The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education

A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the “Jacob method” after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to “muscular activity” in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings, equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the “theory of embodied mathematics”, the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the “Jacob method” may be considered a historical example of didactical application of analogous ideas.     

Ernst Mach and the Epistemological Ideas Specific for Finnish Science Education

Where does Finnish science education come from? Where will it go? The following outside view reflects on relations, which Finns consider ??normal?? (and thus unrecognizable in introspection) in science education. But what is ??normal?? in Finnish culture cannot be considered ??normal?? for science education in other cultures, for example in Germany. The following article will trace the central ideas, which had a larger influence in the development of this difference. The question is, if and why the Finnish uniqueness in the philosophy of science education is empirically important. This puts Finnish science education into the perspective of a more general epistemological debate around Ernst Mach??s Erkenntnistheorie (a German term similar to the meaning of history and philosophy of science, though more general; literally translated ??cognition/knowledge theory??). From this perspective, an outlook will be given on open questions within the epistemology of Finnish science education. Following such questions could lead to the adaptation of the ??successful?? ideas in Finnish science education (indicated by empirical studies, such as the OECD PISA study) as well as the further development of the central ideas of Finnish science education.     

多媒体CAI对应用力学教学的影响

由于多媒体CAI具有人机交互、立即反馈、使知识的保持与记忆更加容易、便于充分发挥学生在教学中的主体作用等诸多优点 ,在《应用力学》的教学中应用 ,发挥了积极的影响作用 ,具有十分美好的发展前景     

Resettling the Thoughts of Ernst Mach and the Vienna Circle in Europe: The Cases of Finland and Germany

Although it is generally assumed that the thoughts of Ernst Mach and the scientific fields he influenced (in this case psychophysics and Gestalt psychology) emigrated from Europe during Second World War they apparently survived in Finland, influencing the Finnish education system. The following article evaluates this relationship and its implications from a historical and an empirical perspective. In empirical studies comparing the education systems of different countries, such as PISA, the Finns are in general regarded as being very successful with their school system. Does this apparent success have anything to do with a Machian influence? Our current research has so far revealed that the Finns have gone through an independent cultural development in two specific aspects: in the idea of the development of the individual personality (Snellman) and in a specific phenomenalism (developed primarily by Eino Kaila, in which Kaila was heavily influenced in this by Ernst Mach). The result can be regarded as a nation-wide “Experiment”, the empirical evaluation of which can be found partly in the statistics of the PISA Studies, especially the evaluation of Finland in relation to other countries.     

谈如何把握好建筑力学课教学中的“度”

教学适度是教师教学总体要求与特定情况具体结合的教学效果。本文着重谈了建筑力学这门课程在教学过程中如何把握适度,真正做到教师教学中突出主干、教好主干,学生学好主干、培育出知识主干。使知识转变为同学们自己的知识。     

材料力学试验教学改革之我见

目前的材料力学实验教学存在很多弊端,为适应社会经济发展对人才的需求,我们必须重视实验、实践教学,必须针对材料力学实验教学中存在的问题进行改革,以提高实验教学质量,培养学生的实践能力和提高学生综合素质.     

力学课程的启发式教学

力学是工科专业较为难教、难学的课程,为了更好地搞好力学教学,本文根据力学教学的特点,从多个不同的角度,对力学课程的启发式教学的方式和方法进行论述。     

《建筑力学》教学必须立足“双基”注重“两法”

学生掌握《建筑力学》基础理论和普通的计算 ,能为学习其他专业技术课打下良好的基础。而要搞好《建筑力学》的教学 ,必须立足“双基”,注重“两法”(教师的教法与学生的学法 )     

