ABSTRACT This study examines Grade 9 students’ mathematics achievement and cognitive engagement under three different instructional approaches: traditional learning, flipped learning with gamification, and online independent study with gamification. The duration of the study lasted an entire school year. The central theories underpinning flipped learning with gamification design were based on the first principles of Instruction and self-determination theory. A mixed methods approach was used with quantitative (i.e., tests and an optional assignment) and qualitative (i.e., student interviews) methods applied. The test results indicate that students in the flipped class (n = 28) significantly outperformed those in the traditional (n = 27) and online independent study (n = 21) classes. In addition, flipped learning with gamification promoted students’ cognitive engagement better than the other two approaches. The findings of student interviews suggest that peer interactions inside the flipped classroom were critical to promoting students’ mathematics achievement and cognitive engagement, as opposed to online learning resources and gamification per se. In future practice, teachers can ground their flipped classroom design in the theoretical framework proposed in this study.
ABSTRACT The purpose of this study is to investigate how mathematics-emphasised STEM PBL lessons develop pre-service teachers’ creative thinking skills in mathematics. A sequential mixed-methods study was applied to deeply understand the results from the quantitative part of the study through qualitative analysis. While pre-service teachers’ creative thinking skills in mathematics were measured through problem-posing tasks, a semi-structured interview was conducted to reveal the features of STEM PBL instruction influencing their creative thinking. The results revealed that although pre-service teachers did not increase their fluency scores of mathematical creativity after receiving STEM PBL intervention, they increased their flexibility and originality scores of mathematical creativity. The associated Hedge’s g for the overall increase in mathematical creativity from pre- to post-test was 0.42. During interviews, pre-service teachers attributed this increase to the ten features of STEM PBL. This study implies that mathematics can be used as a main goal in the STEM PBL context. This may enable pre-service teachers to understand not only the utility but also the beauty of mathematics in an interdisciplinary context.
In this research, we propose a new numerical method for solving a class of distributed-order fractional partial differential equations, specifically focusing on distributed-order time fractional wave-diffusion equations. The method begins by introducing a novel generalization of Bernoulli wavelets and deriving an exact result for the Riemann–Liouville integral of these new basis functions. Utilizing the Gauss–Legendre quadrature formula and a strategically chosen set of collocation points, along with approximations for the unknown function and its derivatives, we transform the problem into a system of algebraic equations. An error analysis is then conducted for the approximation of a bivariate function using fractional-order Bernoulli wavelets. Finally, three examples are solved to demonstrate the method’s applicability and accuracy, with the numerical results confirming its effectiveness. These findings demonstrate that the parameters of the basis functions can be adjusted to suit the given problem, thereby enhancing the accuracy of the method.
Home healthcare has become more and more central in the last decades, due to the advantages it can bring to both healthcare institutions and patients. Planning activities in this context, however, presents significant challenges related to route planning and mutual synchronization of caregivers.In this paper we propose a new compact model for the combined optimization of scheduling (of the activities) and routing (of the caregivers) characterized by fewer variables and constraints when compared with the models previously available in the literature. The new model is solved by a constraint programming solver and compared experimentally with the exact and metaheuristic approaches available in the literature on the common datasets adopted by the community. The results show that the new model provides improved lower bounds for the vast majority of the instances, while producing at the same time high quality heuristic solutions, comparable to those of tailored metaheuristics, for small/medium size instances.
The niche situation can reflect the advantages and disadvantages of biological individuals in the ecosystem environment as well as the overall operational status of the ecosystem. However, higher-order niche systems generally exhibit complex nonlinearities and parameter uncertainties, making it difficult for traditional Type-1 fuzzy control to accurately handle their inherent fuzziness and environmental disturbances in complex environments. To address this, this paper introduces the backstepping control method based on Type-2 T-S fuzzy control, incorporating the niche situation function as the consequent of the T-S backstepping fuzzy control. The stability analysis of the system is completed by constructing a Lyapunov function, and the adaptive law for the parameters of the niche situation function is derived. This design reflects the tendency of biological individuals to always develop in a direction beneficial to themselves, highlighting the bio-inspired intelligent characteristics of the proposed method. The results of case simulations show that the Type-2 backstepping T-S fuzzy control has significantly superior comprehensive performance in dealing with the complexity and uncertainty of high-order niche situation systems compared with the traditional Type-1 control and Type-2 T-S adaptive fuzzy control. These results not only verify the adaptive and self-development capabilities of biological individuals, as well as their efficiency in environmental utilization, but also endow this control method with a solid practical foundation.
