Enhancement of Innovation Competence of College Students Majoring in Mathematics Education through Curriculum Optimization

The innovation competence of K-12 education teachers undoubtedly plays a crucial role in fostering the innovation abilities of their students.K-12 mathematics education equips students with the critical thinking and problem-solving skills essential for their future studies in colleges and universities,helping them grasp complex techniques to address challenges in everyday life and their careers.Therefore,it is of great significance to study strategies for improving the innovation competence of college students majoring in Mathematics Education,as they will likely become K-12 education mathematics teachers directly after graduating from colleges or universities.In this paper,we study strategies for enhancing the innovation competence of college students majoring in Mathematics Education through curriculum optimization.We analyze and explain in detail the importance of innovation competence for college students majoring in Mathematics Education and the difficulties encountered in enhancing college students’innovation competence.With the help of the analysis of the importance and challenges of enhancing college students’innovation competence,we propose several strategies to improve the innovation competence of college students majoring in Mathematics Education based on curriculum optimization.The findings presented in this paper can be applied to develop strategies for college students majoring in Physics and Chemistry Education.

Research on the Teaching Design of Advanced Mathematics Courses Based on Outcome-Based Education Concept

This paper first analyzes the characteristics and current situation of the Advanced Mathematics course;secondly,it proposes a teaching model that integrates the outcome-based education(OBE)philosophy and blended teaching method,reorganizing the teaching objectives,teaching content,and assessment evaluation process of the Advanced Mathematics course;lastly,through practice,it is proved that this approach can effectively improve students’mastery of course content,enhance students’ability to apply mathematical knowledge,and strengthen teaching effectiveness.

Pre-service Early Childhood Teachers’ Attitude Towards Mathematics: A Jamaican Inquiry

The purpose of the study was to evaluate Jamaican early childhood pre-service teachers’attitudes towards mathematics.The study is designed according to the quantitative survey model in the descriptive type.In this study,a modified version of the Fennema-Sherman mathematics attitude scale was used to measure the mathematics attitude of 144 early childhood pre-service teachers in four different categories of the attitude scale(mathematics usefulness,confidence in learning mathematics,mathematics anxiety,and mathematics motivation).The data were collected from participants in the five teachers’colleges that offer the early childhood education program in Jamaica.The findings revealed that Jamaican early childhood pre-service teachers generally have a more positive attitude towards mathematics.A comparison among the different year groups revealed that a significantly greater percentage of the Year two group of participants possessed a more positive mathematics attitude than the other year groups.A significantly higher percentage of the Year three group indicated that they do not want to teach the subject in the future.The findings have implications for the teaching and learning of mathematics in the early childhood education program in Jamaica and,by extension,the teaching and learning of mathematics at the early childhood level of the education system.

Reduced Differential Transform Method for Solving Nonlinear Biomathematics Models

In this paper,we study the approximate solutions for some of nonlinear Biomathematics models via the e-epidemic SI1I2R model characterizing the spread of viruses in a computer network and SIR childhood disease model.The reduced differential transforms method(RDTM)is one of the interesting methods for finding the approximate solutions for nonlinear problems.We apply the RDTM to discuss the analytic approximate solutions to the SI1I2R model for the spread of virus HCV-subtype and SIR childhood disease model.We discuss the numerical results at some special values of parameters in the approximate solutions.We use the computer software package such as Mathematical to find more iteration when calculating the approximate solutions.Graphical results and discussed quantitatively are presented to illustrate behavior of the obtained approximate solutions.

DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

Examining Mathematics Anxiety of Undergraduates Using a Brain-Based Measurement, EEG

This paper reports on an investigation of mathematics anxiety (MA) among 40 Korean undergraduate students, using cognitive neuroscience. In Spring 2015, we collected data on correct response rates and reaction times from computer-based activities related to quadratic functions. We also measured brain response through event related potentials (ERP). Results demonstrate that students with higher mathematics anxiety (HMA) took more time than students with lower mathematics anxiety (LMA), both in translating equations to graphs and in translating graphs to equations. Moreover, based on analysis of ERP, brain waves of the HMA group recorded higher amplitude. In specific, both groups showed higher amplitude in translation from graphs to equation than vice versa. Higher amplitudes indicate greater demands on working memory, which we discuss in the concluding section, especially with regard to MA.

