Search results for: making in mathematics

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: Ajayi Oluwasola Felix

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Management information system (MIS) provides information for the managerial activities in an organization. The main purpose of this research is, MIS provides accurate and timely information necessary to facilitate the decision-making process and enable the organizations planning control and operational functions to be carried out effectively. Management information system (MIS) is basically concerned with processing data into information and is then communicated to the various departments in an organization for appropriate decision-making. MIS is a subset of the overall planning and control activities covering the application of humans technologies, and procedures of the organization. The information system is the mechanism to ensure that information is available to the managers in the form they want it and when they need it.

Keywords: Management Information Systems (MIS), information technology, decision-making, MIS in Organizations

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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: Joel Vilca Tarazona, Igor Aguilar-Alonso

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The problem of this research related to business intelligence is the lack of a tool that supports automated and efficient financial analysis for decision-making and allows an evaluation of the financial statements, which is why the availability of the information is difficult. Relevant information to managers and users as an instrument in decision making financial, and administrative. For them, a business intelligence solution is proposed that will reduce information access time, personnel costs, and process automation, proposing a 4-layer architecture based on what was reviewed by the research methodology.

Keywords: decision making, business intelligence, Google Cloud, Microsoft Power BI

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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: Gennady P. Ginkul, Sergey Yu. Soloviov

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The article proposes to use so-called "quotation-based algorithm" for simulation of decision making process in distributed expert systems and multi-agent systems. The idea was adopted from the techniques for group decision-making. It is based on the assumption that one expert system to perform its logical inference may use rules from another expert system. The application of the algorithm was demonstrated on the example in which the consolidated decision is the decision that requires minimal quotation.

Keywords: backward chaining inference, distributed expert systems, group decision making, multi-agent systems

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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: Yogesh C. Sharma, A. Seetharaman

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The decision-making process in humans is a complicated system influenced by a variety of intrinsic and extrinsic factors. Human decisions have a ripple effect on subsequent decisions. In this study, the scope of human decision making is limited to employees. In an organisation, a person makes a variety of decisions from the time they are hired to the time they retire. The goal of this research is to identify various elements that influence decision-making. In addition, the environment in which a decision is made is a significant aspect of the decision-making process. Employees in today's workplace use artificial intelligence (AI) systems for automation and decision augmentation. The impact of AI systems on the decision-making process is examined in this study. This research is designed based on a systematic literature review. Based on gaps in the literature, limitations and the scope of future research have been identified. Based on these findings, a research framework has been designed to identify various factors affecting employee decision making. Employee decision making is influenced by technological advancement, data-driven culture, human trust, decision automation-augmentation, and workplace motivation. Hybrid human-AI systems require the development of new skill sets and organisational design. Employee psychological safety and supportive leadership influences overall job satisfaction.

Keywords: employee decision making, artificial intelligence (AI) environment, human trust, technology innovation, psychological safety

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Authors: Norfiza Ibrahim, Norshuhada Shiratuddin, Siti Mahfuzah Sarif

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Decision-making system is used to facilitate people in making the right choice for their important daily activities. For the youth, proper guidance in making important decisions is needed. Their skills in decision-making aid decisions will indirectly affect their future. For that reason, this study focuses on the intelligent aspects in the development of intelligent decision support application. The aid apparently integrates Personality Traits (PT) and Multiple Intelligence (MI) data in development of a computerized personal decision aid for youth named as Youth Personal Decision Aid (Youth PDA). This study is concerned with the aid’s helpfulness based on the hybrid intelligent process. There are four main items involved which are reliability, decision making effort, confidence, as well as decision process awareness. Survey method was applied to the actual user of this system, namely the school and the Institute of Higher Education (IPT)’s students. An establish instrument was used to evaluate the study. The results of the analysis and findings in the assessment indicates a high mean value of the four dimensions in helping Youth PDA to be accepted as a useful tool for the youth in decision-making.

