优化解题思路 提高解题能力

日常教学中,通常是通过解题来测试学生的数学水平的.因此,解题能力反映学生的数学水准和数学能力.笔者在多年的教学实践中体会到:解题教学中,让学生在挫折中优化思路,是提高解题能力的重要途径.现举例说明如下:     

数值分析双语教学的探讨

首先指出了数值分析双语教学的目的和意义.其次,分析了数值分析双语教学中存在的问题.最后,给出了数值分析双语教学的一些措施.     

高中数学如何进行有效教学反思

如何最大程度地提高高中数学教学的效率问题,是笔者在多年的教学实践中思考得最多的问题.在教学过程中进行反思,是提高教学效率最有效的途径,笔者在不断的探索过程中,总结出了一些应用到教学实践当中的反思的途径和方法,以下是笔者对此进行具体的阐释.     

两类计数问题的递推式算法

计数问题在奥数教学和竞赛中颇受青睐.在现行中数教材和课堂教学中,涉及计数问题的排列组合与概率统计等内容,既是教学的难点又是命题的重点之一.本文仅就两类难于处理的计数问题.采用递推式算法分述如下.     

高中数学课堂教学设计中教学目标的有效性初探

1问题的提出教学目标是我们数学教师进行教学设计时首先要考虑的问题,而且教学设计中的教学过程要依据教学目标确定框架,教学过程围绕框架而展开.教学目标作为教学过程的出发点和归宿,能最大限度地减少教学中的随意性和盲目性,提高课堂教学的针对性与有效性.可见,教学目标在教学设计中占有重     

课堂提问在大学数学教学中的意义

课堂提问是一种有效的教学组织形式,它既是重要的教学手段,又是完美的教学艺术.这篇文章以高等代数的教学为例,阐述了大学数学教学中课堂提问的重要意义.希望对年轻的教师能有所启迪和帮助.     

高等数学课程教学方法的优化及其案例

在高校公共数学课的教学中,优化教学方法是提高教学效果和教学质量的一条重要途径.提供了高等数学课程中运用讨论型、研究型教学方法的一些具体思路,并给出了在实际教学中的几则教学案例.教学实践表明,在高等数学教学中恰当地使用讨论型、研究型教学方法,可以有效促进学生创新思维的培养和综合素质的提升.     

初中数学探究性活动设计的基本思路

结合自己的教学实践,探索初中数学教学中探究性活动的设计思路.在实际教学过程中,要把握探究性活动中涵盖的数学思想、方法和策略,要重视探究性活动对学生身心发展的整体影响.本文围绕探究性活动的内容,通过一个探究性活动的课堂实例和习题拓展设计探究性活动,展开相关研究.     

高中数学中如何实施问题链教学

高中数学教学中,问题是教学的催化剂,通过问题的设计可以更好地实现教学目标,提升教学效率.因此,高中数学教学过程中实施问题链教学是非常必要的.本文中以“椭圆的离心率”为例对高中数学教学如何实施问题链教学进行说明,并给出了问题链设计的原则与策略.     

将数学实验的思想和方法融入大学数学教学

大学数学教学中应注重理论联系实际,注重数学思想和方法的讲授,强调应用案例中融入数学实验思想的新教学方法.改革课堂教学方法,探索新的教学模式,加强学生的实践性教学环节,培养学生的应用和创新能力.最后,本文给出了几个例子显示了数学实验与大学数学教学结合的效果.     

Fächerübergreifender und fächerverbindender Unterricht in der gymnasialen Lehrerausbildung in Baden-Württemberg

One example each is discussed of a project and a smaller teaching unit, in order to show the difference between these two forms of cross-curricular teaching. Several concrete lessons and project concepts are then presented and explained, which have been elaborated at teacher training seminars together with or by student teachers. The paper examines and points out the advantages of cross-curricular teaching as well as Problems involved. Advantages observed for instance are new approaches for motivation, or a wider range of opportunities to further development of social competences, whereas the Problems encountered had to do with materials acquisition and didactics, questions remaining open, uncertainty, organisational aspects, and design and preparation of tests.     

数学模型在教学效率评价中的应用

利用状态转移矩阵和效率度的概念建立一个了教学效率评价模型,给出了此模型的使用条件.说明了不同的使用条件对模型的影响,并通过对我校几位教师教学效率的分析,说明了此模型的有效性和实用性.     

On a research programme concerning the teaching and learning of linear algebra in the first-year of a French science university

The paper discusses the current approach to the teaching of linear algebra in the first year at a French science university and the main difficulties that students have with this material. A brief account is given of the first steps towards the design of a teaching experiment. From a joint didactical and historical survey a first hypothesis is drawn: epistemological specificity, the use of ‘meta-lever’, the use of changes of settings and points of view, and the importance of the concept of rank. The main aspects and objectives of the teaching design with which we experimented over a whole teaching semester for five years with around 200 students are presented. Finally, the type of evaluations that were set up and the difficulties encountered are explained. The conclusion deals with issues on the teaching and learning of linear algebra as well as issues on methodological and theoretical points in relation to the original didactical framework.     