Linking Real-Life Situations with Classroom Assessment: Development of Real-Life Performance-Based Tasks in Business Mathematics

This study aimed to develop real-life performance-based tasks in Business Mathematics (RLPBTs) following the ADDIE’s model of instructional development. Using the descriptive-developmental research design, the study developed RLPBTS with mathematics experts, mathematics department head, bank manager, mathematics teachers, and students as respondents. The RLPBTs consist of instructional plans. Each instructional plan has these components: Introduction, Learning Competency, Learning Outcome, Task Execution, Scoring Guide, and Generalization. The design and content of the instructional plans were assessed as very good. On the other hand, the design and execution of the Tasks were assessed as favorable. Grade 11 students also agreed that real-life performance-based tasks helped them understand better concepts in business mathematics. They claimed that they enjoyed the tasks because of the inclusion of real-life situations that they simulated. The use of the RLPBTs provides another innovation in the teaching and learning concepts in Business Mathematics.

Mathematics Knowledge of Proof in Geometry： Pre-Service Teachers＇ Perspectives

This article is based on research on pre-service teachers＇ perspectives on their mathematics knowledge of proof in geometry. The study was framed using tile mathematical knowledge for teaching framework. This qualitative study employed the use of a task-based worksheet, focus group sessions and semi-structured individual interviews. The task-based worksheet was completed by 180 pre-service mathematics teachers （second, third and fourth year mathematics education students）. Pre-service mathematics teachers are student teachers who have not yet completed their training to become teachers. After the analysis of the task-based worksheet, 20 participants were invited to participate in focus group sessions and individual interviews. The findings of the study reveal that the participants possess peripheral mathematics knowledge of proof in geometry. The study aims at assisting pre-service teachers and interested educationists to explore innovative methods of acquiring and imparting mathematics knowledge of proof in geometry. The study proposes possible changes in curriculum at school and university level.

Exploration and Practice of Improving Higher Mathematics Teaching Quality of Teaching at Different Levels

Teaching content of Higher Mathematics is systematic and rigor with a high degree of abstraction. Because different students are on the different basis and different disciplines have various requirements, mathematics is generally difficult for students. In order to improve the quality of teaching mathematics, we should make use of individualized teaching and teaching by different levels in order to achieve the best teaching results.

Research for Using Information Technology in the Design of Effective Mathematics Teaching Methods

The development of modem information technology has brought unprecedented impact on mathematics teaching, which affects the content of the curriculum, and teaching and its manifestations, affecting the role of teachers in the teaching process and its relationship with the students, teaching methods and impacting policies the selection and use, affecting organizational form of teaching. Mathematics curriculum standards clearly stated： the design and implementation of the mathematics curriculum should pay attention to the use of modern information technology, particularly to fully consider the impact on mathematics learning content and methods, and to provide students with a more vigorous development of rich learning resources, the modem information technology as a powerful tool for students to learn math and problem-solving, working to change the way students learn, students willing and more energy into reality, exploratory math activities.

Robotics and Mathematics in Citizenship Formation： Associating Negatives Numbers and Education in Traffic

This article reports the experience of the robotics class taught by a student＇s degree in mathematics from the Federal University of Uberlandia, as a requirement for co mp letion of the discip line sup ervised training. The M ineiro Baptist College was chosen in the city of Uberlandia-MG to carry out this work because it is a school that entered the discipline of robotics into their curriculum. The class was held with the students of the seventh grade of elementary school second, linking the areas of mathematics, robotics and traffic education, prioritizing the respect of the contents worked in math classes and civic education of individuals in a dynamic and creative way.

A Research on the Strategy of Integrating PBL with Curriculum Ideological and Political Elements-Taking College Mathematics as an Example

Taking college mathematics as an example,a questionnaire was designed for college mathematics teachers and students to fully comprehend the teaching situation.This paper mainly discusses the problems existing in the teaching of college mathematics and proposes the strategy of integrating PBL with curriculum ideological and political elements in college mathematics,so as to change the teaching process and improve the teaching quality.

Research on HPM Teaching Supported by Hawgent Dynamic Mathematics Software: Take "The Recognition of Circle" as an Example

History and Pedagogy of Mathematics(HPM)is one of the important research fields in mathematics education,which has received widespread attention from the mathematics education community because of its educational value.Modem mathematics education technology plays an important auxiliary role in mathematics teaching.Hawgent is a dynamic mathematics software that can present abstract mathematical knowledge visually and static mathematical knowledge dynamically.In view of this,this research takes"the recognition of circle" as an example to conduct a research on HPM teaching supported by Hawgent Dynamic Mathematics Software in three aspects:analyze the contents and uncover the history of mathematics,make the products and show the history of mathematics,design the teaching and integrate the history of Mathematics.