Keywords: decision support, multiple intelligent, personality traits, youth personal decision aid

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Authors: Abdallah A. Hlayel

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Operations research science (OR) deals with good success in developing and applying scientific methods for problem solving and decision-making. However, by using OR techniques, we can enhance the use of computer decision support systems to achieve optimal management for institutions. OR applies comprehensive analysis including all factors that affect on it and builds mathematical modeling to solve business or organizational problems. In addition, it improves decision-making and uses available resources efficiently. The adoption of OR by universities would definitely contributes to the development and enhancement of the performance of OR techniques. This paper provides an understanding of the structures, approaches and models of OR in problem solving and decision-making.

Keywords: best candidates' method, decision making, decision support system, operations research

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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: P. Bharathiraja

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Computer Aided decision making system is used to enhance diagnosis and prognosis of diseases and also to assist clinicians and junior doctors in clinical decision making. Medical Data used for decision making should be definite and consistent. Data Mining and soft computing techniques are used for cleaning the data and for incorporating human reasoning in decision making systems. Fuzzy rule based inference technique can be used for classification in order to incorporate human reasoning in the decision making process. In this work, missing values are imputed using the mean or mode of the attribute. The data are normalized using min-ma normalization to improve the design and efficiency of the fuzzy inference system. The fuzzy inference system is used to handle the uncertainties that exist in the medical data. Equal-width-partitioning is used to partition the attribute values into appropriate fuzzy intervals. Fuzzy rules are generated using Class Based Associative rule mining algorithm. The system is trained and tested using heart disease data set from the University of California at Irvine (UCI) Machine Learning Repository. The data was split using a hold out approach into training and testing data. From the experimental results it can be inferred that classification using fuzzy inference system performs better than trivial IF-THEN rule based classification approaches. Furthermore it is observed that the use of fuzzy logic and fuzzy inference mechanism handles uncertainty and also resembles human decision making. The system can be used in the absence of a clinical expert to assist junior doctors and clinicians in clinical decision making.

Keywords: decision making, data mining, normalization, fuzzy rule, classification

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Authors: Benmansour Nassima, Benmansour Souheyla

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The appropriate integration of reward processing and decision making provided by the environment is vital for behavioural success and individuals’ well being in everyday life. Functional neurological investigation has already provided an inclusive image on affective and emotional (motivational) processing in the healthy human brain and has recently focused its interest also on the assessment of brain function in anxious and depressed individuals. This article offers an overview on the theoretical approaches that relate emotion and decision-making, and spotlights investigation with anxious or depressed individuals to reveal how emotions can interfere with decision-making. This research aims at incorporating the emotional structure based on response and stimulation with a Bayesian approach to decision-making in terms of probability and value processing. It seeks to show how studies of individuals with emotional dysfunctions bear out that alterations of decision-making can be considered in terms of altered probability and value subtraction. The utmost objective is to critically determine if the probabilistic representation of belief affords could be a critical approach to scrutinize alterations in probability and value representation in subjective with anxiety and depression, and draw round the general implications of this approach.

Keywords: decision-making, motivation, alteration, reward processing, response selection

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Authors: Eugenia Vomvoridi-Ivanovic

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

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

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Authors: Onesimus Bulus Shiaki

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

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

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Authors: Cristina-Maria Păcurar

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

Keywords: analytic geometry, conics, python, quadrics

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Authors: Yong Bum Shin

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This case focuses on Weighted additive difference, Conjunctive, Disjunctive, and Elimination by aspects methodologies in consumer decision-making models and the Simple additive weighting (SAW) approach in the multi-criteria decision-making (MCDM) area. Most decision-making models illustrate that the rank reversal phenomenon is unpreventable. This paper presents that rank reversal occurs in popular managerial methods such as Weighted Additive Difference (WAD), Conjunctive Method, Disjunctive Method, Elimination by Aspects (EBA) and MCDM methods as well as such as the Simple Additive Weighting (SAW) and finally Unified Commensurate Multiple (UCM) models which successfully addresses these rank reversal problems in most popular MCDM methods in decision-making area.