Subhalaxmi Dey, Surender Ontela, P.K. Pattnaik
et al.
In recent trends science and technology is developed due to the utilization of modern devices of high quality and their longevity with potential efficiency. The implementation of nanoparticles now characterizes the effectiveness and efficiency. Specifically, in biomedical research drug delivery into the target, hyperthermia treatment for cancer, etc. the use of nanofluid is vital. The present article brings the characteristic of the blood-based tri-hybrid nanofluid through a porous channel embedding within a porous matrix with the interaction of magnetization and Darcy-Forchheimer inertial drag in the flow behavior. Further, the inclusion of thermal radiation, and heat source energies the heat transport properties. The formulated model for the interaction of alloy nanoparticles AA7072 and AA7075 with Zirconium oxide ZrO2 in the base liquid blood is characterized by their physical properties. The designed model is transformed into a non-dimensional form with the utilization of similarity rules. Further, a semi-analytical approach Adomian Decomposition Method (ADM) is proposed for the solution of the model. The validation with the existing article shows the convergence properties of the current methodology and the significant behavior of the factors involved in the flow phenomena are presented through graphs. Finally, the important findings are reported as; The enhanced Reynolds number decelerates the inertia force and a velocity profile shows a dual characteristic for the increasing deformation factor. Further, in comparison to the single and hybrid nanofluid, the tri-hybrid nanofluid encourages the fluid temperature due to the increasing thermal conductivity.
<p>A hybrid method for the numerical solution of the system of delayed linear fuzzy mixed VolterraFredholm integral equations (FMDVFIES) is introduced. Using the hybrid of Bernstein polynomials and blockpulse functions (HBBFs), an approximate solution for the equations system is provided. Firstly, the HBBFs and their operational matrices are introduced, and some of their characteristics are described. Then by applying the operational matrices on FMDVFIES convert it to the algebraic equations system. The numerical solution is obtained by solving this algebraic system. Then the convergence is investigated and some numerical examples are presented to show the effectiveness of the method.</p>
The present study aimed to assess the perspectives of female secondary school students on the integration of visual mathematics in engineering lessons. Employing a mixed-methods approach, specifically a convergent parallel design, qualitative data were gathered through observations and interviews (both individual and focus groups), while quantitative data were collected using a questionnaire. Video clips of engineering unit lessons were utilized as educational materials. The study included 135 female students in the first year of secondary school, with 74 participating in qualitative segments, divided into focus groups and individual interviews. SPSS was employed for quantitative data analysis, calculating means and standard deviations, while thematic analysis was applied for qualitative data. Key findings indicate that visual displays significantly contributed to enhancing female students’ comprehension of mathematical concepts, facilitating the understanding of inter-concept relationships and their application in engineering. The incorporation of visual aids also positively impacted the mathematical coherence abilities of female students, establishing connections between mathematics, other subjects, and real-life situations. Furthermore, visual presentations in engineering topics were found to improve female students’ attitudes toward learning mathematics, fostering increased self-confidence and enjoyment in learning various engineering subjects. Recommendations from the study include the need for training both male and female teachers in designing effective visual presentations for teaching mathematical concepts.
Josenaide Alves da Silva, Geilsa Costa Santos Baptista, Nataélia Alves da Silva
A pesquisa é qualitativa e o objetivo propõe a análise da comunicação dos licenciandos para desenvolvimento de um ensino intercultural em aulas de ciências. Os envolvidos no trabalho foram dois licenciandos do curso de Ciências Agrárias, do Instituto Federal de Educação, Ciências e Tecnologia Baiano, do campus de Senhor do Bonfim-BA. Para coleta de dados, utilizou-se gravações em vídeos, procedendo a Análise de Conteúdo e a Estrutura de análise das classes comunicativas, para analisá-los. Este artigo apresenta resultados sobre as análises das aulas de ciências dos licenciandos, as quais direcionaram para o desenvolvimento da abordagem comunicativa dialógica, incluindo os saberes socioculturais dos estudantes e os saberes científicos, a partir de uma relação entre essas formas de conhecer. Considera-se que a abordagem comunicativa dialógica é um alicerce para os licenciandos ministrarem a prática de ciências contextualizada.
Special aspects of education, Applied mathematics. Quantitative methods
The aim of the study reported on here was to assess the impact of differentiated instruction in terms of mathematics achievement and the attitudes of secondary school learners to reveal their views on differentiated instruction. The study was designed according to a mixed method design in which both quantitative and qualitative methods were used. The study group, which constituted the quantitative dimension of the study, consisted of 2 control groups and 1 experimental group. The Mathematics Achievement Test, Mathematics Attitude Scale and a semi-structured interview form were used as data collection tools. One-way anova and descriptive analysis techniques were applied for the analysis of the data. We concluded that differentiated instruction in mathematics courses increases secondary school learners’ mathematics achievement, but has no effect on their attitudes towards mathematics.
