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Copyright of Journal of Hubei Open Vocational College is the property of Journal of Hubei Open Vocational College Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Hubei Open Vocational College is the property of Journal of Hubei Open Vocational College Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study delves into the intricacies of the peristaltic mechanism exhibited by a non-Newtonian Ree-Eyring Nano-liquid, investigating its behavior in the presence of varying liquid properties and heat and mass transfer phenomena. The objective of the present investigation is to conduct a thorough analysis of this mechanism, taking into account the influence of wall properties and the dynamic nature of liquid properties. The Buongiorno nanofluid model is adopted to investigate heat and mass transfer phenomena, while the Ree-Eyring non-Newtonian fluid model is employed to comprehend the complex rheological characteristics of the fluid. This complex process’s modeling involves utilizing long wavelengths and low Reynolds number approximations. The resulting non-linear ordinary differential equations are addressed using the homotopy perturbation technique, incorporating appropriate non-dimensional parameters. A strong correlation is observed between homotopy perturbation results and previously existing literature. The magnetic field is a critical factor in shaping the fluid flow behavior, while the interplay between variable liquid properties and nanofluid characteristics significantly affects temperature profiles. The Ree-Eyring fluid and magnetic parameters enhance the heat and mass transfer coefficient. This research advances the understanding of peristalsis in the context of Ree-Eyring Nano-liquids, holding promising implications for diverse applications in both technical and medical domains.

Based on the current situation of advanced mathematics curriculum teaching, this study first constructs a blended learning model for advanced mathematics based on SPOC through literature research from three aspects: curriculum design, teaching implementation, and learning evaluation. And designs a specific blended teaching case combined with the "definite integral concept". Then, we conducted a purposeful sampling in a public school called Qinghai Normal University and selected 82 students from two first-year classes majoring in biotechnology as the research objects, and carried out an 18-week empirical study with experimental control. Finally, the final grades and teaching evaluation questionnaires of students in advanced mathematics were collected for data processing and analysis. The research results showed that students in the SPOC blended learning class had better math scores than those in the traditional teaching class, and blended learning could narrow the gap in students' math proficiency. At the same time, the questionnaire survey found that students believe that blended learning in advanced mathematics courses has abundant resources, frequent interaction and communication, and can improve learning efficiency. However, traditional advanced mathematics learning puts a lot of pressure, and they are busy taking notes in the classroom and cannot respond to the teacher's questions in time.

To understand the quantile regression model, research on a statistical analysis of advanced mathematics teaching quality evaluation was proposed. In the research, based on the test bank and questionnaires, statistical analysis was applied to examine the quality of the test bank and investigate the factors affecting the teaching quality, to understand the students’ scores, find the main factors affecting the teaching quality and use them to analyze the students’ learning status and learning quality. This will help teachers understand and grasp the students’ learning process and improve their teaching ability. And it can provide a theoretical basis for qualitative and quantitative analysis to further improve the high quality.

Self-Regulated Learning (SRL) has been a growing topic since 1983 in the Scopus database. The importance of SRL has been known through several studies because it is proven to be able to improve student learning outcomes, both at school and in life. The purpose of this study is to determine the trend of topics in the field, through bibliometric analysis with the help of the VOSViewer application. Findings reveal that there is still little discussion on the topic of SLR in mathematics learning. The journal that can be used as a reference is the International Journal of Science and Mathematics Education, which the latest topics related to Learning Systems and Education. Suggestions for further research are to make technology-based learning models using the latest theories and research results and evaluate the results achieved for improving students’ learning outcomes in mathematics and in life.

