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This study is based on the bibliometrics analysis of research publications that focus on highlighting the argumentation on mathematics education. The main objective of this study is to analyze the distribution of research results, the main journals for publication, and the most productive authors, the pattern of authorship and the pattern of citation. Data was collected from Scopus database and was analyzed using VOSviewer software. A total of 173 articles published from 1995 to December 2021 were retrieved and perused. Graphs, tables, charts, and maps have been used to analyze and present collected data. The analysis results show that argumentation in mathematics education has been studied frequently with the concepts of proof, reasoning, teacher education, and geometry. Journal of Mathematical Behavior and Educational Studies in Mathematics have been the top journals, and the University of Rutgers has been the most influential institution, and the United States has had a significant prevalence in this field. The results of this study provide insights for researchers interested in mathematics education in this field, suggesting that they can explore various alternatives to the major research trends and the influential articles mentioned. Based on the results, recommendations for future studies are provided.

Teachers' geometric thinking is crucial to teaching efficacy in geometry since teacher knowledge or thinking serves as a basis for the quality of instruction provided for students' learning. Teachers' thinking about geometry has attracted much attention among mathematics education researchers. This study therefore aimed at assessing elementary pre-service teachers' geometric thinking within the first three levels of van Hiele's model. The study was guided by three objectives. The objectives were to (1) assess the distribution of van Hiele's geometric thinking among the study participants, (2) determine if the participating pre-service teachers' geometric thinking is significant for teaching geometry, and (3) find out if any difference in geometric thinking of the pre-service teachers existed with regard to gender. The study used the descriptive survey design. The study participants were prospective mathematics teachers drawn from four Colleges of Education in the Bono Region and Ashanti Region of Ghana. The Colleges were randomly selected for the study. The study participants comprised 217 pre-service teachers. The van Hiele's test instrument was adapted and pilot tested to assess the internal consistency of the items in the various levels. The calculated reliability coefficient of the instrument ranged from 0.71 to 0.74. The instrument was administered to the study participants on the scheduled date. Data generated from the participants were analysed based on the study objectives. Findings from the analyses show that preservice teachers have limited geometric thinking within the first three levels. However, their geometric thinking of the levels assessed was found to be significant which could have some impact on teaching geometry. Findings also reveal gender differences in pre-service mathematics geometric thinking. It is recommended that conscious effort must be made by mathematics teacher educators in the Colleges of Education to deepen the pre-service mathematics teachers' geometric thinking.

This study sought to examine the impact of dynamic mathematics software, GeoGebra, on university mathematics students' understanding of polar coordinates. A quasi-experimental design with an equivalent group of 42 participants in each group was used. A simple random sampling approach was used to select the 84 participants from the population and a purposive sampling technique was used to assign the participants to the various groups. A t-test analysis was conducted on the pre-test and post-test activities. It was revealed that students who were taught polar coordinates with the aid of GeoGebra performed better than those who were taught with the conventional approach. Analysis of students in the experimental group's responses to the questionnaire showed that they demonstrated positive attitudes and perceptions concerning the use of GeoGebra software in the learning of polar coordinates. It was concluded that GeoGebra is more effective in improving university mathematics students' understanding of polar coordinates.

In this article, natural transform iterative method has been used to find the approximate solution of fractional order parabolic partial differential equations of multi-dimensions together with initial and boundary conditions. The method is applicable without any discretization or linearization. Three problems have been taken as test examples and the results are summarized through plots and tables to show the efficiency and reliability of the method. By practice of a few iterations, we observe that the approximate solution of the parabolic equations converges to the exact solution. The fractional derivatives are considered in the Caputo’s sense.

COVID-19 is a novel virus that has spread globally, and governments around the world often implement different strategies to prevent its spread. In the literature, several COVID-19 models have been studied with the bilinear incident rate. In this study, the S1V1E1I1Q1R1 (susceptible-vaccinated-exposed-infective-quarantined-recovered) COVID-19 model is proposed. To investigate how the disease spreads in the population, an algorithm is used. The efficacy of the algorithm is used to calculate the disease-free equilibrium point. A next generation matrix technique is used to find R0. Furthermore, to check the effect of parameters on the basic reproduction number (R0), the sensitivity analysis is conducted. Numerical simulation displays that the disease spreads in the population by increasing the value of the contact rate β while the disease spread in the population reduces by increasing the value of the vaccination rate θ, quarantine rate ϕ, and recovery rate γ. Different optimal control strategies, such as social distance and quick isolation, are also implemented. [ABSTRACT FROM AUTHOR]

