Conceptual and procedural approaches to mathematics in the engineering curriculum: views of qualified engineers*

The research interest underpinning this paper concerns the type of mathematical knowledge engineering students may acquire during their specialised education in terms of the conceptual and procedural dimensions of doing and using mathematics. This study draws on interviews with 25 qualified engineers from South Africa and Sweden regarding their views on the role of mathematics in engineering education, with special focus on the conceptual and procedural aspects of mathematical knowledge. A thematic analysis of the interview data led to the identification of two main themes. According to the conceptual view a predominantly conceptual approach is needed and valued more than procedural skills, while the balanced view emphasises a balance of conceptual understanding and procedural fluency as well as links between them. It is suggested that the mathematical education of engineers would need to be more conceptually oriented to prepare for the demands at the workplace.     

‘Ours is not to reason why,just invert and multiply’: an insight into Irish prospective secondary teachers' conceptual understanding of the division of fractions

This paper reports on an investigation into the conceptual knowledge, through the domain of fraction division, of prospective secondary mathematics teachers in their final/fourth year of undergraduate initial teacher education. The aim of the study is to assess if levels of conceptual knowledge in this domain are sufficient in order for these prospective teachers to teach for understanding. Some impact of conceptual understanding on teaching approaches is also explored. The content of the teacher education program and its suitability for preparing prospective mathematics teachers is also considered. The results indicate that in spite of four years of mathematics teacher education, these prospective mathematics teachers hold a fragmented and limited conceptual understanding of dividing fractions. To address this issue and to ensure the effective implementation of Project Maths, it is argued that initial teacher education programs need to be revised to include an emphasis on school mathematics.     

对数学教育研究文化视角的若干透视

数学教育研究中的文化视角,超越了传统数学教育的认识局限性,但在透视数学教育问题的时候由于相关概念定位不当,某些相关研究出现了一些认识上的偏颇.从数学文化与后现代文化、数学史、传统文化之间复杂关系的重新梳理过程中,提出了数学的文化相关性与文化不相关性概念.对数学文化精神不恰当的认识定位、偏见和极端理解,将会对数学教育造成有害的影响.     

职教大改革背景下的高职数学文化教育

在职教大改革背景下,特别是随着"双高计划"的启动和高职本科层次办学持续深入,传统数学教育教学方式已很难满足高职教育质量发展的需求。为顺应改革和发展需要,切实提升数学基础课助推学生技能素质提升的内在育人作用,高职院校的数学教学,既要在第一课堂中进行教学渗透,更加注重数学文化理念、丰富数学教学内容、扩展数学文化教育方式,切实培养学生的数学应用意识和创新思维;也要重视二、三课堂的实践激发和价值引领,使学生既能在学习生活中提升数学文化素养,也可以在今后实际工作中潜移默化地运用数学知识解决问题。     

高职教育中的数学课程改革探索

数学有着自身的智力价值、文化价值和应用价值，高职教育下的数学课程同样有如此的价值。本文阐述了数学课程在高职教育下的作用以及对于高职数学教学进行改革的若干思路。     

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ABSTRACT— This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education.     

论课程形态的数学文化及其教育价值的实现

数学文化的研究越来越受到关注与重视.作为课程形态的数学文化有其独特的定义及特征.其教育价值包括科学方面的教育价值和人文方面的教育价值,其实现应从树立突出文化特征的数学观、数学课程观、数学教学观开始;同时,还要注意两个方面的问题:(1)要根据实际情况有计划、有步骤渐进式地推行数学的人文方面的教育;(2)不要全盘否定以往的数学教育的价值.     

数学文化在中学数学教育中的作用

数学文化是以数学科学体系为核心,以数学的思想、观念、精神、知识、方法、技术、理论、数学发展史等为主要内容的一个文化体系,在中学数学教育中有着重要作用。要实现数学素质教育,关键之一在于充分体现数学文化的本质,把数学文化理念贯穿于数学教育的全过程。     

基于数学文化观的高等数学教学模式研究

许多教育工作者对高等数学教学模式进行了大量的探索和研究。但对于高等数学教育人们只重视其工具性价值,而忽略了数学的文化教育价值;本研究就是要把高等数学教育提高到数学文化教育的层面,不仅重视数学知识的传授、数学技能的训练、数学能力的培养,而且使数学文化与数学教育相结合,最终目的是提高学生数学素养,为学生的终身学习和可持续发展奠定良好的基础。     

Quality Mathematics Instructional Practices Contributing to Student Achievements in Five High-Achieving Asian Education Systems: An Analysis Using TIMSS 2011 Data

Although teaching quality is seen as crucial in affecting students’ performance, what types of instructional practices constitute quality teaching remains a question. With the theoretical assumptions of conceptual and procedural mathematics teaching as a guide, this study examined the types of quality mathematics instructional practices that affect students’ mathematics learning across five high-performing Asian education systems using the Trends in International Mathematics and Science Study (TIMSS) 2011 dataset. It found that no combinations of the components of conceptual and procedural mathematics teaching practices exist consistently across the five education systems. Results from the study provide important implications for practitioners and policy makers regarding how to improve mathematics teaching and learning in these Asian education systems as well as elsewhere.     

