Search results for: mathematical thinking

Authors: Paula Verdugo-Hernandez, Patricio Cumsille

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We analyze a first-class on the convergence of real number sequences, named hereafter sequences, to foster exploration and discovery of concepts through graphical representations before engaging students in proving. The main goal was to differentiate between sequences and continuous functions-of-a-real-variable and better understand concepts at an initial stage. We applied the analytic frame of mathematical working spaces, which we expect to contribute to extending to sequences since, as far as we know, it has only developed for other objects, and which is relevant to analyze how mathematical work is built systematically by connecting the epistemological and cognitive perspectives, and involving the semiotic, instrumental, and discursive dimensions.

Keywords: convergence, graphical representations, mathematical working spaces, paradigms of real analysis, real number sequences

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Authors: Song Hyok Choe

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This study presented a method to determine the optimum design parameters based on a mathematical model of the operating process in a manual electromagnetic hammer using solenoid electromagnets. The operating process of the electromagnetic hammer depends on the circuit scheme of the power controller. Mathematical modeling of the operating process was carried out by considering the energy transfer process in the forward and reverse windings and the electromagnetic force acting on the impact and brake pistons. Using the developed mathematical model, the initial design data of a manual electromagnetic hammer proposed in this paper are encoded and analyzed in Matlab. On the other hand, a measuring experiment was carried out by using a measurement device to check the accuracy of the developed mathematical model. The relative errors of the analytical results for measured stroke distance of the impact piston, peak value of forward stroke current and peak value of reverse stroke current were −4.65%, 9.08% and 9.35%, respectively. Finally, it was shown that the mathematical model of the operating process of an electromagnetic hammer is relatively accurate, and it can be used to determine the design parameters of the electromagnetic hammer. Therefore, the design parameters that can provide the required impact energy in the manual electromagnetic hammer were determined using a mathematical model developed. The proposed method will be used for the further design and development of the various types of percussion rock drills.

Keywords: solenoid electromagnet, electromagnetic hammer, stone processing, mathematical modeling

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Authors: Zuhairah Abdul Hadi, Mohd Nazir bin Md. Zabit, Zuriadah Ismail

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Metacognitive has been empirically evidenced to be one important element influencing learning outcomes. Expert learners engage in metacognition by monitoring and controlling their thinking, and listing, considering and selecting the best strategies to achieve desired goals. Studies also found that good critical thinkers engage in more metacognition and people tend to activate more metacognition when solving complex problems. This study extends past studies by performing a qualitative analysis to understand metacognitive patterns among two high and two low performing groups by carefully examining video and audio records taken during Problem-based learning activities. High performing groups are groups with majority members scored well in Watson Glaser II Critical Thinking Appraisal (WGCTA II) and academic achievement tests. Low performing groups are groups with majority members fail to perform in the two tests. Audio records are transcribed and analyzed using schemas adopted from past studies. Metacognitive statements are analyzed using three stages model and patterns of metacognitive are described by contexts, components, and levels for each high and low performing groups.

Keywords: academic achievement, critical thinking, metacognitive, problem-based learning

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Authors: Narupot Putwattana

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Changes in global situation such as environmental and economic crisis brought the new perspective for science education called integrative biology. STEM has been increasingly mentioned for several educational researches as the approach which combines the concept in Science (S), Technology (T), Engineering (E) and Mathematics (M) to apply in teaching and learning process so as to strengthen the 21st-century skills such as creativity and critical thinking. Recent studies demonstrated STEM as the pedagogy which described the engineering process along with the science classroom activities. So far, pedagogical contents for STEM explaining the content in biology have been scarce. A qualitative literature review was conducted so as to gather the articles based on electronic databases (google scholar). STEM education, engineering design, teaching and learning of biology were used as main keywords to find out researches involving with the application of STEM in biology teaching and learning process. All articles were analyzed to obtain appropriate teaching and learning model that unify the core concept of biology. The synthesized model comprised of engineering design, inquiry-based learning, biological prototype and biologically-inspired design (BID). STEM content and context integration were used as the theoretical framework to create the integrative biology instructional model for STEM education. Several disciplines contents such as biology, engineering, and technology were regarded for inquiry-based learning to build biological prototype. Direct and indirect integrations were used to provide the knowledge into the biology related STEM strategy. Meanwhile, engineering design and BID showed the occupational context for engineer and biologist. Technological and mathematical aspects were required to be inspected in terms of co-teaching method. Lastly, other variables such as critical thinking and problem-solving skills should be more considered in the further researches.

