Aims and Objectives in the Teaching of Mathematics to non‐Mathematicians∗

After a discussion on what is a non‐mathematician and what is an applied mathematician, aims that have been variously suggested are presented and discussed. Attention is drawn to the importance of an understanding of model building and of mathematics as the language of science, and this leads to a plea for co‐operation between the mathematician and the non‐mathematician. Reference is made to the relevance of the ‘New Mathematics’ and to the demand for mathematical rigour, and the paper closes with a brief discussion of the importance of detailed objectives.

     

Didactics of mathematics as a scientific discipline: A sketch of its development from a personal (autobiographic) point of view

At the 8th International Congress on Mathematical Education (ICME-8) held in Sevilla, Spain, July 1996, Working Group 25 was devoted to the theme “Didactics of Mathematics as a Scientific Discipline”. The proceedings of this activity have been published by Nicolina A. Malara (s. footnote 1). The plenary talk given by the author on “Basic Characteristics and Recent Trends in the Development of Didactics of Mathematics as a Scientific Discipline” as well as the round-table discussion under his chairmanship are documented in the proceedings. Furthermore the author has contributed to the proceedings an autobiographicly oriented paper which goes back to his own time as a schoolboy and refers to his professional development in connections with various national and international institutions and movements. The present slightly extended reproduction of that contribution is mediating aspects of developmental dynamics which can hardly be grasped by highly objectified presentations. As for a similar paper see H. G. Steiner: “Some notable anniversaries and some personal German-Italian memories in didactis of mathematics ZDM 26 (1994), 211–214; also in Italian: L’insegnamento della matematica e delle scienze integrate (Numero Speziale), vol. 5 N.17A-17B, Sept.–Oct. 1994, 425–437.     

‘Experimental pedagogy’ in Germany,elaborated for mathematics – a case study in searching the roots of PME

PME, the International Group for the Psychology of Mathematics Education, was founded in 1976, at the Third International Congress on Mathematical Education in Karlsruhe, organised by the International Commission on Mathematics Instruction (ICMI). While PME is thus beyond coming of age and is reflecting its further orientation – due to the present “social turn” – the origins of investigating psychological aspects of mathematics learning have not yet been systematically studied. I am undertaking here a first such approach, concentrating on Germany, where the first pertinent monographs were published in 1913 and 1916. Different endeavours, focussing in particular on the notion of error, merged into the characteristic approach of ‘experimental pedagogy’. Given the key function of ICMI for founding PME, an additional aspect is whether the forerunner of ICMI: the Internationale Mathematische Unterrichtskommission (IMUK), founded in 1908, had an impact upon promoting research into the psychology of mathematics education. The pertinent research was effected by psychology; doing research themselves was still outside the horizon of mathematics educators. Perspectives of future research, in particular comparative ones, are outlined.     

The Development of an Instrument to Measure Preservice Teachers' Attitudes about Discourse in the Mathematics Classroom

This study explored the themes that comprise preservice teachers' attitudes regarding discourse in the K‐12 mathematics classroom. The initial development of the theory underlying preservice teachers' attitudes regarding mathematical discourse is documented through the development of a 5‐point Likert instrument. Analysis of the Preservice Teachers' Attitudes About Discourse in the Mathematics Classroom (PADM) Instrument (N – 277) resulted in three reliable factors: Promoting Mathematical Reasoning (α₁= .85), Examining Complex Mathematical Concepts (α₂= .81), and Valuing Students' Mathematical Ideas (α₃= .85). These results suggest a framework that mathematics educators can employ to address preservice teachers' attitudes regarding discourse in an effort to support their implementation of reform‐based discourse in the teaching of mathematics in their future classrooms.     

概率统计的多元化教学探讨

概率统计是一门具有独特思想方法的数学学科,我们在传统的理论教学基础上,以概率思想教育为主线,加强实践环节的教学和实际操作,注重提升学生在数学文化层面上的认识.从教学情况来看,收到了较好的教学效果.     

The Edinburgh Mathematical Laboratory and Edmund Taylor Whittaker's role in the early development of numerical analysis in Britain

In 1912, Edmund Taylor Whittaker (1873–1956) was appointed to the Chair of Mathematics at the University of Edinburgh. The following year he opened the Edinburgh Mathematical Laboratory. The purpose of the Laboratory was practical instruction in topics which are now classed together as numerical analysis.In this article I explore the inspiration, purpose, and impact of the Laboratory in the context of early 20th century British applied mathematics.     

经济数学教学改革研究——从问题开放到思维开放

在经济数学教学中适当的引进数学开放题,可以引导学生运用多种思维方式解决问题,促进学生的思维开放,本文以《概率统计》为例,通过具体实例的构建将开放题引入经济数学教学中,以求通过问题的开放培养学生的开放思维。     

The origins of mathematics education research in the UK: a tribute to Brian Griffiths

The meeting of the British Society for Research into Learning Mathematics held at the University of Southampton on 21st June 2008 was dedicated to the memory of Brian Griffiths, who had died earlier that month. At the meeting it was suggested that I write a paper tracing the development of research in mathematics education in the UK up to the writing of Mathematics: Society and Curricula, a book that Brian and I co-authored, published in 1974. This paper is dedicated to Brian's memory: I hope that it will be considered a fitting tribute to a great friend and colleague, and to an outstanding mathematician and mathematics educator.     

