistically compared. The effects of the participants’ gender, year of school completion and study course were determined as reader characteristics. The results of the empirical study indicated that participants generally transferred their mathematics knowledge on coordinates and representation of straight line graphs to the physics contexts, but not in the cases of parabolic and hyperbolic functions or area under graphs. Insufficient understanding of the slope concept contributed to weak performances on this construct in both mathematics and physics contexts. Discipline characteristics seem to play a vital role in students’ understanding, while reader characteristics had insignificant to medium effects on their responses.

Keywords: kinematics graph, discipline characteristics, constructs, coordinates, representations, area and slope

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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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: Zhanna Dedovets

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Fostering a mathematical style of thinking is crucial for cultivating intellectual personalities capable of thriving in modern society. Intuitive thinking stands as a cornerstone among the components of mathematical cognition, playing a pivotal role in grasping mathematical truths across various disciplines. This article delves into the exploration of leveraging search activities rooted in students' intuitive thinking, particularly when tackling geometric problems. Emphasizing both student engagement with the task and their active involvement in the search process, the study underscores the importance of heuristic procedures and the freedom for students to chart their own problem-solving paths. Spanning several years (2019-2023) at the Physics and Mathematics Lyceum of Dushanbe, the research engaged 17 teachers and 78 high school students. After assessing the initial levels of intuitive thinking in both control and experimental groups, the experimental group underwent training following the authors' methodology. Subsequent analysis revealed a significant advancement in thinking levels among the experimental group students. The methodological approaches and teaching materials developed through this process offer valuable resources for mathematics educators seeking to enhance their students' learning experiences effectively.

Keywords: teaching of mathematics, intuitive thinking, heuristic procedures, geometric problem, students.

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Authors: R. M. Kashim

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

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

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Authors: Nazir Amir

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

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

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Authors: N. Dahbi, M. Daoudi

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This paper deals with the use of computational method based on Monte Carlo simulation in order to investigate the transport phenomena of the electron in HgCdTe narrow band gap semiconductor. Via this method we can evaluate the time dependence of the transport parameters: velocity, energy and mobility of electrons through matter (HgCdTe).

Keywords: Monte Carlo, transport parameters, HgCdTe, computational mechanics

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

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

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

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Authors: Eugenia Vomvoridi-Ivanovic

Abstract:

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

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

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Authors: Onesimus Bulus Shiaki

Abstract:

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

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

Procedia PDF Downloads 160

Authors: Cristina-Maria Păcurar

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

Keywords: analytic geometry, conics, python, quadrics

Procedia PDF Downloads 292

Authors: Joanne Hardman

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

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

Procedia PDF Downloads 281