高职院校数学教育研究

本文详细讨论了数学教育在数学教学中的重要作用,分析了数学教育的现状,提出了适于学生接受的教学方法,并在此基础上提出了加强数学史教育尤其是在数学教学中融入数学文化的几点改革建议。     

析数学文化及其教育性

分析了数学的文化含义及其对数学教育的影响，提出了从文化的角度审视和认识数学教育的必要性。     

浅析多元化数学的教育价值及其实现途径

数学史作为数学文化的重要载体,其教育价值是数学教育研究中的热点问题,在关注数学史成为数学教育结构中构成要件的同时,还应该重视数学史中多元化数学在当今文化教育中的价值。本文在介绍了数学史、数学文化和数学史中多元化数学的基础上,从理解多元文化、扩宽世界视野,探索不同思想方法与培养创造性思维的教育理念出发,对多元化数学的教育价值及实现途径进行了行之有效的探讨。     

关于数学文化的若干重要相关研究领域——兼论如何进一步开展数学教育的文化研究

数学文化研究打开了透视数学和数学教育的更为广阔的视角.数学与数学教育观、大众文化、民族与传统文化、数学的社会与历史研究、科学文化与人文文化,这些都是数学文化研究的重要相关领域,也是深入开展数学教育文化研究的突破口.     

Contents or ideology? A case study of mathematical teaching in North Korea

This article addresses mathematics education in one of the most closed countries in the world, North Korea. It is known that ideology permeates all aspects of life in North Korea, but how exactly do the ideological and substantive mathematical components interact in mathematics education there? What concrete form does this interaction take in actual everyday teaching practice? This article seeks to answer these questions based on interviews with former North Korean mathematics teachers and students who have found a refuge in South Korea. With their help, we attempt to analyze the everyday life of North Korean schools, by reconstructing their concrete features and the routines of North Korean mathematics education.     

中国数学文化发展与数学文化学构建

数学文化的研究与教学是中国数学教育最近二三十年内发展最快、普及最广的学科.在中国数学文化发展的历程中,相关数学家的数学方法论研究、数学文化史研究和数学教育改革与数学教育理论研究成为数学文化研究兴起的3个侧面.数学文化研究对研究者从文化传统层面重新审视西方数学,对中国数学史的研究和中国数学教育改革都产生了重要的影响."数学文化学"的构建应围绕数学文化研究范畴的界定、理论追求和方法论等方面.     

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.     

浅析多元化数学的教育价值及其实现途径

数学史作为数学文化的重要载体,其教育价值是数学教育研究中的热点问题,在关注数学史成为数学教育结构中构成要件的同时,还应该重视数学史中多元化数学在当今文化教育中的价值。本文在介绍了数学史、数学文化和数学史中多元化数学的基础上,从理解多元文化、扩宽世界视野,探索不同思想方法与培养创造性思维的教育理念出发,对多元化数学的教育价值及实现途径进行了行之有效的探讨。     

Didactics and History of Mathematics: Knowledge and Self-Knowledge

The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict between the commitments of mathematics education and history of mathematics. But that conclusion was far too peremptory. The present paper, by contrast, takes the position, relying in part on Saussurean semiotics, that the historian's and working mathematician's ways of knowing are complementary. Recognizing this fact, it is argued, brings us to a deeper understanding of ourselves as creatures that do mathematics. This understanding, which is a kind of mathematical self-knowledge, is then proposed as an alternative commitment for mathematics education. In light of that commitment, history of mathematics assumes an essential role in mathematics education both as a subject and as a mediator between the aforementioned ways of knowing.     

融入还是包容——关于《普通高中数学课程标准(实验)》中的“数学文化”的思考

基于数学文化研究的最新成果,重新对《普通高中数学课程标准(实验)》的数学文化及其设置进行考察,从中发现其数学文化内涵界定不清,其设置也存在问题,有待进一步商榷.基于此,试图由数学文化不同内涵的界定而提出数学文化设置的两种方案:第一,调整体现数学的文化价值的阐述;第二,调整数学文化的内容要求.