Tertiary mathematics has a central place in teacher education, yet in recent years there is growing evidence that realizing its potential affordances in secondary mathematics teaching is far from trivial. Research suggests that utilizing tertiary mathematics in secondary teaching requires interweaving it with knowledge for teaching secondary mathematics. Little is known about the underlying processes, which are often tacit and highly personal. In this article we analyze affordances of tertiary mathematics for teaching secondary probability. A group of mathematicians and experienced secondary teachers jointly inquired into the mathematics that could be addressed in school when discussing a popular probability game – the River Crossing game (henceforth "the game"). This context was chosen as an extreme case, in the sense that the mathematics underlying the game is so nuanced and complex that applying tertiary knowledge to mathematize and understand it is generally not feasible for secondary teachers. Thus, it is not clear how tertiary mathematics can inform teachers about using the game in class. Our analysis shows how the conflicting perspectives of teachers and mathematicians on what mathematics students may learn by playing the game initially hindered utilization of tertiary mathematics. Nevertheless, rapprochement was achieved, highlighting four different trajectories for interweaving knowledge of tertiary mathematics with knowledge for teaching secondary mathematics towards using the game in ingenious ways that respect both mathematical and pedagogical concerns. Our findings suggest that tertiary mathematics may have affordances for secondary mathematics teaching even in situations where teachers lack tertiary-level understanding of the underlying subject-matter. [ABSTRACT FROM AUTHOR]

Advanced mathematics is seen as an integral component of secondary teacher preparation, and thus most secondary teacher preparation programs require their students to complete an array of advanced mathematics courses. In recent years, though, researchers have questioned the utility of proposed connections between advanced and secondary mathematics. It is simply not clear in many cases—to researchers, teacher educators, and teachers themselves—exactly how advanced mathematics content is related to secondary content. In this paper, we propose using a conceptual analysis—a form of theory in which one explicitly describes ways of reasoning about a particular mathematical idea—to address this issue. Specifically, we use conceptual analyses for the foundational notions of equivalence and inverse to illustrate how the ways of reasoning needed to support productive engagement with tasks in advanced mathematics can mirror and reinforce those that are similarly productive in school mathematics. To do so, we propose conceptual analyses for the key concepts of equivalence and inverse and show how researchers can use these conceptual analyses to identify connections to school mathematics in advanced mathematical tasks that might otherwise be obscured and overlooked. We conclude by suggesting ways in which conceptual analyses might be productively used by both teacher educators and future teachers. [ABSTRACT FROM AUTHOR]

Contemporary research on mathematics teacher education reveals attention by researchers on mathematics connections (MC). Nevertheless, researchers have not investigated experiential views of mathematics teacher educators (MTEs) around MC. This article addresses the scenario by relating findings of an intrinsic case study involving a purposively chosen MTE. MTE responded to interview questions regarding experiential viewpoints on connections between advanced and school mathematics. Narrative data analysis suggested that MTE prefers special mathematics education courses (MECs). Envisaged MEC are supposed to align with school mathematics but comprised of subject matter, which is neither advanced mathematics nor school mathematics. Such courses coupled with school-based mentorship are expected to acquaint mathematics student teachers with MC. MTE could not provide subject matter-based connections except for pedagogic ones. Study of advanced mathematics was encouraged to foster understanding of MC. These findings motivate further research concerning how advanced mathematics ought to be connected to school mathematics concepts. [ABSTRACT FROM AUTHOR]

This paper refers to the Lagrangian mathematical model and the Rackwitz-Fiessler transform model in modeling advanced mathematics applications. In this paper, the Lagrangian interpolation method and Rackwitz-Fiessler transform are used to calculate the correlation coefficient efficiently. The purpose of this algorithm is to speed up the process of probabilistic modeling. This paper uses integral probability transformation to characterize the output's uncertainty by the production's joint distribution function. The purpose of this process is to improve the reliability of the calculation. Through the algorithm analysis, it is found that the method is reasonable and efficient.

University graduates in the Society 5.0 era need more skills than ever before; thus, a new learning model is needed. To respond this situation, we created a learning model that equips students to think critically, creatively, and independently through Advanced Mathematics courses using hybrid learning. This study aims to produce a model that can meet the needs of Moodle-based hybrid learning. Through research and development (R&D), we developed a learning model through the “Brillian” application. The Critical Creative Hybrid Independent Learning (C-CHIL) model test was conducted regarding (1) quality which includes the content and constructs of the model, and (2) feasibility. The test results of the C-CHIL model show that (1) Content validity test resulted an average of 3.73 which means the model is very valid. (2) The average feasibility test is 3.63, which means it is also very valid. Thus, it can be concluded that the C-CHIL model meets the valid requirements (content and construct) and is suitable for students based on expert opinion. The results of this study imply that the C-CHIL model can be used to improve critical, creative, and independent thinking skills, especially in Advanced Mathematics courses in Higher Education