A Three-Phase Simulation System Written in Pascal

A three-phase simulation system written in Pascal for use on microcomputers, minis and mainframes is presented. The advantages of the three-phase method are discussed, and the basis of the system explained. Although a traditional, textbook example is used to aid explanation and discussion, the system described in this paper has been used in real applications and in the teaching of simulation at Lancaster University and the London School of Economics. It also provides a basis for further research in simulation within both institutions.     

Derivative,maxima and minima in a graphical context

A deeper learning of the properties and applications of the derivative for the study of functions may be achieved when teachers present lessons within a highly graphic context, linking the geometric illustrations to formal proofs. Each concept is better understood and more easily retained when it is presented and explained visually using graphs. In this article, we explore the conditions of necessity or sufficiency of the criteria for determining the maxima and minima of a function. The implications for the teaching of derivatives and functions in undergraduate courses are discussed in light of our analysis of textbooks.     

Mathematics Teaching in Italy: A Cross-Cultural Video Analysis

This study investigates the cultural nature of teaching. It compares a sample of 39 videotaped Italian mathematics lessons to German, Japanese, and U.S. lessons videotaped in TIMSS. This study expands on earlier work that was based on a smaller sample; analysis is also extended to the nature of the mathematical content presented. The results confirm the existence of an Italian cultural pattern for mathematics teaching, whose features we outline here. Italian teachers prefer whole-class instruction to individual seatwork; they engage in teacher talk/demonstration to transmit information; and they often call on students to solve problems at the board before the rest of the class. Italian lessons are characterized by the inclusion of a large number of mathematical principles and properties. These are explained 50% of the time, and simply stated the rest of the time. This study adds yet another perspective from which mathematics teaching can be studied, and, by acknowledging the difficulty to change cultural practices, it offers practical implications for teacher learning.     

Revisiting the didactic triangle: from the particular to the general

The basic notion of a didactic triangle is explained with historical annotations on its origins and subsequent theorization in the literature. Instances of its application to classroom environments to demonstrate its representational capabilities are presented. Generalizations of the triangle are proposed that integrate the role of technology, the researcher in mathematics teaching developmental research, and mediating complexes in the student?Cteacher?Ccontent interfaces. Further, the use of the didactic triangle as a heuristic device is also discussed.     

Elementary theory of factoring trinomials with integer coefficients over the integers

An important component of intermediate and college algebra courses involves teaching students methods to factor a trinomial with integer coefficients over the integers. The aim of this article is to present a theoretical justification of that which is often taught, but really never explained as to why it works. The theory is presented, and a suggestion for an inquiry-based learning project is given.     

Knowing more than their students: Characterizing secondary science teachers’ subject matter knowledge

Despite agreement among teacher educators, scholars, and policymakers on the importance of teachers’ subject matter knowledge (SMK), existing models provide limited information about the nature of this foundational component of teacher knowledge. The common assumption is that teachers need to know more about the science subject matter than their students are expected to learn, but what and how much more is underspecified. In order to more characterize science teachers’ SMK, we present the science knowledge for teaching (SKT) model, which has been adapted from the mathematics education literature to apply to science education. The SKT model includes three domains: core content knowledge, specialized content knowledge, and linked content knowledge. We used this model to explore the SMK new secondary chemistry teachers in South Africa and the United States drew on when they explained the conservation of mass and analyzed a related teaching scenario, two important tasks of teaching. Findings indicated these new teachers drew on knowledge from all three SKT domains in order to engage in these tasks of teaching. This result suggests the potential of the SKT model to characterize the nature of science teachers’ SMK and thereby better inform teacher preparation and professional development programs.     

Mathematik als Grundlage beruflicher Kompetenz

A concept of teaching basic mathematical knowledge and skills related to the vocational training of master craftsmen in the field of electrical engineering and metal engineering is described. The provision of application-oriented mathematics is pointed out as an important basis of competence needed by master craftsmen in their professional surroundings. A framework for the development of training supporting materials for mathematics learning is explained on the basis of earlier experiences as well as on newer constructivitically oriented instructional approaches of educational psychology and in consideration of current professional guidelines and examination regulations of the Chambers of Industry and Commerce. These materials are developed into three CBT-units which are to be of fundamentally different design in order to enable learning on different levels using the material on the learners' own initiative. Active self-organization is offered to the course participants via the use of interactive multimedia-based presentations.