谈“教”数学发展出“聊”数学

“教、学、做合一”是陶行知先生重要的教育思想。数学教学方式关系到学生在课堂中能否更好地获取知识、得到能力的提升。在教学的过程中,如何不断学习、总结并创新教学方式是每个优秀教师必须思考的问题,从“教”数学发展出“聊”数学就是践行陶行知先生教育思想的一个表现。

“教学做合一”在高中数学教学中的实践

“做”数学的含义,怎样“做”数学:(一)教师变学生——“做”数学的前提;(二)教学生活化——“做”数学的关键;(三)思维创新性——“做”数学的目标。

现代小学数学实践教学研究与探讨

教材并不是培养当今社会所需人才的圣经、宝典。我们要从把教材内容从枯燥无味转化为富有情趣、把书本数学转化为生活数学、把学生由简单的操作工转化为知识的探究者、把计算方法统一化转化为计算方法多样化等几个方面对教材进行合理、灵活的利用,使自己成为教材的积极实践者和创建者!

Analysis of the Current Situation of Spoken Foreign Language Teaching and Learning in Ethnic Regions

With the enhancement of friendship between different nations, foreign language learning has become more and more important. In particular, spoken language is playing a vital role in foreign language learning and practice. In order to improve foreign language teaching and learning proficiency in ethnic regions, the author analyses the current situation of spoken foreign language teaching and learning in ethnic regions and suggests some ways to solve the existing problems.

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.

Strong Laws of Large Numbers for Weighted Sums of Ч-mixing Sequence

In this paper, strong laws of large numbers for weighted sums of ■-mixing sequence are investigated. Our results extend the corresponding results for negatively associated sequence to the case of ■-mixing sequence.

Fuzzy MP-filters Lattice on a Given FI-algebra

In this paper, the properties of fuzzy MP-filters are discussed by using methods of Domain theory in FI-algebras. It is proved that all fuzzy MP-filters of a given FI-algebra form a distributive algebraic lattice, particularly form a frame.

Complete Moment Convergence for Arrays of Rowwise Negatively Associated Random Variables

In this paper, the authors present some new results on complete moment convergence for arrays of rowwise negatively associated random variables. These results improve some previous known theorems.

On Reverses of the Blaschke-Santalo Inequality for Convex Bodies

Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty＇s conjecture for projection bodies, respectively.

Simplicities and Automorphisms of a Special Infinite Dimensional Lie Algebra

In this paper, a special infinite dimensional Lie algebra is studied. The infinite dimensional Lie algebra appears in the fields of conformal theory, mathematical physics, statistic mechanics and Hamilton operator. The infinite dimensional Lie algebras is pop ularized Virasoro-like Lie algebra. Isomorphisms, homomorphisms, ideals of the infinite dimensional Lie algebra are studied.

The Realistic Review on Elementary School Mathematics Teaching Reform

It is of benefit to the development of the elementary school quality-oriented mathematics education to deepen the elementary school mathematics classroom teaching reform and review the fruits of classroom teaching. In this paper, the author, with his own teaching practice, has summarized and reviewed the fruits of elementary school classroom teaching reform in four respects： 1） ＂integration of theory with practice＂ should be highlighted in this reform; 2） the classroom teaching should focus on the improvement of students＂ ＂mathematical thinking ability＂;3） mathematics classroom teaching should conform to the reality of our daily life; and 4） mathematics classroom teaching should help the students to build the ＂mathematical model thinking＂.

CPS Modeling of CNC Machine Tool Work Processes Using an Instruction-Domain Based Approach

Building cyber-physical system(CPS) models of machine tools is a key technology for intelligent manufacturing. The massive electronic data from a computer numerical control(CNC) system during the work processes of a CNC machine tool is the main source of the big data on which a CPS model is established. In this work-process model, a method based on instruction domain is applied to analyze the electronic big data, and a quantitative description of the numerical control(NC) processes is built according to the G code of the processes. Utilizing the instruction domain, a work-process CPS model is established on the basis of the accurate, real-time mapping of the manufacturing tasks, resources, and status of the CNC machine tool. Using such models, case studies are conducted on intelligent-machining applications, such as the optimization of NC processing parameters and the health assurance of CNC machine tools.

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.