As a result of COVID-19 and tuberculosis (TB) co-infection, public health is at risk. Various organs in the body may be affected by a co-infection of COVID-19 and TB. It has been shown that COVID-19 and TB co-infect humans through a bilinear incidence rate. An analysis of the efficacy of quarantine compartments for individuals with COVID-19 and who are co-infected with COVID-19 and TB is conducted using a mathematical model of COVID-19 and TB co-infection. To model the dynamics of COVID-19 and TB co-infection, we first illustrate the disease dynamics schematically and then apply the law of mass action to obtain nonlinear ordinary differential equations. Analysis of the boundedness, positivity, and equilibrium points of the system has been performed. On the basis of the next-generation matrix (NGM) technique, the reproduction number is calculated to determine the stability of the free equilibrium point. Whenever R0 < 1, the equilibrium points that are disease-free are locally asymptotically stable, but not globally. Numerical simulation shows that the use of quarantine strategies, θ1 (quarantine rates for people suffering from COVID-19) and ϕ (quarantine rates for co-infected individuals), was found to be impactful in the control of TB infection and TB–COVID-19 co-infection spread in the population if the values of those coefficients were increased. To prevent the spread of infection in the community, it is important that government stakeholders focus on the key criteria of quarantine for COVID-19 and TB co-infection. [ABSTRACT FROM AUTHOR]

The article explores the three-dimensional stream of silver (Ag), magnesium oxide (MgO), and motile microorganism water-based hybrid nanofluids as independent of time through a circular cylinder with a sinusoidal radius. The goal of this research is to optimize the rate of energy and mass transfer through a circular cylinder having a periodic radius. The phenomena are simulated as a system of partial differential equations containing momentum, temperature, concentration, and the profile of motile microbes, which were then simplified to a dimensionless system of ordinal differential equations using the similarity technique. The problem is solved by using the parametric continuation method, which is a numerical methodology. From the analysis, it has been perceived that both the energy and velocity fields significantly enhance with the rising effect of hybrid nanoparticles (Ag–MgO). The effect of chemical reaction enhances the mass transition rate because chemical reaction parameter influence exercises the molecules inside the fluid. The motile microorganism outline is elevated with the increment of Lewis and Peclet number.

This work inspects the thermal transportation of the magnetohydrodynamic Casson trihybrid nanofluid flow over a convectively heated bidirectional elongating sheet. The flow is considered as three dimensional passing over the sheet, which is placed in a porous medium. The effects of thermal radiations and space- and thermal-dependent heat sources are used in energy equations, while magnetic effects are used in momentum equations. Appropriate variables have been used to convert the modeled equations into a dimensionless form, which have then been solved using the homotopy analysis method. In this work, it is uncovered that both the primary and secondary velocities are weakened with an upsurge in porosity and magnetic factors. The thermal transportation is augmented with growth in thermal- and space-dependent heat source factors and the thermal Biot number. The convergence of the method used in this work is ensured through ℏ-curves. The results of this investigation have also been compared with the existing literature with a fine agreement among all the results that ensured the validation of the model and method used in this work. [ABSTRACT FROM AUTHOR]

In recent decades, because of the speedy progress of the smart grid and the deepening of the reforms of the energy system, demand-side users can contribute to the collaboration of the energy network, with the main right to public energy procurement and the main right to sell energy. The demand side of the smart grid and the open energy market provides users with more adoptions, and game theory is expected to become an important tool for optimizing multi-stakeholder decision-making and solving many problems in this area. In this regard, this review article first reviews the recent development of game theory application in modern power systems, in addition to discussing in detail the typical gaming behavior of the current energy demand side. Second, it focuses on the application of game theory mainly in three aspects: distributed energy users, high-energy energy users, and medium- and low-energy users. Game theory is used in optimizing the distributed energy coordination, optimizing the energy purchasing strategy, responding to the needs of commercial and residential users, and ensuring network communication. Later, a comprehensive analysis of recent trends in game theory application in power systems is carried out in detail. [ABSTRACT FROM AUTHOR]