Search results for: mathematical reasoning

Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Morteza Khorrami

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The logic as an intellectual infrastructure plays an essential role in the Islamic sciences. Hence, there are a few of the verses of the Holy Quran that their interpretation is not possible due to lack of proper logic. In many verses in the Quran, argument and the respondent has requested from the audience that shows the logic rule is in the Quran. The paper which use a descriptive and analytic method, tries to show the role of logic in understanding of the Quran reasoning methods and display some of Quranic statements with mathematical symbols and point that we can help these symbols for interesting and interpretation and answering to some questions and doubts. In this paper, this problem has been mentioned that the Quran did not use two-valued logic (Aristotelian) in all cases, but the fuzzy logic can also be searched in the Quran.

Keywords: aristotelian logic, fuzzy logic, interpretation, Holy Quran

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Authors: Maximilian Winkens, Peter Nyhuis

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Components with sensory properties such as gentelligent components developed at the Collaborative Research Center 653 offer a new angle on the full utilization of the remaining service life in case of a preventive maintenance. The developed methodology of component status driven maintenance analyses the stress data obtained during the component's useful life and on the basis of this knowledge assesses the type of maintenance called for in this case. The procedure is derived from the case-based reasoning method and will be elucidated in detail. The method's functionality is demonstrated with real-life data obtained during test runs of a racing car prototype.

Keywords: gentelligent component, preventive maintenance, case-based reasoning, sensory

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Authors: Ben G. Weber, Michael Mateas

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We present a case-based reasoning technique for selecting build orders in a real-time strategy game. The case retrieval process generalizes features of the game state and selects cases using domain-specific recall methods, which perform exact matching on a subset of the case features. We demonstrate the performance of the technique by implementing it as a component of the integrated agent framework of McCoy and Mateas. Our results demonstrate that the technique outperforms nearest-neighbor retrieval when imperfect information is enforced in a real-time strategy game.

Keywords: case based reasoning, real time strategy systems, requirements elicitation, requirement analyst, artificial intelligence

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Authors: Zhangquan Zhou, Guilin Qi

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Materialization is an important reasoning service for applications built on the Web Ontology Language (OWL). To make materialization efficient in practice, current research focuses on deciding tractability of an ontology language and designing parallel reasoning algorithms. However, some well-known large-scale ontologies, such as YAGO, have been shown to have good performance for parallel reasoning, but they are expressed in ontology languages that are not parallelly tractable, i.e., the reasoning is inherently sequential in the worst case. This motivates us to study the problem of parallel tractability of ontology materialization from a theoretical perspective. That is we aim to identify the ontologies for which materialization is parallelly tractable, i.e., in the NC complexity. Since the NC complexity is defined based on Boolean circuit that is widely used to investigate parallel computing problems, we first transform the problem of materialization to evaluation of Boolean circuits, and then study the problem of parallel tractability based on circuits. In this work, we focus on datalog rewritable ontology languages. We use Boolean circuits to identify two classes of datalog rewritable ontologies (called parallelly tractable classes) such that materialization over them is parallelly tractable. We further investigate the parallel tractability of materialization of a datalog rewritable OWL fragment DHL (Description Horn Logic). Based on the above results, we analyze real-world datasets and show that many ontologies expressed in DHL belong to the parallelly tractable classes.

Keywords: ontology materialization, parallel reasoning, datalog, Boolean circuit

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Authors: Preeda Sansakorn, Min An

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In order to be capable of dealing with uncertainties, subjectivities, including vagueness arising in building construction projects, the application of fuzzy reasoning technique based on fuzzy set theory is proposed. This study contributes significantly to the development of a fuzzy reasoning safety risk assessment model for building construction projects that could be employed to assess the risk magnitude of each hazardous event identified during construction, and a third parameter of probability of consequence is incorporated in the model. By using the proposed safety risk analysis methodology, more reliable and less ambiguities, which provide the safety risk management project team for decision-making purposes.

