组合数学中链与反链的教学探索及实践

组合数学作为计算机科学的基础课程,在计算机领域有着重要地位。为了改进数学学科传统的定义、定理、证明的教学模式,以组合数学中链与反链的知识点为例,探索如何将数学类课程讲解得更加通俗易懂,并发掘数学与计算机学科的结合点,提升数学类课程的应用性。首先,用矩阵形象地解释链与反链长度与个数的关系,帮助学生更好地理解。然后,给出反链在计算机领域的一个应用实例及其应用前景。通过一“讲”二“应用”的教学方式,极大地调动了学生兴趣,加深了对知识的理解,从而成为数学教学过程中的一个经典案例,非常值得借鉴与推广。     

提高农村中学物理教师新课程实施能力策略

当前农村中学物理新课程实施现状不容乐观,许多教师缺乏把计算机技术和物理教学进行有效整合的知识和能力;只重视考试成绩,而忽视科学探究过程。要提高农村中学物理教师新课程实施能力,就必须转变观念,加强学习;加强合作以求优势互补;要改进实验,努力创新;开展评教,交流促进。     

Mathematics Teacher Educators' Perceptions and Use of Cognitive Research

Instructors (N = 204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain‐specific topics, and that they emphasize topics prominent in psychology studies of mathematical thinking in their courses. However, instructors reported seldom accessing this research through primary or secondary sources. A mediation analysis indicated that mathematics methods instructors' perception of the importance of the research predicts their incorporation of it in their courses, and that this relation is partially mediated by their accessing of it. Implications for psychologists who have an interest in education and recommendations for facilitating the use of cognitive research in teacher preparation are discussed.     

创设物理情境,改善数学教学效果

针对高职院校高等数学教学效果不佳的现状,以及数学与物理在发展过程中互相影响、互相促进的独特关系,通过实践教学案例发现,合理运用物理情境辅助数学教学,可以使得数学教学具体、生动和形象,进而达到启发学生实际应用和培养学生综合素质的教学目的。     

University Mathematics and Science Faculty Modeling Their Understanding of Reform Based Instruction in a Teacher Preparation Program: Voices of Faculty and Teacher Candidates

This study was conducted in a reform-based mathematics and science teacher education program in the USA, the Maryland Collaborative for Teacher Preparation(MCTP). The goal of the undergraduate program was to prepare upper elementary/middle level specialists in mathematics and science. One significant aspect of the MCTP was the expectation that the program's professors (in mathematics and science) would model a new vision of effective pedagogy based on reform-based recommendations. We determined, in general, that the program's mathematics and science content professors accepted the dual role of modeling effective instruction at the same time they were delivering content. However, this dual responsibility raised in their minds an ‘issue of appropriate balance’ between content and pedagogical foci in their courses. Previously, the professors' had not questioned a focus heavily tilted toward content coverage. We also determined that the program's teacher candidates believed that the mathematics and science professors modeled effective instruction. One of the primary reasons that the teacher candidates believed that their professors were modeling effective instruction was that the focus in the courses was primarily on conceptual understanding, not memorization. A major implication was that the professors' modeling of reform-based instruction prompted the teacher candidates to develop a new vision of mathematics and science teaching shaped by their professors' example.     

Faculty behavior in low-paradigm versus high-paradigm disciplines: A case study

The notion of academic disciplines being characterized as high- or low-paradigm technologies was developed by Lodahl and Gordon from Kuhn's concept of a paradigm. Using this concept, the voting pattern of high-paradigm faculty (chemistry, physics, mathematics, and engineering) was compared to low-paradigm faculty (sociology, political science, history, and education) concerning a controversial campus issue to liberalize curriculum choices for students. It was found that high-paradigm faculty were not willing to grant students more latitude to select courses for degree requirements, while low-paradigm faculty members were in favor of giving students more latitude to select academic courses for degree requirements. The unique aspect of this study is that faculty behavior, as described in an actual case study, corresponds to theoretical positions supported by questionnaire data.     

Who succeeds in advanced mathematics and science courses?

Few students (particularly few girls) currently choose to take their Final School Examination (FSE) in advanced mathematics, chemistry and physics, a combination of subjects that is the best preparation for a science‐oriented study in higher education. Are these subjects attainable by more students than is currently the case? This study examined 6033 students in upper secondary education, including 720 students who took their FSE in advanced mathematics, chemistry and physics. The results show that the latter group (and in particular the girls in that group) had higher scores on math ability than students who chose other examination subjects. Regression analyses demonstrated the relative importance of math ability and achievement motivation for attainment in these science subjects. However, an expected positive effect of homework time as well as possible mediating and moderating effects of the predictors could not be confirmed.     

Identifying potential “dropouts” from college physics classes

Hudson and Rottman (1981) established that mathematics ability is probably a secondary factor influencing dropout from college physics courses. Other factors remain to be found for predicting who will drop out or at least have difficulty with the course. When mathematics ability is coupled with general indicators of performance (total GPA and ACT natural science), prediction of performance for those who complete the course is substantially improved. Moreover, discriminant analyses reveal who will have at least some difficulty, but not who will drop out. The problem of isolating specific weaknesses of students who have difficulty persists. Physics achievement appears to depend on mathematics ability only to the extent that students possess the ability to utilize mathematics knowledge for solving physics problems. Identification of the specific aspects of this ability as well as the specific deficiencies leading to dropout should be the object of future research. For the present, interviews might be more revealing than group testing methods.     