In traditional advanced mathematics lectures the instructor usually provides definitions, theorems, and proofs on the board rather quickly. The students often cannot make sense of these during the lecture as they are busy writing. In order to gain an understanding of the content, an intensive post-class processing on the basis of their notes would therefore be necessary for many students. However, students often do not post-class process lectures carefully. Furthermore, they often do not record the lecturer's oral explanations that are essential to make sense of the formal lecture content. One approach to address these problems is a flipped classroom, in which students come into contact with new content before class, while the in-class time is used for activities that help students make sense of it. We implemented an adaptation of this approach in a proof-oriented analysis course, in which the instructor used the in-class time to illustrate how experts in mathematics make sense of new definitions, theorems, and proofs, while keeping the lecture as the mode of teaching. In this article we describe this adaptation, its possible benefits for addressing students' problems in learning from traditional mathematics lectures, and its actual effects, which we investigated in an empirical study. [ABSTRACT FROM AUTHOR]

A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall's framework of the three worlds of mathematics. Tall's framework describes the aspects and the development of mathematical thinking from early childhood to university-level mathematics. In this theoretical article, we further elaborate Tall's framework. First, we present a division between the subjective-social and objective sides of mathematics. Then, we combine Tall's distinction to ours and present a framework of six dimensions of mathematics. We demonstrate this framework by discussion on the definition of continuity and by presenting a visual construction of a nowhere differentiable function and analyzing the way in which this construction is communicated visually. In this connection, we discuss the importance to distinguish the subjective-social from the objective side of mathematics. We argue that the framework presented in this paper can be useful in developing mathematics teaching at all levels and can be applied in educational research to analyze mathematical communication in authentic situations. [ABSTRACT FROM AUTHOR]

The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year of study, which are less compartmentalized and allow for an extended acquisition of rationales of advanced mathematical practices and concepts. Against this background, subject-specific potentials of advanced mathematics are examined in this contribution. The Anthropological Theory of the Didactic (ATD) serves as the theoretical framework and in the analyses notions from its 4T-model are applied. Structural observations in praxeological terms are illustrated by examples chosen from a presentation of a classical result in Nonlinear Approximation. At the specific focus of the praxeological analyses are aspects for bridging and extending concepts within and across Analysis. On this basis, tasks designed for first-year university Analysis courses are analysed in detail. Moreover, general characteristics of the methodological approach realized in this contribution are discussed. [ABSTRACT FROM AUTHOR]

A good understanding of the mathematical processes of solving the first-order linear ordinary differential equations (ODEs) is the foundation for undergraduate students in science and engineering programs to progress smoothly to advanced ODEs and/or partial differential equations (PDEs) later. However, different methods for solving the first-order linear ODEs are presented in various textbooks and resources, which often confuses students in their choice of the method for solving the ODEs. This special tutorial note presents the practices the author used to address such confusions in solving the first-order linear ODEs for students engaged in the bachelorette engineering studies at a regional university in Australia in recent years. The derivation processes of the four commonly adopted methods for solving the first-order linear ODEs, including three explicit methods and one implicit method presented in many textbooks, are presented first, followed by the logical interconnections that unify these four methods to clarify student's confusions on different presentations of the procedures and the solutions in different sources. Comparisons among these methods are also made.

A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall’s framework of the three worlds of mathematics. Tall’s framework describes the aspects and the development of mathematical thinking from early childhood to university-level mathematics. In this theoretical article, we further elaborate Tall’s framework. First, we present a division between the subjective-social and objective sides of mathematics. Then, we combine Tall’s distinction to ours and present a framework of six dimensions of mathematics. We demonstrate this framework by discussion on the definition of continuity and by presenting a visual construction of a nowhere differentiable function and analyzing the way in which this construction is communicated visually. In this connection, we discuss the importance to distinguish the subjective-social from the objective side of mathematics. We argue that the framework presented in this paper can be useful in developing mathematics teaching at all levels and can be applied in educational research to analyze mathematical communication in authentic situations.