Independence and creativity in developing evaluations of mathemetics learning based on the comprehension of the Understanding by Design (UbD) concept are skills that mathematics teachers in inclusive schools must possess. This research aimed to obtain an accurate and comprehensive picture of teacher independence and creativity in developing evaluations of mathematics learning based on understanding the concept of Understanding by Design (UbD). It used mixed methods by design, which combined quantitative and qualitative approaches. The population was all mathematics teachers in inclusive schools in the provinces of Bali, Nusa Tenggara Barat (NTB), and Nusa Tenggara Timur (NTT). The sample selection used the cluster random sampling technique, with a total sample of 465 math teachers. Furthermore, the data were collected using a questionnaire. The results of the group mean difference test on teacher independence in developing evaluations of learning mathematics in inclusive schools were obtained at 11500.249, and on teacher creativity in developing learning mathematics evaluations in inclusive schools, they were obtained at 13129.593. It showed that understanding the concept of Understanding by Design (UbD) influences teacher independence and creativity in developing evaluations of learning mathematics in inclusive schools. Increasing the independence and creativity of teachers in the provinces of Bali, NTB, and NTT to develop Understanding by Design (UbD)-based learning evaluations can be done by preparing guidelines for developing Understanding by Design (UbD)-based learning evaluations that can be utilized by teachers studying independently.
Riyan Hidayat, Nurihan Nasir, Sobiratul Asiah
et al.
The peer tutoring approach is a student-cantered teaching method in which students learn in pairs with teacher supervision. The study discussed in this paper is a systematic literature review related to the effectiveness of peer tutoring approaches which has been published within the last 5 years. A complete text analysis was conducted using 20 research papers stating the impact of the peer mentoring approach for this writing. Among the things obtained from previous studies are the variety of ways to implement peer tutoring approach, the impact on 3 aspects in students which are mathematical achievement, social skills and cognitive skills and the teaching theories used. The findings of the study indicate that most past studies used quantitative research methods with the concept of age peer approach. Then, constructivism theory was the most frequently applied with a sample of high school students. In conclusion, this systematic literature review shows that the peer tutoring approach in mathematics education has many benefits in various aspects and needs to be extended to improve the quality of education.
Introduction Procrastination is a complex psychological and behavioral construct that is strongly influenced by certain personality traits. In mathematics learning, students find it difficult to master the concepts because of less exposure to learning styles. Poor knowledge of mathematical concepts leads to academic procrastination in the subject of Mathematics among students. Therefore, this study aims to identify students’ learning styles in Mathematics, identify the stages of students’ academic procrastination in Mathematics, and determine whether there is a significant influence of learning styles (visual, auditory, and kinesthetic) on academic procrastination among secondary school students in Mathematics. Methods A quantitative approach with a survey was applied. A total of 500 Form Two and Form Four students in five national secondary schools in the Kota Bharu district, Kelantan, were selected using simple random sampling. The duration of data gathering started from 4 October 2022 until 31 January 2023. The Learning Styles Questionnaire and the Academic Procrastination Questionnaire were adapted and verified by eight experts in psychology and counseling. Descriptive and multiple regression tests were carried out using IBM SPSS version 26.0. Results The results revealed that the visual learning style was the most dominant learning style among students in the subject of Mathematics, followed by auditory and kinesthetic. The level of students’ academic procrastination in Mathematics was low. Besides, multiple regression showed that visual and kinesthetic learning styles were significant contributors or predictors, which amounted to 14.1% of the variation in students’ academic procrastination in Mathematics. Discussion The implications of this study highlight the possibility to improve programs in schools by exposing students to suitable learning styles so that they can practice effective learning styles in Mathematics and consequently overcome academic procrastination. Further research can be carried out by identifying other factors that encourage academic procrastination in the subject of Mathematics in order to increase students’ motivation and self-efficacy.
Tuberculosis remains one of the most dangerous diseases globally and has affected many people in Sub-Saharan Africa. In this paper, a fractional stochastic model of tuberculosis disease was formulated and analyzed. The existence and uniqueness of solutions are presented in the new approach far from the deterministic fractional operators. We carry out numerical simulations of the model using three fractional operators. Our numerical results suggest that the Caputo–Fabrizio operator has a more random effect among the three different operators than the Atangana–Baleanu and the Caputo operators. Further, it is envisaged that the fractional-order derivatives significantly impact the dynamics of the disease.