Keywords: safety risk assessment, building construction safety, fuzzy reasoning, construction risk assessment model, building construction projects

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Authors: Yaojun Wang, Yaoqing Wang

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Stock selection is an important decision-making problem. Many machine learning and data mining technologies are employed to build automatic stock-selection system. A profitable stock-selection system should consider the stock’s investment value and the market timing. In this paper, we present a hybrid system including both engage for stock selection. This system uses a case-based reasoning (CBR) model to execute the stock classification, uses a decision-tree model to help with market timing and stock selection. The experiments show that the performance of this hybrid system is better than that of other techniques regarding to the classification accuracy, the average return and the Sharpe ratio.

Keywords: case-based reasoning, decision tree, stock selection, machine learning

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Authors: Bruno Trstenjak, Dzenana Donko

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Data mining and classification of objects is the process of data analysis, using various machine learning techniques, which is used today in various fields of research. This paper presents a concept of hybrid classification model improved with the expert knowledge. The hybrid model in its algorithm has integrated several machine learning techniques (Information Gain, K-means, and Case-Based Reasoning) and the expert’s knowledge into one. The knowledge of experts is used to determine the importance of features. The paper presents the model algorithm and the results of the case study in which the emphasis was put on achieving the maximum classification accuracy without reducing the number of features.

Keywords: case based reasoning, classification, expert's knowledge, hybrid model

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Authors: Petros Roussos

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The present study focused on students' statistical reasoning related to Null Hypothesis Statistical Testing and p-values. Its objective was to test the hypothesis that neither the place (classroom, at a distance, online) nor the medium that actually supports the learning (ICT, internet, books) has an effect on understanding of statistical concepts. In addition, it was expected that students' attitudes towards statistics would not predict understanding of statistical concepts. The sample consisted of 385 undergraduate and postgraduate students from six state and private universities (five in Greece and one in Cyprus). Students were administered two questionnaires: a) the Greek version of the Survey of Attitudes Toward Statistics, and b) a short instrument which measures students' understanding of statistical significance and p-values. Results suggest that attitudes towards statistics do not predict students' understanding of statistical concepts, whereas the medium did not have an effect.

Keywords: attitudes towards statistics, blended learning, e-learning, statistical reasoning

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Authors: Kamalendu Pal

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This paper describes the main features of a knowledge-based system evaluation method. System evaluation is placed in the context of a hybrid legal decision-support system, Advisory Support for Home Settlement in Divorce (ASHSD). Legal knowledge for ASHSD is represented in two forms, as rules and previously decided cases. Besides distinguishing the two different forms of knowledge representation, the paper outlines the actual use of these forms in a computational framework that is designed to generate a plausible solution for a given case, by using rule-based reasoning (RBR) and case-based reasoning (CBR) in an integrated environment. The nature of suitability assessment of a solution has been considered as a multiple criteria decision making process in ASHAD evaluation. The evaluation was performed by a combination of discussions and questionnaires with different user groups. The answers to questionnaires used in this evaluations method have been measured as a combination of linguistic variables, fuzzy numbers, and by using defuzzification process. The results show that the designed evaluation method creates suitable mechanism in order to improve the performance of the knowledge-based system.

Keywords: case-based reasoning, fuzzy number, legal decision-support system, linguistic variable, rule-based reasoning, system evaluation

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Authors: Ozgu Hafizoglu

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Analogy is an essential tool of human cognition that enables connecting diffuse and diverse systems with attributional, deep structural, casual relations that are essential to learning, to innovation in artificial worlds, and to discovery in science. Cognitive Model of Analogy (CMA) leads and creates information pattern transfer within and between domains and disciplines in science. This paper demonstrates the Cognitive Model of Analogy (CMA) as an evolutionary approach to scientific research. The model puts forward the challenges of deep uncertainty about the future, emphasizing the need for flexibility of the system in order to enable reasoning methodology to adapt to changing conditions. In this paper, the model of analogical reasoning is created based on brain cells, their fractal, and operational forms within the system itself. Visualization techniques are used to show correspondences. Distinct phases of the problem-solving processes are divided thusly: encoding, mapping, inference, and response. The system is revealed relevant to brain activation considering each of these phases with an emphasis on achieving a better visualization of the brain cells: glial cells, axons, axon terminals, and neurons, relative to matching conditions of analogical reasoning and relational information. It’s found that encoding, mapping, inference, and response processes in four-term analogical reasoning are corresponding with the fractal and operational forms of brain cells: glial, axons, and neurons.

