Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking

While many engineering educators have proposed changes to theway that mathematics is taught to engineers, the focus has oftenbeen on mathematical content knowledge. Work from the mathematicseducation community suggests that it may be beneficial to considera broader notion of mathematics: mathematical thinking. Schoenfeldidentifies five aspects of mathematical thinking: the mathematicscontent knowledge we want engineering students to learn as wellas problem-solving strategies, use of resources, attitudes andpractices. If we further consider the social and material resourcesavailable to students and the mathematical practices studentsengage in, we have a more complete understanding of the breadthof mathematics and mathematical thinking necessary for engineeringpractice. This article further discusses each of these aspectsof mathematical thinking and offers examples of mathematicalthinking practices based in the authors' previous empiricalstudies of engineering students' and practitioners' uses ofmathematics. The article also offers insights to inform theteaching of mathematics to engineering students.     

Embodied Cognition and the Mathematical Emotional Orientation

The common image of mathematics is one of a solitary and unemotional activity. In contrast, this article views both emotions and social discourse as central to mathematical activity. What defines mathematics is a set of shared preferences that has been referred to as an emotional orientation. This article describes the key features of emotional orientations, their bodily bases, and their relation to language and social contexts. The concept of a mathematical emotional orientation provides an interpretive frame that is informative and useful for analyzing mathematical activity in educational research and practice.     

Embodied Cognition and the Mathematical Emotional Orientation

The common image of mathematics is one of a solitary and unemotional activity. In contrast, this article views both emotions and social discourse as central to mathematical activity. What defines mathematics is a set of shared preferences that has been referred to as an emotional orientation. This article describes the key features of emotional orientations, their bodily bases, and their relation to language and social contexts. The concept of a mathematical emotional orientation provides an interpretive frame that is informative and useful for analyzing mathematical activity in educational research and practice.     

新课标下高师数学分析教学实践与研究

主要论述了在高中新课标下,高师数学专业数学分析课程与高中数学的脱节问题,接着作者根据自身的教学经验和教学心得提出衔接的相应方法和教学手段,从而提高数学分析课程的教学效果和教学质量.     

数学建模是开启数学大门的金钥匙

作为大学《数学建模》课程的导言,对什么是数学建模,以及数学建模在推动数学学科发展及培养创新型人才方面的重要性,作充分的阐述.同时,针对数学建模的特点,对数学建模课程的教学,提出一些必要的建议.     

科学思维、科学方法在概率论与数理统计教学中的应用研究

根据我们的教学体会,讨论了在高等教育成为大众化教育的今天,在阐述科学思维、科学方法与数学思维、数学方法之间关系的基础上,如何在概率论与数理统计教学中培养大学生的科学思维和科学方法,并结合实例进行了探讨.     

Individual and Collective Mathematical Development: The Case of Statistical Data Analysis

In the first part of this article, I clarify how we analyze students' mathematical reasoning as acts of participation in the mathematical practices established by the classroom community. In doing so, I present episodes from a recently completed classroom teaching experiment that focused on statistics. Against the background of this analysis, I then broaden my focus in the final part of the article by developing the themes of change, diversity, and equity.     

OntoMathPRO: An Ontology of Mathematical Knowledge

Doklady Mathematics - The article describes OntoMathPRO, the first Linked Open Data ontology of professional mathematical knowledge. The ontology is designed to represent mathematical concepts. The...     

经济活动中的几个数学模型及其应用

随着市场经济的不断发展，利用数学知识解决实际问题变得越来越重要。本文重点探讨了经济活动中几个非常实用的数学模型的构建与应用问题。     

Decomposition in global optimization

The purpose of this article is to propose a simple framework for the various decomposition schemes in mathematical programming.Special instances are discussed. Particular attention is devoted to the general mathematical programming problem with two sets of variables. An economic interpretation in the context of hierarchical planning is done for the suggested decomposition procedure.The framework is based on general duality theory in mathematical programming and thus focussing on approaches leading to global optimality.     

悖论与数学基础问题(Ⅱ)

在本文中,主要讨论悖论定义问题,此外,还将对‘悖论的起源’、‘数学三次危机’和‘Zermelo解决悖论的方案’等内容作简要的综述和评论。至于Russell对悖论的解决方案与悖论成因等内容的讨论将在本文的续篇中给出。     

财经类院校数学建模的教学与实践

针对经济、管理类专业学生的特点 ,介绍了在财经类院校开展数学建模活动的意义、方法和步骤 ,总结了开展数学建模竞赛的经验 .     