Gianluigi Rozza, Oliver Schütze, Nicholas Fantuzzi
This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal <i>Mathematical and Computational Applications</i> (MCA), as well as outstanding scholars working in the core research fields of MCA [...]
Adriana Bigido Rocha, Solange Wagner Locatelli, Leonardo André Testoni
Este artigo apresenta e discute os resultados de uma pesquisa realizada com um grupo de quatro professores unidocentes, em um curso de extensão oferecido por uma universidade pública brasileira, cujo objetivo foi compreender como os professores unidocentes elaboram suas aulas de Ciências. Para analisar os resultados da pesquisa foi utilizada a análise do conteúdo (Bardin, 2011), articulada a uma abordagem qualitativa. Coletados por meio de uma ferramenta digital (Padlet), os dados foram sistematizados e categorizados pelos pesquisadores. Os resultados evidenciaram quatro categorias que emergiram das escritas desses docentes, permitindo observar que os professores unidocentes elaboram suas aulas (1) por meio da sua ação docente, (2) considerando o planejamento, (3) utilizando recursos para motivar e facilitar o aprendizado e, ainda (4) demonstrando muita dificuldade por não dominar o conhecimento de conteúdo.
Special aspects of education, Applied mathematics. Quantitative methods
The sparrow search algorithm (SSA) is a metaheuristic algorithm developed based on the foraging and anti-predatory behavior of sparrow populations. Compared with other metaheuristic algorithms, SSA also suffers from poor population diversity, has weak global comprehensive search ability, and easily falls into local optimality. To address the problems whereby the sparrow search algorithm tends to fall into local optimum and the population diversity decreases in the later stage of the search, an improved sparrow search algorithm (PGL-SSA) based on piecewise chaotic mapping, Gaussian difference variation, and linear differential decreasing inertia weight fusion is proposed. Firstly, we analyze the improvement of six chaotic mappings on the overall performance of the sparrow search algorithm, and we finally determine the initialization of the population by piecewise chaotic mapping to increase the initial population richness and improve the initial solution quality. Secondly, we introduce Gaussian difference variation in the process of individual iterative update and use Gaussian difference variation to perturb the individuals to generate a diversity of individuals so that the algorithm can converge quickly and avoid falling into localization. Finally, linear differential decreasing inertia weights are introduced globally to adjust the weights so that the algorithm can fully traverse the solution space with larger weights in the first iteration to avoid falling into local optimum, and we enhance the local search ability with smaller weights in the later iteration to improve the search accuracy of the optimal solution. The results show that the proposed algorithm has a faster convergence speed and higher search accuracy than the comparison algorithm, the global search capability is significantly enhanced, and it is easier to jump out of the local optimum. The improved algorithm is also applied to the Heating, Ventilation and Air Conditioning (HVAC) system control optimization direction, and the improved algorithm is used to optimize the parameters of the HVAC system Proportion Integral Differential (PID) controller. The results show that the PID controller optimized by the improved algorithm has higher control accuracy and system stability, which verifies the feasibility of the improved algorithm in practical engineering applications.
Ramin Ghiasi, Mohammad N. Noori, Wael A. Altabey
et al.
Recent advancements in sensor technology have resulted in the collection of massive amounts of measured data from the structures that are being monitored. However, these data include inherent measurement errors that often cause the assessment of quantitative damage to be ill-conditioned. Attempts to incorporate a probabilistic method into a model have provided promising solutions to this problem by considering the uncertainties as random variables, mostly modeled with Gaussian probability distribution. However, the success of probabilistic methods is limited due the lack of adequate information required to obtain an unbiased probabilistic distribution of uncertainties. Moreover, the probabilistic surrogate models involve complicated and expensive computations, especially when generating output data. In this study, a non-probabilistic surrogate model based on wavelet weighted least squares support vector machine (WWLS-SVM) is proposed to address the problem of uncertainty in vibration-based damage detection. The input data for WWLS-SVM consists of selected wavelet packet decomposition (WPD) features of the structural response signals, and the output is the Young’s modulus of structural elements. This method calculates the changes in the lower and upper boundaries of Young’s modulus based on an interval analysis method. Considering the uncertainties in the input parameters, the surrogate model is used to predict this interval-bound output. The proposed approach is applied to detect simulated damage in the four-story benchmark structure of the IASC-ASCE SHM group. The results show that the performance of the proposed method is superior to that of the direct finite element model in the uncertainty-based damage detection of structures and requires less computational effort.