In this paper, we examine mathematicians' views on the value of advanced mathematics for secondary mathematics teachers. The data comprise semi-structured interviews with 24 mathematicians from 10 universities. The findings indicate that the value of advanced mathematics courses for prospective secondary mathematics teachers lies in their potential to offer connections across mathematical domains, mathematical experience for the development of problem-solving abilities, and increased epistemological awareness of the subject. Additionally, mathematicians' examples that connect advanced and school mathematics are presented and discussed. While the mathematicians provided rich examples of such connections, we noted that such examples were relatively scarce and accordingly sought possible explanations in the discussion of the findings. [ABSTRACT FROM AUTHOR]

Our study evaluated the effectiveness of a new tracking policy called self-selection (SS). The purpose of SS was to increase the representation of students of color in ad- vanced mathematics courses at an urban mid-western middle school. We conducted a multinomial logistic regression to determine the effect of the SS on enrollment trends among 2,627 students. The results of our analysis indicate that Black and Latinx students were less likely to enroll in advanced mathematics courses after the implementation of self-selection. Based on our findings, SS did not statistically significantly increase the ethnic representation of historically underserved students of color in advanced middle school mathematics courses. Implications and considerations for future research on SS are discussed. [ABSTRACT FROM AUTHOR]

Recently Lin Xin gave an explicit formula for the integer part of reciprocals of ∑ k = n ∞ k − 2 . In this paper we extend the result of Lin Xin on k 2 to (a k) 2 , where a is a positive integer. We give the formulas for an alternating sum of the reciprocals of k 2 and reciprocals of squares of the odd integers. Further, we give the formulas for reciprocal sums of (2 k) 4 and (2 k − 1) 4 . [ABSTRACT FROM AUTHOR]

Layer adaptive meshes are developed in order to solve a class of singularly perturbed parabolic convection-diffusion Robin type problems. To discretize the problem, an upwind method in the space direction on layer-adapted Shishkin and Bakhvalov-Shishkin meshes and a backward Euler method in the time direction on uniform meshes are used. It is demonstrated that the proposed method is parameter uniformly convergent. Three numerical examples are considered for numerical experimentation to demonstrate the method's applicability, and the results are presented in tables and graphs. The results show that the Bakhvalov-Shishkin mesh outperforms the Shishkin mesh in terms of accuracy. The use of Bakhvalov-Shishkin has an advantage over the standard Shishkin mesh at the same computational cost because Bakhvalov-Shishkin mesh is not affected by logarithmic term. [ABSTRACT FROM AUTHOR]

The classical mortality models such as the Cairns-Blake-Dowd (CBD), Lee-Carter (LC), Linear Regression (LR) models are used to model Systematic Mortality Risk (SMR) for many developed countries populations for actuarial product valuations. This research study aims at incorporating the Bühlmann credibility approach (BCA) to improve the SMR models to fit sub-Saharan African populations like Kenya. Since the Kenyan population does not exhibit the Gaussian properties used in modeling the classical error terms, we proposed using Normal Inverse Gaussian distribution to model these error terms instead of a Gaussian distribution. We model the error terms of the classical models (LC, CBD, and LR) as a Normal Inverse Gaussian (NIG) distribution through the Bühlmann credibility approach. This novel approach demonstrates an improved precision of the predicted SMR as shown by the values of MAPE and RMSE measures compared to those under classical mortality risk models. Ultimately, we have done actuarial valuations of annuities and assurances using our determined SMR, thus concluding that this BCA approach improves the accuracy of actuarial products sold in the Kenyan market. [ABSTRACT FROM AUTHOR]