Keywords: multiple criteria decision making, rank inconsistency, unified commensurate multiple, analytic hierarchy process

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Authors: Han Hyuk Cho, Hanik Jo

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

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

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Authors: Adriana Avila Zuniga Nordfjeld

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This paper provides a literature review to document the state of the art with respect to handling 'human bias' in decision making within the established quality management systems (QMS) and LEAN theory, in the context of shipbuilding. Previous research shows that in shipbuilding there is a huge deviation from the planned man-hours under the project management to the actual man-hours used because of errors in planning and reworks caused by human bias in the information flows among others. This reduces the efficiency and increases operational costs. Thus, the research question is how QMS and LEAN handle biases. The findings show the gap in studying the integration of methods to handle human bias in decision making into QMS and lean, not only within shipbuilding but also in general. Theoretical and practical implications are discussed for researchers and practitioners in the areas of decision making QMS, LEAN, and future research is suggested.

Keywords: human bias, decision making, LEAN shipbuilding, quality management systems

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Authors: Joanne Hardman

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

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

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

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

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

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Authors: Josephine Shamash, Stuart Smith

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

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

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Authors: Muhammad Saqlain, Poom Kumam

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Language being an abstract system and creative act, is quite complicated as its meaning varies depending on the context. The context is determined by the empirical knowledge of a person, which is derived from observation and experience. About further subdivided attributes, the decision-making challenges may entail quantitative and qualitative factors. However, because there is no norm for putting a numerical value on language, existing approaches cannot carry out the operations of linguistic knowledge. The assigning of mathematical values (fuzzy, intuitionistic, and neutrosophic) to any decision-making problem; without considering any rule of linguistic knowledge is ambiguous and inaccurate. Thus, this paper aims to provide a generic model for these issues. This paper provides the linguistic set structure of the fuzzy hypersoft set (FLHSS) to solve decision-making issues. We have proposed the definition some basic operations like AND, NOT, OR, AND, compliment, negation, etc., along with Topology and examples, and properties. Secondly, the operational laws for the fuzzy linguistic hypersoft set have been proposed to deal with the decision-making issues. Implementing proposed aggregate operators and operational laws can be used to convert linguistic quantifiers into numerical values. This will increase the accuracy and precision of the fuzzy hypersoft set structure to deal with decision-making issues.

Keywords: linguistic quantifiers, aggregate operators, multi-criteria decision making (mcdm)., fuzzy topology

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Authors: Murray Olowa

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

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

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Authors: Gladys Maame Akua Setordzie

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Decision on one’s future career is said to have both beneficial and detrimental effects on one’s mental health, social and economic standing later in life, making it an important developmental problem for young people. In this light, the study’s overarching goal was to assess how different personality traits serve as a determinant of career decision-making difficulties experienced by university students in Ghana. Specifically, for the purpose of shaping the future of individualized career counselling support, the study investigated whether the “Big Five” personality traits influenced the difficulties students at the University of Ghana encounter while making career decisions. Cross-sectional survey design using a stratified random sampling technique, sampled 494 undergraduate students from the University of Ghana, who completed the Big Five Questionnaire and the Career Decision-making Difficulties Questionnaire. Hierarchical multiple regression analyses indicated that neuroticism, consciousness, and openness, accounted for a significant proportion of the variance in career decision-making difficulties. This study provides empirical evidence to support the idea that neuroticism is not necessarily a negative emotion when it comes to career decisionmaking, as has been suggested in previous studies, but rather it allows students to perform better in career decision-making. These results suggests that personality traits play a significant role in the career decision-making process of students of the University of Ghana. Therefore, a better understanding of how different personal and interpersonal factors impact career indecision in students could help career counsellors develop more focused vocational and career guidance interventions.

Keywords: career decision-making difficulties, dysfunctional career beliefs, personality traits, young people

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Authors: Farhaz Amyn Rajabali, Collins Odour

Abstract:

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

Keywords: AR, mathematics, system development, augmented reality

Procedia PDF Downloads 60

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

Abstract:

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

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

Procedia PDF Downloads 28

Authors: Zhidong Zhang, Amanda Resendez

Abstract:

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

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

Procedia PDF Downloads 111