Keywords: biomimicry, engineering approach, STEM education, teaching and learning model

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Authors: N. Ibrahim-Rassoul, A. Kessi, E. K. Si-Ahmed, N. Djilali, J. Legrand

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The static and dynamic formation of liquid water bridges is analyzed using a combination of visualization experiments in a microchannel with a mathematical model. This paper presents experimental and theoretical findings of water plug/capillary bridge formation in a 250 μm squared microchannel. The approach combines mathematical and numerical modeling with experimental visualization and measurements. The generality of the model is also illustrated for flow conditions encountered in manipulation of polymeric materials and formation of liquid bridges between patterned surfaces. The predictions of the model agree favorably the observations as well as with the experimental recordings.

Keywords: green energy, mathematical modeling, fuel cell, water plug, gas diffusion layer, surface of revolution

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Authors: Richard Harrison

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

Keywords: competency, development, intervention, scaffolding

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Authors: Zahid Ullah, Atlas Khan

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The rapid advancements in data collection, storage, and processing capabilities have led to an explosion of data in various domains. In this era of big data, mathematical sciences play a crucial role in uncovering valuable insights and driving informed decision-making through data analytics. The purpose of this abstract is to present the latest advances in mathematical sciences and their application in harnessing the power of data analytics. This abstract highlights the interdisciplinary nature of data analytics, showcasing how mathematics intersects with statistics, computer science, and other related fields to develop cutting-edge methodologies. It explores key mathematical techniques such as optimization, mathematical modeling, network analysis, and computational algorithms that underpin effective data analysis and interpretation. The abstract emphasizes the role of mathematical sciences in addressing real-world challenges across different sectors, including finance, healthcare, engineering, social sciences, and beyond. It showcases how mathematical models and statistical methods extract meaningful insights from complex datasets, facilitating evidence-based decision-making and driving innovation. Furthermore, the abstract emphasizes the importance of collaboration and knowledge exchange among researchers, practitioners, and industry professionals. It recognizes the value of interdisciplinary collaborations and the need to bridge the gap between academia and industry to ensure the practical application of mathematical advancements in data analytics. The abstract highlights the significance of ongoing research in mathematical sciences and its impact on data analytics. It emphasizes the need for continued exploration and innovation in mathematical methodologies to tackle emerging challenges in the era of big data and digital transformation. In summary, this abstract sheds light on the advances in mathematical sciences and their pivotal role in unveiling the power of data analytics. It calls for interdisciplinary collaboration, knowledge exchange, and ongoing research to further unlock the potential of mathematical methodologies in addressing complex problems and driving data-driven decision-making in various domains.

Keywords: mathematical sciences, data analytics, advances, unveiling

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Authors: Mohammed Abubakar Ndanusa, A. A. Hassan, R. W. Gimba, A. M. Alfa, M. T. Abari

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This study investigated the Impact of Mathematical Modeling on Mathematics Achievement, Attitude and Interest of Pre-Service Teachers in Niger States, Nigeria. It was an attempt to ease students’ difficulties in comprehending mathematics. The study used randomized pretest, posttest control group design. Two Colleges of Education were purposively selected from Niger State with a sample size of eighty-four 84 students. Three research instruments used are Mathematical Modeling Achievement Test (MMAT), Attitudes Towards Mathematical Modeling Questionnaire (ATMMQ) and Mathematical Modeling Students Interest Questionnaire (MMSIQ). Pearson Product Moment Correlation (PPMC) formula was used for MMAT and Alpha Cronbach was used for ATMMQ and MMSIQ to determine their reliability coefficient and the values the following values were obtained respectively 0.76, 0.75 and 0.73. Independent t-test statistics was used to test hypothesis One while Mann Whitney U-test was used to test hypothesis Two and Three. Findings revealed that students taught Mathematics using Mathematical Modeling performed better than their counterparts taught using lecture method. However, there was a significant difference in the attitude and interest of pre-service mathematics teachers after being exposed to mathematical modeling. The strategy, therefore, was recommended to be used by Mathematics teachers with a view to improving students’ attitude and interest towards Mathematics. Also, modeling should be taught at NCE level in order to prepare pre-service teachers towards real task in the field of Mathematics.