Keywords: analogy, analogical reasoning, cognitive model, brain and glials

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Authors: Yu Du, Jian-Guo Wang

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Green consumption is a key link to develop the ecological economy, and consumers are vital to carry out green consumption. With environmental awareness gradually being aroused, consumers often fail to turn their positive attitude into actual green consumption behavior. According to behavior reasoning theory, reasons for adoption have a direct (positive) influence on consumers’ attitude while reasons against adoption have a direct (negative) influence on consumers’ adoption intentions, the incongruous coexistence of which leads to the attitude-behavior gap of green consumption. Based on behavior reasoning theory, this research integrates reasons for adoption and reasons against adoption into a proposed model, in which reasons both for and against green consumption mediate the relationship between consumer’ values, attitudes, and behavioral intentions. It not only extends the conventional theory of reasoned action but also provides a reference for the government and enterprises to design the repairing strategy of green consumption attitude-behavior gap.

Keywords: green product, attitude-behavior gap, behavior reasoning theory, green consumption, SEM

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Authors: Flaurence Benjamain, Michel Casperance

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We present in this paper, first, a comparative study of three mathematical theories to achieve the fusion of information sources. This study aims to identify the characteristics inherent in theories of possibilities, belief functions (DST) and plausible and paradoxical reasoning to establish a strategy of choice that allows us to adopt the most appropriate theory to solve a problem of fusion in order, taking into account the acquired information and imperfections that accompany them. Using the new theory of plausible and paradoxical reasoning, also called Dezert-Smarandache Theory (DSmT), to fuse information multi-sources needs, at first step, the generation of the composites events witch is, in general, difficult. Thus, we present in this paper a new approach to construct pertinent paradoxical classes based on gray levels histograms, which also allows to reduce the cardinality of the hyper-powerset. Secondly, we developed a new technique for order and coding generalized focal elements. This method is exploited, in particular, to calculate the cardinality of Dezert and Smarandache. Then, we give an experimentation of classification of a remote sensing image that illustrates the given methods and we compared the result obtained by the DSmT with that resulting from the use of the DST and theory of possibilities.

Keywords: segmentation, image, approach, vision computing

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Authors: Ozgu Hafizoglu

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An analogy is an essential tool of human cognition that enables connecting diffuse and diverse systems with physical, behavioral, principal relations that are essential to learning, discovery, and innovation. The Cognitive Model of Analogy (CMA) leads and creates patterns of pathways to transfer information within and between domains in science, just as happens in the brain. The connectome of the brain shows how the brain operates with mental leaps between domains and mental hops within domains and the way how analogical reasoning mechanism operates. This paper demonstrates the CMA as an evolutionary approach to science, technology, and life. The model puts forward the challenges of deep uncertainty about the future, emphasizing the need for flexibility of the system in order to enable reasoning methodology to adapt to changing conditions in the new era, especially post-pandemic. In this paper, we will reveal how to draw an analogy to scientific research to discover new systems that reveal the fractal schema of analogical reasoning within and between the systems like within and between the brain regions. Distinct phases of the problem-solving processes are divided thusly: stimulus, encoding, mapping, inference, and response. Based on the brain research so far, the system is revealed to be relevant to brain activation considering each of these phases with an emphasis on achieving a better visualization of the brain’s mechanism in macro context; brain and spinal cord, and micro context: glia and neurons, relative to matching conditions of analogical reasoning and relational information, encoding, mapping, inference and response processes, and verification of perceptual responses in four-term analogical reasoning. Finally, we will relate all these terminologies with these mental leaps, mental maps, mental hops, and mental loops to make the mental model of CMA clear.

Keywords: analogy, analogical reasoning, brain connectome, cognitive model, neurons and glia, mental leaps, mental hops, mental loops

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Authors: Kay Thi Yar, Khin Mar Lar Tun

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Nowadays, social networks are so popular and widely used in all over the world. In addition, searching personal information of each person and searching connection between them (peoples’ relation in real world) becomes interesting issue in our society. In this paper, we propose a framework with three portions for exploring peoples’ relations from their connected information. The first portion focuses on the Graph database structure to store the connected data of peoples’ information. The second one proposes the graph database searching algorithm, the Modified-SoS-ACO (Sense of Smell-Ant Colony Optimization). The last portion proposes the Deductive Reasoning Algorithm to define two persons’ relationship. This study reveals the proper storage structure for connected information, graph searching algorithm and deductive reasoning algorithm to predict and analyze the personnel relationship from peoples’ relation in their connected information.