The epistemic,the cognitive,the human: a commentary on the mathematical working space approach

ZDM – Mathematics Education - This article is a commentary on the mathematical working space (MWS) approach and draws on the articles contained in this ZDM issue. The article is divided into...     

How do we understand mathematical practices in non-mathematical fields? Reflections inspired by cases from 12th and 13th century China

Recent studies of the history of mathematics have shed light on the diversity of mathematical practices in the ancient world. In this article, I address this issue from two perspectives. First, I analyze different mathematical instruments used in different domains in 12^th and 13^th century China. Second, by analyzing how the text is related to the problems written down in the same period, I argue that there existed two categories of mathematical problems. As a result, I suggest that problems, textual procedures, and material operations should be considered together when regarding various mathematical practices in mathematical and non-mathematical fields.     

Collective Mathematical Understanding as Improvisation

This article explores the phenomenon of mathematical understanding, and offers a response to the question raised by Martin (2001) at the Annual Meeting of the Psychology of Mathematics Education Group (North American Chapter) about the possibility for and nature of collective mathematical understanding. In referring to collective mathematical understanding, we point to the kinds of learning and understanding we may see occurring when a group of learners work together on a piece of mathematics. We characterize the growth of collective mathematical understanding as a creative and emergent improvisational process and illustrate how this can be observed in action. In doing this, we demonstrate how a collective perspective on mathematical understanding can more fully explain its growth. We also discuss how considering the growth of mathematical understanding as a collective process has implications for classroom practice and in particular for the setting of mathematical tasks.     

Les Récréations Mathématiques d'Édouard Lucas: quelques éclairages

The article is devoted to Edouard Lucas's contribution to the development of mathematical recreations in the France of the post 1870 war period. Lucas's name is associated to four volumes of Récréations mathématiques published between 1882 and 1894 (the last two having been published posthumously) and to a posthumous volume L'Arithmétique amusante, which appeared in 1895. The author analyzes the context of reform of science education in relation to which mathematical recreations appeared as a means of attracting a wider public to scientific activities and inspiring young people to study science. The article brings to light how the milieu of new associations which took shape to promote science (Association Française pour l'Avancement des Sciences, Société Mathématique de France) allowed the constitution of social groups internationally connected and quite active in the promotion and development of mathematical recreations. Lastly, the article suggests that this type of mathematical activity allowed the cultivation of fields that at the time the French academic milieu perceived as marginal such as number theory and analysis situs as well as their applications.     

The sound of music and its link with mathematics

This article discusses a relatively unnoticed application ofmathematics by describing its connection with an aspect of music,in particular, the musical scales. Stemming from a problem foundin a Year 9 mathematics textbook commonly used in Singapore,the article illustrates the role of mathematics in musical scalesby first considering the frequency ratios of consecutive musicalnotes in the ‘just scale’ and secondly explaininghow an anomaly in the ‘just scale’ caused by theuneven frequency ratios is resolved with the help of mathematics,thereby leading to the development of the well-tempered scale.The article ends with an exploration of the frequency ratiosof consecutive musical notes in the well-tempered scale. Notonly does the article aim to broaden the teachers’ horizonswith such an introduction to the mathematical aspect of music,it also hopes to enrich their mathematical experiences as well.     

A locus for transnational exchanges: European mathematical journals for students and teachers, 1860s–1914

While there were a few mathematical journals aimed at teachers and students as early as the 1840s, it was only in the late 19th century that they became more numerous in Europe. This article is based on the analysis of a corpus of European mathematical journals published between the 1860s and World War I, selected in the first place because they were aimed at high school teachers and high school or/and first two years university students, which are often referred to as “intermediate journals”. All these journals had focused on the teaching of mathematics and, as such, they were shaped by the educational context of the country in which they were published. However, leafing through theses journals, one is struck by the fact that the mathematics they published was in fact highly commensurable, and can see that they were the locus of transnational exchanges on mathematical knowledge. This article shows that several aspects of “internationalisation” were in fact at stake in mathematical journals for students: making knowledge from elsewhere available and of publicizing to the whole world the mathematics produced in one country; making people from different countries collaborate. Finally, it focuses on the effects of transnational exchanges between journals for teachers and students: what was the mathematical knowledge that was circulated through them, and in what respect was it different from that published in other mathematical journals?