Higher Mathematical Modeling Thinking and Method Application

As The Times advances, innovating teaching methods, optimizing teaching resources and building online and offline blended teaching environment have become the top priority. Therefore, this paper constructs a BOPPPS model based on active introduction, problem formation, pre-evaluation, participatory learning, evaluation feedback and summary, which aims to help students deeply understand and master the key knowledge of the course and helps teachers effectively improve the teaching effect of the course. The BOPPPS model integrates the education information technology and undergraduate teaching, establishes the closed-loop feedback framework of teaching and learning and gives full play to the main role of students in teaching, which at the same time, provides students with a learning atmosphere of independent inquiry, cooperative learning, knowledge exchange and critical reflection, and achieves good results in teaching practice. The results show that after applying BOPPPS teaching model in the college public basic mathematics course, the scores of students have been primarily more than 90 points, and at the same time, the proportion of students with scores of 80-90 points has been significantly increased, and the percentage of students failing has dropped dramatically. This indicates that the BOPPPS teaching method can significantly increase the proportion of students with high scores, perfect the learning effect, reduce the failure rate, and improve students’ learning enthusiasm and ability to master knowledge.

Teaching mathematics in an EFL context at higher education; before, during and after the COVID-19 pandemic: a comparative study

The selection of K–12 mathematics curricula has become a polarizing issue for schools, teachers, parents, and other educators and has raised important questions about the long-term influence of these curricula. This study examined the impact of participation in either a National Science Foundation–funded or commercially developed mathematics curriculum on the difficulty level of the first university mathematics course a student enrolled in and the grade earned in that course. The results provide evidence that National Science Foundation–funded curricula do not prepare students to initially enroll in more difficult university mathematics courses as well as commercially developed curricula, but once enrolled students earn similar grades. These findings have important implications for high school mathematics curriculum selection and for future research in this area.

The application of mathematics has become an important task of mathematics education. Mathematical modeling is a bridge between mathematics and the real world, a mathematical abstraction of real problems, and a higher level of comprehensive literacy. It can effectively improve students’ comprehensive practical ability and their ability to acquire knowledge independently, and at the same time, it is conducive to students’ achievement of other core mathematical literacy goals. Therefore, it is very necessary to apply the thought of mathematical modeling in mathematics classes of colleges and universities. It is found that the specific method and case implementation of applying mathematical modeling idea to classroom teaching is not thorough enough. The purpose of this paper is to study the method of integrating mathematical modeling into higher mathematics teaching in applied universities under the epidemic situation. In this article, through classroom practice and take the questionnaire research method, from the Angle of subjective and objective respectively from students’ mathematical modeling ideas on the improvement of their teaching and learning situation, etc to investigate, using mathematical modeling thought teaching can change students’ attitude and understanding of mathematics, and the ability to change students mathematics study, help students to set up the correct view of mathematics and mathematics learning concept. The proportion that “modeling ideas can stimulate learning interest” is above 40%.

BackgroundThe study attempts to integrate Civic and Political Psychoeducation to optimize the teaching content of traditional mathematics courses in colleges and universities, in order to alleviate college students’ anxiety in the process of mathematics learning, as the difficulty of mathematics courses in colleges and universities increases.Subjects and MethodsAs subjects for this study, 120 students majoring in Mathematics Applications at one of China’s universities were chosen. The 120 college students were randomly and equally divided into two groups, the control group and the experimental group, with 60 students in each group. The students in the experimental group were taught utilizing the Civic Psychology intervention in their mathematics courses, whereas the students in the control group were taught using the usual mathematics lecture approach. The trial ran for a semester. After one semester, the students’ anxiety psychological ratings under various instructional approaches were compared. The data changes during the experiment were recorded and analyzed using SPSS23.0.ResultsThe study’s findings demonstrate that after one semester of mathematics instruction, the average anxiety level of the experimental group dropped from 28.56 to 5.21, whereas the average anxiety score of the control group did not change appreciably. It can be demonstrated that the experimental group’s teaching style can more successfully ease college students’ anxiety during the arithmetic learning process.ConclusionsA college mathematics teaching strategy that mixes ideological and psychological education can successfully reduce college students’ anxiety during the mathematics learning process.