Keywords: achievement, attitude, interest, mathematical modeling, pre-service teachers

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Authors: E. Maoz

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Background: As a teaching method, project-based learning is strongly linked to developing students’ critical thinking skills. It combines creative independent thinking, team work, and disciplinary subject-field integration. In the 'Introduction to Nursing Research Methods' course (year 3, Generic Track), project based learning is used to teach the topic of 'Evidence-Based Nursing'. This topic examines a clinical care issue encountered by students in the field. At the end of their project, students present proposals for managing the said issue. Proposals are the product of independent integrative thinking integrating a wide range of factors influencing the issue’s management. Method: Papers by 27 groups of students (165 students) were content analyzed to identify which themes emerged from the students' recommendations for managing the clinical issue. Findings: Five main themes emerged—current management approach; adapting procedures in line with current recent research recommendations; training for change (veteran nursing staff, beginner students, patients, significant others); analysis of 'economic benefit vs. patient benefit'; multidisciplinary team engagement in implementing change in practice. Two surprising themes also emerged: advertising and marketing using new technologies, which reflects how the new generation thinks. Summary and Recommendations: Among the main challenges in nursing education is training nursing graduates to think independently, integratively, and critically. Combining PBL with classical teaching methods stimulates students cognitively while opening new vistas with implications on all levels of the profession: management, research, education, and practice. Advanced students can successfully grasp and interpret the current state of clinical practice. They are competent and open to leading change and able to consider the diverse factors and interconnections that characterize the nurse's work.

Keywords: evidence based nursing, critical thinking skills, project based learning, students education

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Authors: Marinel Dayawon

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Student participation in classroom activities is vital in the teaching- learning the process as it develops self-confidence, social relationships and good academic performance of students. It is the teacher’s empathetic manner and creativity to create solutions that encourage teamwork and mutual support while dropping the academic competition within the class that hinder every shy student to walk with courage and talk with conviction because they consider their ideas, weak, as compared to the bright students. This study aimed to explore the different design thinking strategies that will change the mindset of shy students in classroom activities, maximizing their participation in all given tasks while sharing their views through ideation and providing them a wider world through compromise agreement within the members of the group, sensitivity to one’s idea, thus, arriving at a collective decision in the development of a prototype that indicates improvement in their classroom involvement. The study used the qualitative type of research. Triangulation is done through participant observation, focus group discussion and interview, documented through photos and videos. The respondents were the second- year Bachelor of Secondary Education students of the Institute of Teacher Education at Isabela State University- Cauayan City Campus. The result of the study revealed that reticent students when involved in game activities through a slap and tap method, writing their clustered ideas, using sticky notes is excited in sharing ideas as it doesn’t use oral communication. It is also observed after three weeks of using the design thinking strategies; shy students volunteer as secretary, rapporteur or group leader in the team- building activities as it represents the ideas of the heterogeneous group, removing the individual identity of the ideas. Superior students learned to listen to the ideas of the reticent students and involved them in the prototyping process of designing a remediation program for high school students showing reticence in the classroom, making their experience as a benchmark. The strategies made a 360- degrees transformation of the shy students, producing their journal log, in their journey to being open. Thus, faculty members are now adopting the design thinking approach.

Keywords: design thinking activities, qualitative, reticent students, Isabela, Philippines

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Authors: Felicitas Pielsticker, Christoph Pielsticker, Ingo Witzke

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Neurological findings provide foundational results for many different disciplines. In this article we want to discuss these with a special focus on mathematics education. The intention is to make neuroscience research useful for the description of cognitive mathematical learning processes. A key issue of mathematics education is that students often behave as if their mathematical knowledge is constructed in isolated compartments with respect to the specific context of the original learning situation; supporting students to link these compartments to form a coherent mathematical society of mind is a fundamental task not only for mathematics teachers. This aspect goes hand in hand with the question if there is such a thing as abstract general mathematical knowledge detached from concrete reality. Educational Neuroscience may give answers to the question why students develop their mathematical knowledge in isolated subjective domains of experience and if it is generally possible to think in abstract terms. To address these questions, we will provide examples from different fields of mathematics education e.g. students’ development and understanding of the general concept of variables or the mathematical notion of universal proofs. We want to discuss these aspects in the reflection of functional studies which elucidate the role of specific brain regions in mathematical learning processes. In doing this the paper addresses concept formation processes of students in the mathematics classroom and how to support them adequately considering the results of (educational) neuroscience.