Some Recent Developments in Teacher Education in Mathematics and Science: A Review and Commentary

Teacher preparation in science and mathematics will be best served, says the author of this roundup, by improvements both in the pedagogy and content of the undergraduate science and mathematics courses required of future teachers and in the reform of required science and mathematics methods courses. In a review of the history and politics of teacher education, the author underscores the twin goals of achieving program coherence and higher standards. She compares the place of mathematics education in mathematics departments with that of science education in science departments and recommends the replacement of bare bones methods courses with those combining pedagogy and content. Included is a selective bibliography.     

Students’ Overuse of Linearity: An Exploration in Physics

In mathematics education, a vast amount of research has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. However, also history of science provides several cases of thinkers who inadequately postulated linear relations to describe situations. This article focuses on secondary school students’ over-reliance on linearity in physics. Now and then, science educators report students’ tendency to assume and impose linear relations in physics, but—as far as we know—no substantial efforts were undertaken to study this phenomenon systematically. We conducted an empirical investigation aimed at identifying the competence of 8th- and 11th-graders—before and after being taught the relevant physical topics—to qualitatively grasp various situations in physics, as well as their tendency to quantify that qualitative insight linearly. The results provide an ambivalent picture of students’ overuse of linearity in physics: Although linear reasoning is sometimes used as a default strategy, even after instruction that addresses the relevant physical contents, this study also indicates that context is taken into account more often than is suggested by research on mathematical problem solving.     

大学科研队伍应当成为中国冲击诺贝尔科学奖的先锋队

中国在自然科学领域如数学、生命科学、化学、物理学等领域已经取得举世瞩目的成就,但是,与发达国家相比,中国在科学研究中仍然存在一些诸如急于求成和担心失败、过分强调研究条件、缺少合作等亟待解决的问题。中国科学家应当在正确研究方法指引下,通过不懈努力,在自然科学领域取得辉煌成就并获得诺贝尔科学奖。大学是优秀人才聚集的地方,为自然科学研究创造了一支活力较强、敢于创新的人才队伍,发挥着既是培养科学家的摇篮,又是科学研究主力军的作用。大学科学研究队伍应当成为中国冲击诺贝尔科学奖的先锋队。     

数学与数学教育观念探析

在科学技术日益推陈出新的今天,虽然数学的应用日益广泛和深入,但是其基础却日益脆弱,不断发现的悖论、逻辑困境和无尽的选择依然令人困惑和茫然。现代数学基本上是各自为政,对数学结论的各种质疑常见诸文字。数学教育工作应该通过对数学历史、数学观念的考察与分析,将其回归数学的本质属性。     

A sense of history: History of science and the teaching of introductory quantum theory

This paper argues that some kind of historical perspective is a conditio sine qua non in the teaching of physics. Without a proper historical perspective the student will not experience physics as the living, human endeavour it is; in addition, the historical-exemplaric approach is often beneficial also to the technical and conceptual aspects of physics education by offering a deeper and more critical look at particular physical problems. However, the relationship between physics and history of physics is intrinsically problematic in that the lessons to be learned from history are often counterproductive to those aimed at in science teaching. The tensions between the two approaches may lead to a historically unsatisfactory quasi-history adapted to the perceived needs of science education, but although this dilemma is genuine, there is no reason why it should block a historically oriented teaching of physics. Based on the example of the history of the photoelectric effect as a case in the teaching of introductory quantum theory it is argued that the dilemma between historical truth and didactic usefulness may be circumvented by focussing on a few, carefully selected case studies. The didactic potentials of one such example, the early introduction of the light-quantum, are discussed.Roskilde University Centre, P.O. Box 260, 4000 Roskilde, Denmark.     

Galileo and pendulum motion: A case for history and philosophy in the science classroom

There are encouraging signs that the history and philosophy of science are becoming more important in the teaching of science and in the preparation of science teachers. This tendency is supported here by looking at the widespread treatment of Galileo's account of pendulum motion in science texts and classrooms, indicating that it is a less than adequate account of the historical facts, and suggesting that the teaching of this commonplace topic can be considerably enhanced if science teachers have some familiarity with basic research in the history and philosophy of science.     

Gender,science choice and achievement: a Maltese perspective

Drawing on a number of studies, this paper explores gender differentials in the choice of science subjects at secondary school level, factors influencing choice, differences in achievement and recruitment to science courses at a higher level in the particular educational context of the Maltese Islands. In this context all secondary schools are single‐sex, the state system is highly centralized, selection and streaming are widely practised, a high proportion of students (25%) attend private schools, and physics is compulsory. The results show that: more girls than boys study physics and biology at the lower secondary level (ages 11‐16); more boys study chemistry; achievement at this level is on a par in biology and chemistry; girls achieve slightly lower in physics. At the upper secondary level (ages 16‐18), almost equal numbers of boys and girls study biology and chemistry but boys predominate in physics. Girls avoid the option of physics and mathematics, a popular choice with boys. Consequently, at tertiary level very few girls opt for courses in engineering and prefer to subscribe to courses relating to medicine.     

科学方法论的历史演变及其价值重估

不论在物理学、数学、还是在历史学、哲学领域,都有一批著名的科学家、思想家,他们把人类客观知识体系的建构看作是至高无上的历史使命,他们在摒弃个人主观臆断的同时,尽力把人类的理性思维与现实世界的客观规律结合起来,使科学成为一种有别于宗教、政治、伦理的知识体系,并形成了一种以客观精神为主旨的研究方法,特别是科学哲学的方法论建构,更体现出当代学术视阈从本体论、认识论到方法论的历史性转向。     

Physics and Mathematics as Interwoven Disciplines in Science Education

The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.     

高等数学知识在大学物理中的应用

数学是物理的基础,数学是研究物理学的工具,大学物理中所有的内容均广泛涉及到高等数学知识.可见,掌握相应的高等数学知识是学好大学物理的基础.     

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students’ problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.