Keywords: personnel information, graph storage structure, graph searching algorithm, deductive reasoning algorithm

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Authors: Ananda Perera

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Computer-Assisted Medical Evaluation of Symptoms (CAMEOS) is a medical expert system designed to help General Practices (GPs) make an accurate diagnosis. CAMEOS comprises a knowledge base, user input, inference engine, reasoning module, and output statement. The knowledge base was developed by the author. User input is an Html file. The physician user collects data in the consultation. Data is sent to the inference engine at servers. CAMEOS uses set theory to simulate diagnostic reasoning. The program output is a list of differential diagnoses, the most probable diagnosis, and the diagnostic reasoning.

Keywords: CDSS, computerized decision support systems, expert systems, general practice, diagnosis, diagnostic systems, primary care diagnostic system, artificial intelligence in medicine

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Authors: Danielle Schneider, Ying Xie

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Middle school science, technology, engineering, and math (STEM) teachers experience an exceptional challenge in the expectation to incorporate curricula that builds strong spatial reasoning skills on rudimentary geometry concepts. Because spatial ability is so closely tied to STEM students’ success, researchers are tasked to determine effective instructional practices that create an authentic learning environment within the immersive virtual reality learning environment (IVRLE). This study looked to investigate the effect of the IVRLE on middle school STEM students’ spatial reasoning skills as a methodology to benefit the STEM middle school students’ spatial reasoning skills. This experimental study was comprised of thirty 7th-grade STEM students divided into a treatment group that was engaged in an immersive VR platform where they engaged in building an object in the virtual realm by applying spatial processing and visualizing its dimensions and a control group that built the identical object using a desktop computer-based, computer-aided design (CAD) program. Before and after the students participated in the respective “3D modeling” environment, their spatial reasoning abilities were assessed using the Middle Grades Mathematics Project Spatial Visualization Test (MGMP-SVT). Additionally, both groups created a physical 3D model as a secondary measure to measure the effectiveness of the IVRLE. The results of a one-way ANOVA in this study identified a negative effect on those in the IVRLE. These findings suggest that with middle school students, virtual reality (VR) proved an inadequate tool to benefit spatial relation skills as compared to desktop-based CAD.

Keywords: virtual reality, spatial reasoning, CAD, middle school STEM

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Authors: Huda Alazmi

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Social studies educational research has, so far, devoted very little attention towards spatial thinking in classroom teaching. To help address such paucity, this study explores the spatial thinking instructional experiences of middle school social studies teachers in Kuwait. The goal is to learn their teaching practices and assess teacher understanding for the spatial thinking concept to enable future improvements. Using a qualitative study approach, the researcher conducted semi-structured interviews to examine the relevant experiences of 14 social studies teachers. The findings revealed three major themes: (1) concepts of space, (2) tools of representation, and (3) spatial reasoning. These themes illustrated how social studies teachers focus predominantly upon simple concepts of space, using multiple tools of representation, but avoid addressing critical spatial reasoning. The findings help explain the current situation while identifying weaker areas for further analysis and improvement.

Keywords: spatial thinking, concepts of space, spatial representation, spatial reasoning

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Authors: Javier Parra-Domínguez, Juan Manuel Corchado

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At present, public efficiency is a concept that intends to maximize return on public investment focus on minimizing the use of resources and maximizing the outputs. The concept takes into account statistical criteria drawn up according to techniques such as DEA (Data Envelopment Analysis). The purpose of the current work is to consider, more precisely, the theoretical application of CBR (Case-Based Reasoning) from economics and computer science, as a preliminary step to improving the efficiency of law enforcement agencies (public sector). With the aim of increasing the efficiency of the public sector, we have entered into a phase whose main objective is the implementation of new technologies. Our main conclusion is that the application of computer techniques, such as CBR, has become key to the efficiency of the public sector, which continues to require economic valuation based on methodologies such as DEA. As a theoretical result and conclusion, the incorporation of CBR systems will reduce the number of inputs and increase, theoretically, the number of outputs generated based on previous computer knowledge.