Keywords: brain regions, concept formation processes in mathematics education, proofs, teaching-learning processes

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Authors: A. A. A. Aboalnour, Ahmed M. Amasaib, Mohammed-Almujtaba A. Mohammed-Farah, Abdelhakam, A. Noreldien

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This paper presents a design and study of Parabolic Trough Solar Collector (PTC). Mathematical models were used in this work to find the direct and reflected solar radiation from the air layer on the surface of the earth per hour based on the total daily solar radiation on a horizontal surface. Also mathematical models had been used to calculate the radiation of the tilted surfaces. Most of the ingredients used in this project as previews data required on several solar energy applications, thermal simulation, and solar power systems. In addition, mathematical models had been used to study the flow of the fluid inside the tube (receiver), and study the effect of direct and reflected solar radiation on the pressure, temperature, speed, kinetic energy and forces of fluid inside the tube. Finally, the mathematical models had been used to study the (PTC) performances and estimate its thermal efficiency.

Keywords: CFD, experimental, mathematical models, parabolic trough, radiation

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Authors: S. Shamohammadi, L. Razavi

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This paper based on the principle concepts of SCS-CN model, a new mathematical model for computation of retention potential (S) presented. In the mathematical model, not only precipitation-runoff concepts in SCS-CN model are precisely represented in a mathematical form, but also new concepts, called “maximum retention” and “total retention” is introduced, and concepts of potential retention capacity, maximum retention, and total retention have been separated from each other. In the proposed model, actual retention (F), maximum actual retention (Fmax), total retention (S), maximum retention (Smax), and potential retention (Sp), for the first time clearly defined, so that Sp is not variable, but a function of morphological characteristics of the watershed. Indeed, based on the mathematical relation of the conceptual curve of SCS-CN model, the proposed model provides a new method for the computation of actual retention in watershed and it simply determined runoff based on. In the corresponding relations, in addition to Precipitation (P), Initial retention (Ia), cumulative values of actual retention capacity (F), total retention (S), runoff (Q), antecedent moisture (M), potential retention (Sp), total retention (S), we introduced Fmax and Fmin referring to maximum and minimum actual retention, respectively. As well as, ksh is a coefficient which depends on morphological characteristics of the watershed. Advantages of the modified version versus the original model include a better precision, higher performance, easier calibration and speed computing.

Keywords: model, mathematical, retention, watershed, SCS

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Authors: Faroogh Khakzad, Marzieh Dehghani, Elahe Hejazi

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The present study investigates the effect of teaching a Thinking and Research lesson by cooperative and traditional methods on the creativity of sixth-grade students in Piranshahr province. The statistical society includes all the sixth-grade students of Piranshahr province. The sample of this studytable was selected by available sampling from among male elementary schools of Piranshahr. They were randomly assigned into two groups of cooperative teaching method and traditional teaching method. The design of the study is quasi-experimental with a control group. In this study, to assess students’ creativity, Abedi’s creativity questionnaire was used. Based on Cronbach’s alpha coefficient, the reliability of the factor flow was 0.74, innovation was 0.61, flexibility was 0.63, and expansion was 0.68. To analyze the data, t-test, univariate and multivariate covariance analysis were used for evaluation of the difference of means and the pretest and posttest scores. The findings of the research showed that cooperative teaching method does not significantly increase creativity (p > 0.05). Moreover, cooperative teaching method was found to have significant effect on flow factor (p < 0.05), but in innovation and expansion factors no significant effect was observed (p < 0.05).