Abstract—Analog circuit is an important compulsory basic course for electronic information majors, which has complex theories, abstract concepts, strong logic, and a single experimental project and form that leads to certain limitations for students to have a deep understanding of circuits. By improving the degree of freedom of experimental exploration, students can further deepen their understanding and knowledge of theoretical knowledge and the actual working situation of circuits, improve students' enthusiasm for learning, enhance students' independent thinking and practical ability, and improve the teaching effect.

Aim/Purpose: The purpose of this study is to identify how Advanced level Mathematics and Mathematics course units offered at university level do impact on the academic performance of theoretical Computer Science course units. Background: In Sri Lankan state universities, students have been enrolled only from the Physical Science stream to do a degree program in Computer Science. In addition to that, universities have been offering some course units in Mathematics to provide the required mathematical maturity to Computer Science undergraduates. Despite of this it is observed that the failure rates in fundamental theoretical Computer Science course units are much higher than other course units offered in the general degree program every year. Methodology : Academic records comprised of all 459 undergraduates from three consecutive batches admitted to the degree program in Computer Science from a university were considered for this study. Contribution: This study helps academics in identifying suitable curricula for Mathematics course units to improve students’ performance in theoretical Computer Science courses. Findings: Advanced level Mathematics does not have any significant effect on the academic performance of theoretical Computer Science course units. Even though all Mathematics course units offered were significantly correlated with academic performance of every theoretical Computer Science course unit, only the Discrete Mathematics course unit highly impacted on the academic performance of all three theoretical Computer Science course units. Further this study indicates that the academic performance of female undergraduates is better than males in all theoretical Computer Science and Mathematics course units. Future Research: Identifying other critical success factors contributing to the students’ academic performance of the theoretical Computer Science through empirical studies

Starting from the characteristics of students at application-oriented undergraduate institutions, this paper takes Dalian University of Technology City College as an example. Using the Chaoxing platform, it explores blended teaching models for university mathematics courses such as Advanced Mathematics and Linear Algebra. The focus of the research includes designing and constructing online teaching content, implementing blended teaching practices, and reforming and implementing course assessment mechanisms, effectively enhancing the effectiveness of university mathematics teaching.

Solving mathematical problmes is a favourite pastime of many people, from school students to professional research mathematicians. The aim of this book is to provide a wide variety of problems suitable for teenagers and students which will stimulate interest in mathematical ideas and methods outside the usual school syllabus. The problems vary in their difficulty, but are all intended to encourage independent investigation, to demonstrate different approaches to problem-solving, and to illustrate some of the famous problems that famous mathematicians have attempted to solve. For each problem the author has provided hints and a detailed discussion of their solution. Consequently, the book will provide a valuable teaching resource for schools, teacher training, and university mathematics courses. The problems themselves range from the easy to the unsolved and will provide much enjoyment for all those fascinated by mathematical ideas.

Scores from the Descriptive Tests of Mathematics Skills (DTMS) (a set of tests designed to reflect the content of beginning mathematics courses and to assist in placement decisions) were compared with scores from the College Board Scholastic Aptitude Test-Mathematics (SAT-M) in predicting grades in freshman level mathematics courses at two institutions. For more advanced courses (elementary functions and calculus), the DTMS and SAT performed about equally well. But for remedial algebra courses, predictions from the DTMS were clearly superior to those from the SAT-M. General aptitude tests that are valid for selection decisions may be considerably less valid for predicting success in specific courses.

This paper examines the various ways in which university lecturers of large first-year university mathematics courses receive and use feedback on their students’ learning with particular emphasis on feedback collected at a mathematics support centre in an Irish university. Drawing on findings from interviews conducted with 13 lecturers at three intervals in a teaching semester, we present ten ways, identified by lecturers, in which they receive feedback on their students’ learning. We examine the utility of mathematics support centre feedback to lecturers wishing to monitor their students’ progress as the module unfolds. This electronic feedback, supplied by the attending mathematics support tutor(s), gives a brief summary of each student’s query to the centre. We describe lecturers’ reports of where this feedback sits in the general context of other feedback sources from large classes and how it can be useful. Lecturers’ responses were analysed using thematic analysis, and three key aspects of feedback emanating from a mathematics support centre were identified: its uniqueness and value; its detail and specificity; and, its impact on practice. We found that lecturers perceive this form of feedback to be one of the most valuable available to them in terms of formatively assessing their students’ learning.