Application of Case Teaching in Primary Mathematics Pedagogy Class in Normal University

Objective： Case Teaching Method used in Primary Mathematics Pedagogy course can highlight the characteristics of pedagogy course. This method can transform learning process from the passive one in the conventional classroom to an active one, so that classroom atmosphere will become active, inspiring students＇ interest in learning, and students would have the initiative to study. Meanwhile the Case Teaching Method also put forward higher requirements for teachers. This author does some analyses of the meaning of the case teaching method implementation methods and problems based on years of teaching experience. Detailed analyses can be shown as follow

Using Multiple Intelligences Approach in Designing Classroom Activities

In 1983, Horward Gardner, a professor of education at Harvard Universiy introduced the theory of Multiple Intelligence. This theory states that people have a unique blend of capabilities and skills （intelligences）. In the classroom context, it implies that students possess different kinds of minds and therefore learn, remember, perform, and understand in different ways. Based on the theory, Gardner challenged the previous practices that gauged intelligence using IQ test which focused more on the ability to use language and/or logic. According to him, the measurement of people＇s intelligence should not be limited to linguistic and logical-mathematical abilities only, but should also cover other abilities. In addition to language and logic, Gardner proposed six other intelligences, which in the past were known as aptitudes or interests, namely： Visual-Spatial Intelligence, Musical Intelligence, Bodily-Kinesthetic Intelligence, Intrapersonal Intelligence, Interpersonal Intelligence, and Naturalist Intelligence. As an English teacher, we often have to deal with the fact that our classes consist of students who posses different intelligences. To help the students reach their maximum learning potential, teacher needs to respect students＇ uniqueness and accommodate the variety of intelligences. This can be done by applying multiple intelligences approach in designing classroom activities.

Research on the integration of the mathematical culture into the mathematical teaching in universities

In the university education, the mathematical teaching is an important and indispensable part. And now the integration of the mathematical culture in the university teaching is the effective method to improve the timeliness of the teaching and the enthusiasm of the students, and it also can effectively alleviate the problem of the disconnection in the university mathematical teaching, with the successful implementation of the transition. The university mathematics has very high demands in the teaching contents, the teaching ideas and the teaching methods, so the reasonable integration of the mathematical culture into the university mathematics is very important. The mathematical culture in the teaching of college mathematics is discussed and analyzed in this paper.

Anti-control of Hopf Bifurcation in a Delayed Predator-prey Gompertz Model

A delayed predator-prey Gompertz model is investigated. The stability is analyzed. Anti-control of Hopf bifurcation for the model is presented. Numerical simulations are performed to confirm that the new feedback controller using time delay is efficient in creating Hopf bifurcation. Finally, main conclusions are included.

The Relations between Discrete Frames and Continuous Frames with Respect to （N, μ）

The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

ELT Professionals＇ Perceptions on Self-Image： A Comparison Between Gender

The study is conducted to examine the differences of gender perception among educators who are teaching in local higher learning institutions in Malaysia, in viewing their roles as the ＇~teacher＂. Several higher learning institutions were randomly targeted. Several researchers were involved in the data collection by means of using questionnaires in the survey over a period of several weeks. The questionnaires were used to fred out about their academic and professional backgrounds, requiring them to list their roles pertinent to their experiences in teaching, ranked them and provided the rationale behind the choices made. Twenty-five samples were collected to scrutinize the data by categorizing the information according to gender and teaching experiences and recording the frequencies of answers. From the study, it is found that regardless of gender and teaching experiences, most participants would consider themselves as ＂Provider of knowledge＂, followed by ＂N^r＂, especially those who are relatively new in teaching. There is also an indication that teacher＇s experiences and gender might affect their perception in mirroring themselves. A larger scale of study is needed in validating the findings of this study for it to be empirical, thus promoting in-depth investigations in viewing whether gender and cultural background may be vital factors that has profound effects towards their professionalism. It is hoped that future studies will shed some light to this rather controversial claims.

On Pseudo Small Injective Modules

The definition of principally pseudo injectivity motivates us to generalize tae notion of injectivity, noted SP pseudo injectivity. The aim of this paper is to investigate characterizations and properties of SP pseudo injective modules. Various results are devel- oped, many extending known results. As applications, we give some characterizations on Noetherian rings, QI rings, quasi-Frobenius rings.