This prospective study adopted Vygotsky's concept of perezhivanie to examine students' lived experiences in learning mathematics and how they were related to subject choice plans and actual decisions. Most research has considered students' mathematics subject choice as a decision predictable using important cognitive and social variables. Due attention has not been given to examining how students' lived experiences in learning mathematics relate and contribute to their subject choice plans and decisions over time. Perezhivanie is a psychological structure for understanding dynamic influences derived from personal and contextual sources. In this study, two case studies were crafted using multiple data sources including interviews, observations, surveys and fieldnotes collected over three years on two achieving students who had studied in the same class. Despite this shared context, their perezhivanija differed, revealing complex dynamic interplay between factors derived from personal and external realms. This study described the identified perezhivanija of these two students and explained how they were related to their subject choice plans and their eventual subject choice decisions. The findings revealed that perezhivanija, including both heightened experiences and meta-experiences, were vital personal sources informing subject choice plans and decisions. [ABSTRACT FROM AUTHOR]

Helping people move to independence is often cited as a primary goal of public assistance policies in the United States. Over the past several decades, welfare reform efforts in the US have promoted the idea of a work-first approach. Research shows that this approach has discouraged or at least made it harder for some students to attend college while meeting the work requirements for aid. How can those students who need public assistance increase their chances of finding a sustainable job and thus not need to rely on the public support system after high school? To address this question, this study used a sample of 3,384 student responses from the National Longitudinal Study of Adolescent to Adult Health and a recursive bivariate probit model to analyze the association between advanced math course-taking in high school and the probability of subsequent receipt of public assistance. The empirical results suggest that taking advanced math courses in high school is associated with a lower probability of receiving public assistance for recent graduates. These findings are particularly important for school social workers who work in conjunction with teachers and school counselors to help at-risk students improve their chances of future financial independence. [ABSTRACT FROM AUTHOR]

Prospective secondary mathematics teachers are usually required to complete several university advanced mathematics courses before being certified to teach secondary mathematics. However, teachers usually do not find these courses to be valuable for their teaching. We designed an experimental real analysis course with the goal of making real analysis content useful and relevant to teaching. Our approach was to ground the real analysis content in pedagogical situations that problematized a secondary mathematics topic, where the nuances of teaching secondary mathematics could be informed by the real analysis that was covered. The experimental course was implemented in a graduate teacher education programme with 32 pre- and in-service teachers (PISTs). After the course, we conducted focus group interviews with 20 of these PISTs to get feedback on how the course was valuable to their teaching practice. Many PISTs found the course to be valuable for teaching secondary mathematics, as well as for their understanding of secondary mathematics and real analysis. [ABSTRACT FROM AUTHOR]

An alternative pedagogical design is discussed that aims to guide engineering students to solve first-order ordinary differential equations (ODEs), and is based on students’ learning weaknesses identified from previous teaching and learning activities. This approach supported student’s self-enrichment through exploration of relevant resources in ODEs, and guided students towards the choice of their own effective ways for solving ODEs for different problems. This paper presents the practices on designing and delivering solution techniques for first-order linear ODEs using this approach for more than 400 undergraduate engineering students at a regional university in Australia during 2014–2017. The timeline involved initial experimentation in 2014 and 2015, followed by refinements to the pedagogy based on student’s feedback. The refined pedagogy was then used for the advanced mathematics course in 2016 and 2017. Significant improvements were made in student’s learning outcomes in effectively and accurately solving the first-order linear ODEs over this period.

Dynamic study of iterative methods has become more common in recent decades thanks to the development of computers, something that illustrates the importance of including these methods in curricula. There are several types of software whose didactic application in the classroom is very useful, but they have not been designed in response to students' difficulties related to learning of the dynamics of iterative methods. It should also be noted that there is no software exclusively designed for teaching iterative methods, and this, along with the difficulties students encounter in this area, has caused many students problems with understanding fundamental concepts as it is a subject with a large visual component. Taking into account all the above factors, we have designed a software program to help students understand this subject and allow teachers to perform simulations in the classroom while preventing students from using the tool or the parametric plane or dynamic plane that is appropriate for the particular situation they face. This article considers the development of a methodological proposal in which the software we designed is used with a sample of students from the Discrete and Continuous Dynamic Systems module on the Master's degree in Mathematical Engineering and Computing at the Universidad Internacional de La Rioja, and their results are compared with another sample of students who did not have access to this mathematical tool. The result that emerges is that the group that followed the new methodology obtained much higher average score than the groups taught with the previous methodology. [ABSTRACT FROM AUTHOR]