Keywords: cooperative teaching method, traditional teaching method, creativity, flow, innovation, flexibility, expansion, thinking and research lesson

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Authors: Luc de Brabandere

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Searchers in various disciplines have long tried to understand how a human being thinks. Most of them seem to agree that the brain works in two very different modes. For us, the first phase of thought imagines, diverges, and unlocks the field of possibilities. The second phase, judges converge and choose. But if we were to stop there, that would give the impression that thought is essentially an individual effort that seldom depends on context. This is, however, not the case. Whether we be a champion in creativity, so primarily in induction, or a master in logic where we are confronted with reality, the ideas we layout are indeed destined to be presented to third parties. They should therefore be exposed, defended, communicated, negotiated, or even sold. Regardless of the quality of the concepts we craft (creative thinking) and the interferences we build (logical thinking) we will take one day, or another, be confronted by people whose beliefs, opinions and ideas differ from ours (critical thinking). Logic and critique: The shared characteristics of logical and critical thoughts include a three-level structure of reasoning invented by the Greeks. For the first time in history, Aristotle tried to model thought deployable in three stages: the concept, the statement, and the reasoning. The three levels can be assessed according to different criteria. A concept is more or less useful, a statement is true or false, and reasoning is right or wrong. This three-level structure allows us to differentiate logic and critique, where the intention and words used are not the same. Logic only deals with the structure of reasoning and exhausts the problem. It regards premises as acquired and excludes the debate. Logic is in all certainty and pursues the truth. Critique is most probably searching for the plausible. Logic and creativity: Many known models present the brain as a two-stroke engine (divergence vs convergence, fast vs. slow, left-brain vs right-brain, Yin vs Yang, etc.). But that’s not the only thing. “Why didn’t we think of that before?” How often have we heard that sentence? A creative idea is the outcome of logic, but you can only understand it afterward! Through the use of exercises, we will witness how logic and creativity work together. A third theme is hidden behind the two main themes of the conference: logical thought, which the author can shed some light on.

Keywords: creativity, logic, critique, digital

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Authors: Maryam Ramezankhani

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The present research tries to study the possibility of formalizing the sense relation of hyponymy. It applied mathematical tools and also uses mathematical logic concepts especially those from propositional logic. In order to do so, firstly, it goes over the definitions of hyponymy presented in linguistic dictionaries and semantic textbooks. Then, it introduces a formal translation of the sense relation of hyponymy. Lastly, it examines the efficiency of the suggested formula by some examples of natural language.

Keywords: sense relations, hyponymy, formalizing, words’ sense relation, formalizing sense relations

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Authors: Alica Höpken, Hergen Pargmann

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The resource-efficient planning of the complex production planning processes in the meat industry and the reduction of food waste is a permanent challenge. The complexity of the production planning process occurs in every part of the supply chain, from agriculture to the end consumer. It arises from long and uncertain planning phases. Uncertainties such as stochastic yields, fluctuations in demand, and resource variability are part of this process. In the meat industry, waste mainly relates to incorrect storage, technical causes in production, or overproduction. The high amount of food waste along the complex supply chain in the meat industry could not be reduced by simple solutions until now. Therefore, resource-efficient production planning by conventional methods is currently only partially feasible. The realization of intelligent, automated production planning is basically possible through the application of machine learning algorithms, such as those of reinforcement learning. By applying the adapted design thinking method, machine learning methods (especially reinforcement learning algorithms) are used for the complex production planning process in the meat industry. This method represents a concretization to the application area. A resource-efficient production planning process is made available by adapting the design thinking method. In addition, the complex processes can be planned efficiently by using this method, since this standardized approach offers new possibilities in order to challenge the complexity and the high time consumption. It represents a tool to support the efficient production planning in the meat industry. This paper shows an elegant adaption of the design thinking method to apply the reinforcement learning method for a resource-efficient production planning process in the meat industry. Following, the steps that are necessary to introduce machine learning algorithms into the production planning of the food industry are determined. This is achieved based on a case study which is part of the research project ”REIF - Resource Efficient, Economic and Intelligent Food Chain” supported by the German Federal Ministry for Economic Affairs and Climate Action of Germany and the German Aerospace Center. Through this structured approach, significantly better planning results are achieved, which would be too complex or very time consuming using conventional methods.