This thesis aims at developing efficient mathematical methods for solving hierarchical dynamic optimization problems. The main motivation is to model processes in nature, for which there is evidence to assume that they run optimally. We describe models of such processes by optimal control problems (called optimal control models (OCMs)). However, an OCM typically includes unknown parameters that cannot be derived entirely on a theoretical basis, which is in particular the case for the cost function. Therefore, we develop parameter estimation techniques to estimate the unknowns in an OCM from observation data of the process. Mathematically, this leads to a hierarchical dynamic optimization problem with a parameter estimation problem on the upper level and an optimal control problem on the lower level. We focus on multi-stage equality and inequality constrained optimal control problems based on nonlinear ordinary differential equations. The main goal of this thesis is to derive numerically efficient mathematical methods for solving hierarchical dynamic optimization problems, and to use these methods to estimate parameters in high-dimensional OCMs from real-world measurement data. We develop parameter-dependent OCMs for the gait of cerebral palsy patients and able-bodied subjects. The unknown parameters in the OCMs are then estimated from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg by using the mathematical methods developed within this work. The main novelties and contributions of this thesis to the field of hierarchical dynamic optimization are summarized herein. - We establish a novel mathematical method, a so-called direct all-at-once approach, for solving hierarchical dynamic optimization problems based on the direct multiple shooting method and first-order optimality conditions. - Furthermore, we propose an efficient numerical algorithm for large-scale hierarchical dynamic optimization problems, which fully exploits the structures inherited from both the hierarchical setting and the discretization. - Pontryagin's maximum principle is used to analyze solution properties of hierarchical dynamic optimization problems like second-order optimality conditions of the lower-level problem. - In addition, we propose and discuss alternative methods for hierarchical dynamic optimization that are based on derivative-free optimization and a bundle approach. These methods keep the hierarchical problem setting and do not reformulate the lower-level problem using first-order optimality conditions. - We establish a novel lifting method for regularizing mathematical programs with complementarity constraints, which is discussed and numerically investigated by means of a well-known collection of benchmark problems. - Proofs of regularity and convergence results for sequential quadratic programming methods applied to lifted mathematical programs with complementarity constraints are provided. - Efficient state-of-the-art implementations of all mathematical methods derived in this thesis, as well as a benchmark collection of hierarchical dynamic optimization problems are presented. - High-dimensional optimal control gait models for cerebral palsy patients and able-bodied subjects are developed. The mathematical methods derived in this thesis are used to estimate the unknown model parameters from real-world motion capture data provided by the Heidelberg MotionLab of the Orthopedic University Clinic Heidelberg. The theoretical and practical results presented in this thesis can be considered an initial motivating step towards answering open questions in current medical research in fields like treatment planning, classification of gaits, or the evaluation of surgeries by means of hierarchical dynamic optimization.

To integrate the mathematical history and the idea of mathematical modeling into the teaching of mathematics timely, so that students can get deeper understanding of how to get and apply the mathematics concepts and theories to real life. In order to prove the feasibility, the advanced mathematics teaching quality evaluation system is designed. And, the effectiveness of the implementation of the advanced mathematics teaching quality evaluation system in our university is verified.

A computer science aptitude predictor was administered to students enrolled in a first technical course in computer science to determine potential for success. The study revealed significant differences in the scoring between students who withdrew from the course and those students who did not. The causes for the differences all related to the students' mathematical background: high school performance, previous computer science education, and the number of college mathematics courses taken.

In this exploratory study, we developed a portrait of the challenges and strategic responses of secondary mathematics teacher educators (MTEs) in Chinese universities. The MTEs reported encountering more challenges when teaching pedagogical courses and supervising student teachers than when teaching college mathematics courses and teaching mathematical problem-solving courses. This finding reflects a key difference between the content, goals, and teaching demands of these 2 elements of mathematics teacher education programs (acting in the role of an MTE versus the role of a mathematics teacher). In this study, we also analyzed the strategies that MTEs use to deal with the challenges that arise in their work and the suggestions they have for the training of future MTEs.