On the Cultivation of Innovation Ability of Mathematics Normal Students Based on the Second Classroom

This paper analyses the mathematics teachers need and urgency of cultivating the ability of innovation,discusses the mathematics students innovation consciousness lack of factors,put forward the theoretical basis for using first class,through the second classroom for mathematics teachers to carry out flexible space,rich contents,various forms of activities,promote students using the brain and hand,give full play to students’subjective initiative,in time to find new problem solving new problems,so as to promote the innovation ability of students.

A Study on Computer Consciousness on Intuitive Geometry Based on Mathematics Experiments and Statistical Analysis

In this paper, we present our research on building computing machines consciousness about intuitive geometry based on mathematics experiments and statistical inference. The investigation consists of the following five steps. At first, we select a set of geometric configurations and for each configuration we construct a large amount of geometric data as observation data using dynamic geometry programs together with the pseudo-random number generator. Secondly, we refer to the geometric predicates in the algebraic method of machine proof of geometric theorems to construct statistics suitable for measuring the approximate geometric relationships in the observation data. In the third step, we propose a geometric relationship detection method based on the similarity of data distribution, where the search space has been reduced into small batches of data by pre-searching for efficiency, and the hypothetical test of the possible geometric relationships in the search results has be performed. In the fourth step, we explore the integer relation of the line segment lengths in the geometric configuration in addition. At the final step, we do numerical experiments for the pre-selected geometric configurations to verify the effectiveness of our method. The results show that computer equipped with the above procedures can find out the hidden geometric relations from the randomly generated data of related geometric configurations, and in this sense, computing machines can actually attain certain consciousness of intuitive geometry as early civilized humans in ancient Mesopotamia.

Erratum to “Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)” [Advances in Pure Mathematics 4 (2014), 494-497]

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

A Successful Mathematics Teacher

“What is a successful math teacher?”is only a question but the answer to this relatively simple question is the main purpose of this paper.Namely,I will mention teachers’roles and try to give the answer of question“What kind of a teacher do students like?”Cleary,it is much simpler to mention which characteristics a successful mathematics teacher must not have or use.In the end,I would like to address every“successful teacher”with some motivation words.

Music as Mathematics of Senses

It is often said that music has reached its supreme and highest level in the 18th and 19th centuries. One of the main reasons for this achievement seems to be the robust structure of compositions of music, somewhat remindful of robust structure of mathematics. One is reminded of the words of Goethe: Geometry is frozen music. Here, we may extend geometry to mathematics. For the Middle Age in Europe, there were seven main subjects in the universities or in higher education. They were grammar, logic and rhetoric—these three (tri) were regarded as more standard and called trivia (trivium), the origin of the word trivial. And the remaining four were arithmetic, geometry, astronomy and music—these four (quadrus) were regarded as more advanced subjects and were called quadrivia (quadrivium). Thus for Goethe, geometry and mathematics seem to be equivocal. G. Leibniz expresses more in detail in his letter to C. Goldbach in 1712 (April 17): Musica est exercitium arithmeticae occultum nescientis se numerari animi (Music is a hidden arithmetic exercise of the soul, which doesn’t know that it is counting). Or in other respects, J. Sylvester expresses more in detail: Music is mathematics of senses. Mathematics is music of reasons. Thus, the title arises. This paper is a sequel to [1] and examines mathematical structure of musical scales entailing their harmony on expanding and elaborating material in [2] [3] [4] [5], etc. In statistics, the strong law of large numbers is well-known which claims that This means that the relative frequency of occurrences of an event A tends to the true probability p of the occurrences of A with probability 1. In music, harmony is achieved according to Pythagoras’ law of small numbers, which claims that only the small integer multiples of the fundamental notes can create harmony and consonance. We shall also mention the law of cyclotomic numbers according to Coxeter, which elaborates Pythagoras’ law and suggests a connection with construction of n-gons by ruler and compass. In the case of natural scales (just intonation), musical notes appear in the form 2p3q5r (multiples of the basic note), where p∈Z,?q=-3, -2, -1, 0, 1, 2, 3 and r=-1, 0, 1. We shall give mathematical details of the structure of various scales.