Keywords: change management, design thinking method, machine learning, meat industry, reinforcement learning, resource-efficient production planning

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Authors: Lisa Kasmer

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Teachers’ instructional decisions shape the structure and content of mathematics lessons and influence the mathematics that students are given the opportunity to learn. Therefore, it is important to better understand how teachers make instructional decisions and thus find new ways to help practicing and future teachers give their students a more effective and robust learning experience. Understanding the relationship between teachers’ instructional decisions and their goals, resources, and orientations (beliefs) is important given the heightened focus on geometric transformations in the middle school mathematics curriculum. This work is significant as the development and support of current and future teachers need more effective ways to teach geometry to their students. The following research questions frame this study: (1) As middle school mathematics teachers plan and enact instruction related to teaching transformations, what thinking processes do they engage in to make decisions about teaching transformations with or without a coordinate system and (2) How do the goals, resources and orientations of these teachers impact their instructional decisions and reveal about their understanding of teaching transformations? Teachers and students alike struggle with understanding transformations; many teachers skip or hurriedly teach transformations at the end of the school year. However, transformations are an important mathematical topic as this topic supports students’ understanding of geometric and spatial reasoning. Geometric transformations are a foundational concept in mathematics, not only for understanding congruence and similarity but for proofs, algebraic functions, and calculus etc. Geometric transformations also underpin the secondary mathematics curriculum, as features of transformations transfer to other areas of mathematics. Teachers’ instructional decisions in terms of goals, orientations, and resources that support these instructional decisions were analyzed using open-coding. Open-coding is recognized as an initial first step in qualitative analysis, where comparisons are made, and preliminary categories are considered. Initial codes and categories from current research on teachers’ thinking processes that are related to the decisions they make while planning and reflecting on the lessons were also noted. Surfacing ideas and additional themes common across teachers while seeking patterns, were compared and analyzed. Finally, attributes of teachers’ goals, orientations and resources were identified in order to begin to build a picture of the reasoning behind their instructional decisions. These categories became the basis for the organization and conceptualization of the data. Preliminary results suggest that teachers often rely on their own orientations about teaching geometric transformations. These beliefs are underpinned by the teachers’ own mathematical knowledge related to teaching transformations. When a teacher does not have a robust understanding of transformations, they are limited by this lack of knowledge. These shortcomings impact students’ opportunities to learn, and thus disadvantage their own understanding of transformations. Teachers’ goals are also limited by their paucity of knowledge regarding transformations, as these goals do not fully represent the range of comprehension a teacher needs to teach this topic well.

Keywords: coordinate plane, geometric transformations, instructional decisions, middle school mathematics

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Authors: Krongthong Khairiree

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The purpose of this research study is to explore mathematics project-based learning approach and the use of technology in the context of school mathematics in Thailand. Data of the study were collected from 6 sample secondary schools and the students were 6-14 years old. Research findings show that through mathematics project-based learning approach and the use of GSP, students were able to make mathematics learning fun and challenging. Based on the students’ interviews they revealed that, with GSP, they were able to visualize and create graphical representations, which will enable them to develop their mathematical thinking skills, concepts and understanding. The students had fun in creating variety of graphs of functions which they can not do by drawing on graph paper. In addition, there are evidences to show the students’ abilities in connecting mathematics to real life outside the classroom and commercial products, such as weaving, patterning of broomstick, and ceramics design.

Keywords: mathematics, project-based learning, Geometer’s Sketchpad (GSP), commercial products

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Authors: N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev

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Nonlinear analysis of the phase locked loop (PLL)-based circuits is a challenging task. Thus, the simulation is widely used for their study. In this work, we consider a mathematical model of the optical Costas loop and demonstrate the limitations of simulation approach related to the existence of so-called hidden oscillations in the phase space of the model.