Keywords: case-based reasoning, knowledge, police, public efficiency

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Authors: Hao-Hsiang Ku, Ching-Ho Chi

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Big data applications have become an imperative for many fields. Many researchers have been devoted into increasing correct rates and reducing time complexities. Hence, the study designs and proposes an Ontology-based backpropagation neural network classification and reasoning strategy for NoSQL big data applications, which is called ON4NoSQL. ON4NoSQL is responsible for enhancing the performances of classifications in NoSQL and SQL databases to build up mass behavior models. Mass behavior models are made by MapReduce techniques and Hadoop distributed file system based on Hadoop service platform. The reference engine of ON4NoSQL is the ontology-based backpropagation neural network classification and reasoning strategy. Simulation results indicate that ON4NoSQL can efficiently achieve to construct a high performance environment for data storing, searching, and retrieving.

Keywords: Hadoop, NoSQL, ontology, back propagation neural network, high distributed file system

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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: Sonia Anand Knowlton

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With the rise of artificial intelligence, computer science is becoming increasingly integrated in virtually every area of life. Of course, the law is no exception. Through argumentation frameworks (AFs), computer scientists have used abstract algebra to structure the legal reasoning process in a way that allows conclusions to be drawn from a formalized system of arguments. In AFs, arguments compete against each other for logical success and are related to one another through the binary operation of the attack. The prevailing arguments make up the preferred extension of the given argumentation framework, telling us what set of arguments must be accepted from a logical standpoint. There have been several developments of AFs since its original conception in the early 90’s in efforts to make them more aligned with the human reasoning process. Generally, these developments have sought to add nuance to the factors that influence the logical success of competing arguments (e.g., giving an argument more logical strength based on the underlying value it promotes). The most cogent development was that of the Extended Argumentation Framework (EAF), in which attacks can themselves be attacked by other arguments, and the promotion of different competing values can be formalized within the system. This article applies the logical structure of EAFs to current theoretical understandings of judicial reasoning to contribute to theories of judging and to the evolution of AFs simultaneously. The argument is that the main limitation of EAFs, when applied to judicial reasoning, is that they require judges to themselves assign values to different arguments and then lexically order these values to determine the given framework’s preferred extension. Drawing on John Rawls’ Theory of Justice, the examination that follows is whether values are lexical and commensurable to this extent. The analysis that follows then suggests a potential extension of the EAF system with an approach that formalizes different “planes of attack” for competing arguments that promote lexically ordered values. This article concludes with a summary of how these insights contribute to theories of judging and of legal reasoning more broadly, specifically in indeterminate cases where judges must turn to value-based approaches.

Keywords: computer science, mathematics, law, legal theory, judging

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Authors: Ang Ling Weay, Mona Masood

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This paper discusses the potential benefits of an interactive multimedia information representation in enhancing students’ critical thinking aligned with history reasoning in learning history between Secondary School students in Malaysia. Two modes of multimedia information representation implemented which are chronological and thematic information representation. A qualitative study of an unstructured interview was conducted among two history teachers, one history education lecturer, two i-think expert and program trainers and five form 4 secondary school students. The interview was to elicit their opinions on the implementation of thinking maps and interactive multimedia information representation in history learning. The key elements of interactive multimedia (e.g. multiple media, user control, interactivity, and use of timelines and concept maps) were then considered to improve the learning process. Findings of the preliminary investigation reveal that the interactive multimedia information representations have the potential benefits to be implemented as instructional resource in enhancing students’ higher order thinking skills (HOTs). This paper concludes by giving suggestions for future work.