习题课在工程力学教学中的应用

习题课是工程力学教学中不可缺少的一种授课形式,通过练习和问答,巩固和拓宽知识面,增强解题能力,本文总结了一套上好工程力学习题课的方法。     

浅析机械基础教学中抽象与具体的转化

抽象和具体是对立的,教学中将概念与实际结合起来,使抽象变具体,通过实例理解概念,可收到良好的教学效果。     

The History of Teaching Quantum Mechanics in Greece

In this work, our goal is to examine the attitude of the Greek scientific community towards Quantum Mechanics and establish the history of teaching of this theory in Greece. We have examined Physics textbooks written by professors of the University of Athens, as well as records of public speeches, university yearbooks from 1923 to 1970, articles in popular scientific magazines, political and philosophical publications and lemmas of encyclopedias that were influencing the public at the time. Our research shows that Quantum Mechanics in Greece was involved in the debate between the political left and right and the church organizations of the period, leading to an extremely idealistic misinterpretation of the theory. As a result, Quantum Mechanics was late to establish itself in Greece, with the first structured and autonomous course on Quantum Mechanics appearing as late as 1962.     

力学史知识在材料力学教学中的结合与实践

材料力学课程涉及力学人物、力学原理发展、工程应用历史等诸多力学史知识。如何有效地将这些力学史知识融入到课程教学中是目前材料力学课程教学的一个主要研究内容。本文针对材料力学的课程特点,对力学史在课程教学中的结合模式进行了有益的探索和实践,丰富了材料力学的课堂教学内容,增强了学生的学习兴趣,培养了学生的人文素质,激发了学生探索新知识的激情和创新意识。     

理论力学教学改革的实践与探索

理论力学的教学目标是发展学生的科学素养。通过优化教学内容、改进教学方法、加强科学方法教育、实施人文教育等措施进行教学改革。     

工程力学专业的教学发展研究

针对工程力学专业的教学和培养,通过调研比较了国内外著名高校工程力学专业的培养目标、教学体系和课程体系.以美国高校为主要研究对象,总结了其在培养学生理论与实践相结合方面成功经验,对国内工程力学专业培养提出了改进建议.     

启发式教学在土力学课程教学中的具体应用

土力学课程有较强的理论性和实践性,涉及概念众多,比较难学。启发式教学是高校研究性教学中的一种方法,注重引导学生主动、积极地掌握知识。本文选取土的形成、土的变形和土的强度三个知识点,具体阐述了启发式教学模式在土力学课程教学过程中的应用。     

《力学》课程课堂教学改革的实践

高等教育是社会培养人才的重要方式,高校课堂教学直接影响到人才的培养。目前课堂教学中存在许多的问题,进行课程课堂教学改革尝试是一种必然。课堂教学作为一种最为常用的教学形式,关键在于教师的教和学生的学之间的关系。抓住了课堂教学,也就抓住了教和学的根本。本文介绍了中国计量大学院理学院为了提高课堂教学质量,努力做到因材施教,在应用物理系基础课《力学》课程进行课堂教学改革的尝试,阐述阶段性的成果,分析其存在的不足,为后续继续进行课程课堂教学改革提供了一种思路。     

力学实验教学改革实践

本回顾了力学和机械工程系力学实验课程教学改革的历程,其中着重介绍了高水平大学建设的成果与特色,并对教学课程改革过程中存在的问题进行了探讨。     

对材料力学教学改革的研究

面向未来,以素质教育为目的,针对我校材料力学的教学现状,从教学次序的优化调整、教学方法和手段的改进、以及实验内容的更新三个方面,进行了材料力学的教学改革探索,提出了联系工程实践的改革措施,对提高学生的分析能力、培养学生的动手能力和解决工程实际问题的能力具有一定的启发意义和引导作用。     

MATLAB在理论力学教学现代化中的应用

基于MATLAB的数值计算,结合图形处理,以某摆动系统为例,得到需要的物理量变化规律和摆动轨迹曲线,以此说明现代化理论力学教学中引入MATLAB的可行性,及MATLAB在理论力学教学现代化和提高教学效果中的重要作用。     

在力学教学中学生创造性思维的培养

知识经济已初见端倪,人的素质发生了急剧的变化。高等职业教育应注重培养和锻炼学生的创造思维。因此,我们应丛改革教学方法和内容出发,采用启发式教学,引导学生掌握归纳法、求同求异思维、聚合和发散等多种思维方法,从而培养学生的创造性思维和解决问题的能力。