Keywords: optical Costas loop, mathematical model, simulation, hidden oscillation

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Anne-Marie Tuomala

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Education for sustainable development (ESD) aims to provide students with the attitudes, values, and behaviors necessary for the contribution to sustainability. The research was implemented as a part of the Horizons Europe research project, where each partner organization had at least one pilot project locally. The pilot in question was an online course about the basics of the natural stone industry in Finland and its sustainability and circular economy aspects. The course was open to all students of applied universities in Finland, and it was implemented twice during the research. The Stone from Finland association participated in the course design, and it was also an expert in the local context and real-life provider. The multiple case-study method was chosen, as it enables purposeful sampling of cases that are tailored to the specific study. It was also assumed that it predicts quite comparable results of two different course implementations of the course with the same topic and content. The Curtin University of Technology’s Attitudes Towards Thinking and Learning Survey was adapted. The results show the importance of the trans-disciplinary nature of sustainability education. In addition, the new industry areas with the general - but also industry-specific sustainability issues - must be introduced to students and encourage them to do critically reflective learning. Surveys that guide them to analyze their own attitudes to thinking and learning may expose students to their weaknesses but also result in forms of more active sustainability interaction.

Keywords: education for sustainable development, learning attitudes, learning of circular economy, virtual learning

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Authors: Risti Suryantari, Flaviana

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The aim of this research is to design calibration method of Thermochromic Liquid Crystal for temperature distribution measurement based on mathematical morphology of hue image A glass of water is placed on the surface of sample TLC R25C5W at certain temperature. We use scanner for image acquisition. The true images in RGB format is converted to HSV (hue, saturation, value) by taking of hue without saturation and value. Then the hue images is processed based on mathematical morphology using Matlab2013a software to get better images. There are differences on the final images after processing at each temperature variation based on visualization observation and the statistic value. The value of maximum and mean increase with rising temperature. It could be parameter to identify the temperature of the human body surface like hand or foot surface.

Keywords: thermochromic liquid crystal, TLC, mathematical morphology, hue image

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

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Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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Authors: Kalliopi Kanaki, Michael Kalogiannakis

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Nowadays, in the digital era, the early acquisition of basic programming skills and knowledge is encouraged, as it facilitates students’ exposure to computational thinking and empowers their creativity, problem-solving skills, and cognitive development. More and more researchers and educators investigate the introduction of computational thinking in K-12 since it is expected to be a fundamental skill for everyone by the middle of the 21st century, just like reading, writing and arithmetic are at the moment. In this paper, a doctoral research in the process is presented, which investigates the infusion of computational thinking into science curriculum in early childhood education. The whole attempt aims to develop young children’s computational thinking by introducing them to the fundamental concepts of object-oriented programming in an enjoyable, yet educational framework. The backbone of the research is the digital environment PhysGramming (an abbreviation of Physical Science Programming), which provides children the opportunity to create their own digital games, turning them from passive consumers to active creators of technology. PhysGramming deploys an innovative hybrid schema of visual and text-based programming techniques, with emphasis on object-orientation. Through PhysGramming, young students are familiarized with basic object-oriented programming concepts, such as classes, objects, and attributes, while, at the same time, get a view of object-oriented programming syntax. Nevertheless, the most noteworthy feature of PhysGramming is that children create their own digital games within the context of physical science courses, in a way that provides familiarization with the basic principles of object-oriented programming and computational thinking, even though no specific reference is made to these principles. Attuned to the ethical guidelines of educational research, interventions were conducted in two classes of second grade. The interventions were designed with respect to the thematic units of the curriculum of physical science courses, as a part of the learning activities of the class. PhysGramming was integrated into the classroom, after short introductory sessions. During the interventions, 6-7 years old children worked in pairs on computers and created their own digital games (group games, matching games, and puzzles). The authors participated in these interventions as observers in order to achieve a realistic evaluation of the proposed educational framework concerning its applicability in the classroom and its educational and pedagogical perspectives. To better examine if the objectives of the research are met, the investigation was focused on six criteria; the educational value of PhysGramming, its engaging and enjoyable characteristics, its child-friendliness, its appropriateness for the purpose that is proposed, its ability to monitor the user’s progress and its individualizing features. In this paper, the functionality of PhysGramming and the philosophy of its integration in the classroom are both described in detail. Information about the implemented interventions and the results obtained is also provided. Finally, several limitations of the research conducted that deserve attention are denoted.