有限离散时间金融市场模型

本文希望有助于数学（特别是概率方向的）工作者理解在进入数理金融领域时可能会遇到的概念和问题。为此,我们选取最简单的数学模型－有限离散时间金融市场模型。讨论该模型可以减少数学上的困难,从而注意金融背景,这也是数学工作者比较陌生和更为需要的。     

Exploring MLD in mathematics education: Ten years of research

Mathematical learning disabilities or difficulties (MLD) are an increasing source of educational inequalities. This article explores research about MLD in Mathematics Education over the past ten years. The methodology focuses on specific, validated keywords. These keywords are used to identify articles in leading journals in mathematics education. Our work makes several new contributions to the field of mathematics education, notably: a reusable methodology and keywords for a literature review; an exhaustive list of articles about MLD in leading mathematics education journals; a discussion of the definitions and features of MLD used in these articles; and a tool to classify research dealing with MLD (categories that characterize students with MLD). We also highlight some unexplored dimensions regarding MLD in Mathematics Education research.     

Pure mathematics applied in early twentieth-century America: The case of T.H. Gronwall,consulting mathematician

Thomas Hakon Gronwall (1877–1932) was a Swedish-American mathematician with a broad range of interests in mathematical analysis, physics, and engineering. Though he was primarly known for his results in pure mathematics, his career as a “consulting mathematician” in America from 1912 to his death in 1932 provides a backdrop against which one can discuss contemporary issues involved in the increasing application of mathematics to engineering, industrial, and scientific problems. This paper attempts a summary of his major mathematical contributions to industrial, governmental, and academic institutions while relating his often difficult life during these years.     

Mathematical working space and paradigms as an analysis tool for the teaching and learning of analysis

ZDM – Mathematics Education - Mathematical working space (MWS) is a model that is used in research in mathematics education, particularly in the field of geometry. Some MWS elements are...     

Some Thoughts on Mathematical Education

This paper explores the growth of mathematical studies in recent times and suggests future patterns that may occur in mathematical curricula. It is proposed that courses in the History and Methods of Mathematics, Mathematical Engineering (rather than Engineering Mathematics) and Mathematics and Education should be used to widen the curriculum choices for the mathematical student of the future. Finally, in illustrating the application of mathematics to the study of Noise and Vibration it is shown that, in such an investigation, mathematics cannot be an end in itself but can be greatly helped by a knowledge of other physical disciplines.

     

Jack Howlett, 1912-1999

Dr Jack Howlett, who died on 5 May 1999 at the age of 86, aFounder Fellow of the Institute of Mathematics and its Applications,was a mathematician with a special interest in numerical analysiswho early recognised the power of computing methods and whostrongly influenced the development of some mechanical computingmachines and electronic computers as we know them today. Thewidespread advance of the use of computer models in all scientificdisciplines was made possible thanks to the efforts of a smallnumber of mathematicians who laid the foundations of modernnumerical analysis during the late 1930s to early 1960s, a periodwhich covered the greater part of Jack's working life and inwhich he was a star player.     

Paradox,programming, and learning probability: A case study in a connected mathematics framework

Formal methods abound in the teaching of probability and statistics. In the Connected Probability project, we explore ways for learners to develop their intuitive conceptions of core probabilistic concepts. This article presents a case study of a learner engaged with a probability paradox. Through engaging with this paradoxical problem, she develops stronger intuitions about notions of randomness and distribution and the connections between them. The case illustrates a Connected Mathematics approach: that primary obstacles to learning probability are conceptual and epistemological; that engagement with paradox can be a powerful means of motivating learners to overcome these obstacles; that overcoming these obstacles involves learners making mathematics—not learning a “received” mathematics and that, through programming computational models, learners can more powerfully express and refine their mathematical understandings.     

The emergence of women on the international stage of mathematics education

In this article, I consider the history of the International Commission on Mathematical Instruction (ICMI) from its inception until the International Congress on Mathematical Education (ICME) held in 1969. In this period, mathematics education developed as a scientific discipline. My aim is to study the presence and the contribution of women (if any) in this development. ICMI was founded in 1908, but my history starts before then, at the end of the nineteenth century, when the process of internationalization of mathematics began, thanks to the first International Congress of Mathematicians. Already in those years, the need for internationalizing the debate on mathematics teaching was spreading throughout the mathematical community. I use as my main sources of information the didactics sections in the proceedings of the International Congresses of Mathematicians and the proceedings of the first ICME. The data collected are complemented with information from the editorial board of two journals that for different reasons are linked to ICMI: L’Enseignement Mathématique and Educational Studies in Mathematics. In particular, as a result of my analyses, I have identified four women who may be considered as pioneer women in mathematics education. Some biographical notes on their professional life are included in the paper.     

The origins and history of the fields medal

The Fields Medal is the most distinguished unternational award in mathematics. John Charles Fields felt strongly the lack of a Novel Prize in mathematics. He was also disturbed, as Chairman of the Committee of the 1924 International Mathematical Congress, by the scars left from the Versailles Treaty which marred the international character of the Congress. This paper traces the evolution of the award from incidents in Fields' background, through its formal inception at meetings of the University of Toronto Committee fir the 1924 Congress, to its eventual establishment and the first awards at the Oslo International Congress in 1936. Included are a list of all Fields Medal winners to date, the text of Fields' proposal for the establishment of the award, and relevant excerpts from minutes of the Toronto Committee, and a photograph of the medal.     

数学科教博览专栏(ICIAM2015)

<正>The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists and entrepreneurs from around the world will gather in Beijing,China for the 8th ICIAM to be held at China National Convention Center inside the Beijing Olympic Green.     

Logic and Religion

We first start by describing the happening of the 1st World Congress on Logic and Religion. We then explain the motivation for developing the interaction between logic and religion. In a third part we discuss some papers presented at this event published in the present special issue.