Keywords: multimedia information representation, critical thinking, history reasoning, chronological and thematic information representation

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Authors: Luis Miguel Méndez Díaz

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

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

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Authors: Hooriya Sadr Dadras, Shiva Seyed Erfani

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Speaking skills merit meticulous attention both on the side of the learners and the teachers. In particular, accuracy is a critical component to guarantee the messages to be conveyed through conversation because a wrongful change may adversely alter the content and purpose of the talk. Different types of tasks have served teachers to meet numerous educational objectives. Besides, negotiation of meaning and the use of different strategies have been areas of concern in socio-cultural theories of SLA. Negotiation of meaning is among the conversational processes which have a crucial role in facilitating the understanding and expression of meaning in a given second language. Conversational strategies are used during interaction when there is a breakdown in communication that leads to the interlocutor attempting to remedy the gap through talk. Therefore, this study was an attempt to investigate if there was any significant difference between the effect of reasoning gap tasks and information gap tasks on the frequency of conversational strategies used in negotiation of meaning in classrooms on one hand, and on the accuracy in speaking of Iranian intermediate EFL learners on the other. After a pilot study to check the practicality of the treatments, at the outset of the main study, the Preliminary English Test was administered to ensure the homogeneity of 87 out of 107 participants who attended the intact classes of a 15 session term in one control and two experimental groups. Also, speaking sections of PET were used as pretest and posttest to examine their speaking accuracy. The tests were recorded and transcribed to estimate the percentage of the number of the clauses with no grammatical errors in the total produced clauses to measure the speaking accuracy. In all groups, the grammatical points of accuracy were instructed and the use of conversational strategies was practiced. Then, different kinds of reasoning gap tasks (matchmaking, deciding on the course of action, and working out a time table) and information gap tasks (restoring an incomplete chart, spot the differences, arranging sentences into stories, and guessing game) were manipulated in experimental groups during treatment sessions, and the students were required to practice conversational strategies when doing speaking tasks. The conversations throughout the terms were recorded and transcribed to count the frequency of the conversational strategies used in all groups. The results of statistical analysis demonstrated that applying both the reasoning gap tasks and information gap tasks significantly affected the frequency of conversational strategies through negotiation. In the face of the improvements, the reasoning gap tasks had a more significant impact on encouraging the negotiation of meaning and increasing the number of conversational frequencies every session. The findings also indicated both task types could help learners significantly improve their speaking accuracy. Here, applying the reasoning gap tasks was more effective than the information gap tasks in improving the level of learners’ speaking accuracy.

Keywords: accuracy in speaking, conversational strategies, information gap tasks, reasoning gap tasks

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Authors: Jeansou Moun

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This study argues that constructivism and structuralism, which have been the two important schools of mathematical philosophy since the mid-19th century, can and should be synthesized into structure-constructivism. In fact, the philosophy of mathematics is divided into more than ten schools depending on the point of view. However, the biggest trend is Platonism which claims that mathematical objects are "abstract entities" that exists independently of the human mind and material objects. Its opposite is constructivism. According to the latter, mathematical objects are products of the construction of the human mind. However, whether the basis of the construction is a logical device, a symbolic system, or an empirical perception, it is subdivided into logicism, formalism, and intuitionism. However, these three schools themselves are further subdivided into various variants, and among them, structuralism, which emerged in the mid-20th century, is receiving the most attention. On the other hand, structuralism which emphasizes structure instead of individual objects, is divided into non-eliminative structuralism, which supports the a priori of structure, and non-eliminative structuralism, which rejects any abstract entity. In this context, it is believed that the structure itself is not an a priori entity but a result of the construction of the cognitive subject and that no object has ever been given to us in its full meaning from the outset. In other words, concepts are progressively structured through a dialectical cycle between sensory perception, imagination (abstraction), concepts, judgments, and reasoning. Symbols are needed for formal operation. However, without concrete manipulation, the formal operation cannot have any meaning. However, when formal structurization is achieved, the reality (object) itself is also newly structured. This is the "structure-constructivism".

Keywords: philosophy of mathematics, platonism, logicism, formalism, constructivism, structuralism, structure-constructivism

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

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Authors: Apkar Salatian

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To relieve the burden of reasoning on a point to point basis, in many domains there is a need to reduce large and noisy data sets into trends for qualitative reasoning. In this paper we propose and describe a new architectural design pattern called REDUCER for reducing large and noisy data sets that can be tailored for particular situations. REDUCER consists of 2 consecutive processes: Filter which takes the original data and removes outliers, inconsistencies or noise; and Compression which takes the filtered data and derives trends in the data. In this seminal article, we also show how REDUCER has successfully been applied to 3 different case studies.

Keywords: design pattern, filtering, compression, architectural design

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Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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