Keywords: computational thinking, early childhood education, object-oriented programming, physical science courses

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Authors: B. El Fadil, R. Najar

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STEM education is promoted by many scholars and curricula around the world, but it is not yet well established in the province of Quebec in Canada. In addition, effective instructional STEM activities and design methods are required to ensure that students and teachers' needs are being met. One potential method is the Engineering Design Process (EDP), a methodology that emphasizes the importance of creativity and collaboration in problem-solving strategies. This article reports on a case study that focused on using the EDP to develop instructional materials by means of making a technological artifact to teach mathematical variables and functions at the secondary level. The five iterative stages of the EDP (design, make, test, infer, and iterate) were integrated into the development of the course materials. Data was collected from different sources: pre- and post-questionnaires, as well as a working document dealing with pupils' understanding based on designing, making, testing, and simulating. Twenty-four grade seven (13 years old) students in Northern Quebec participated in the study. The findings of this study indicate that STEM activities have a positive impact not only on students' engagement in classroom activities but also on learning new mathematical concepts. Furthermore, STEM-focused activities have a significant effect on problem-solving skills development in an interdisciplinary approach. Based on the study's results, we can conclude, inter alia, that teachers should integrate STEM activities into their teaching practices to increase learning outcomes and attach more importance to STEM-focused activities to develop students' reflective thinking and hands-on skills.

Keywords: engineering design process, motivation, stem, integration, variables, functions

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Authors: Rosanna M. Rooney, Sharinaz Hassan, Maryanne McDevitt, Jacob D. Peckover, Robert T. Kane

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Anxiety and depression are the most common mental health problems experienced by Australian children and adolescents. Research into youth mental health points to the importance of considering emotional competence, parental influence on the child’s emotional development, and the fact that cognitions are still developing in childhood when designing and implementing positive psychology interventions. Additionally, research into such interventions has suggested the inclusion of a coaching component aimed at supporting those implementing the intervention enhances the effects of the intervention itself. In light of these findings and given the burden of anxiety and depression in the longer term, it is necessary to enhance the Aussie Optimism Positive Thinking Skills program and evaluate its efficacy in terms of children’s mental health outcomes. It was expected that the enhancement of the emotional and cognitive aspects of the Aussie Optimism Positive Thinking Skills program, the addition of coaching, and the inclusion of a parent manual would lead to significant prevention effects in internalizing problems at post-test, 6- and 18-months after the completion of the intervention. 502 students (9-11 years old) were randomly assigned to the intervention group (n = 347) or control group (n = 155). At each time point (baseline, post-test, 6-month follow-up, and 18-month follow-up), students completed a battery of self-report measures. The ten intervention sessions making up the enhanced Aussie Optimism Positive Thinking Skills program were run weekly. At post-test and 6-month follow-up, the intervention group reported significantly lower depression than the control group, with no group differences at the 18-month follow-up. The intervention group reported significantly lower anxiety than the control group only at the 6-month follow-up, with no group differences in the post-test or at the 18-month follow-up. Results suggest that the enhanced Aussie Optimism Positive Thinking Skills program can reduce depressive and anxious symptoms in the short term and highlight the importance of universally implemented positive psychology interventions.

Keywords: positive psychology, emotional competence, internalizing symptoms, universal implementation

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Ayse Ozturk

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The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

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Authors: Hanbey Hazar, Hakan Gul

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In this study; piston, exhaust, and suction valves of a diesel engine were coated in 300 mm thickness with Tungsten Carbide (WC) by using the HVOF coating method. Mathematical modeling of a coated and uncoated (standardized) engine was performed by using ANN (Artificial Neural Networks). The purpose was to decrease the number of repetitions of tests and reduce the test cost through mathematical modeling of engines by using ANN. The results obtained from the tests were entered in ANN and therefore engines' values at all speeds were estimated. Results obtained from the tests were compared with those obtained from ANN and they were observed to be compatible. It was also observed that, with thermal barrier coating, hydrocarbon (HC), carbon monoxide (CO), and smoke density values of the diesel engine decreased; but nitrogen oxides (NOx) increased. Furthermore, it was determined that results obtained through mathematical modeling by means of ANN reduced the number of test repetitions. Therefore, it was understood that time, fuel and labor could be saved in this way.

Keywords: Artificial Neural Network, Diesel Engine, Mathematical Modelling, Thermal Barrier Coating

Procedia PDF Downloads 515