小波方法及其力学应用研究进展

小波理论在进行信号处理与函数逼近时体现出非常独特的时频局部性与多分辨分析能力,小波基函数则可兼具正交性、紧支性、低通滤波与插值性等优良的数学性质,这均使得小波分析理论在计算数学与计算力学领域具有很大的应用潜力,也进一步为这些领域的突破性发展带来了新的契机.自20世纪90年代以来,大量的研究已经证明,基于小波理论的数值方...     

The role of applications within the reviewing service zbMATH

Zentralblatt MATH (zbMATH) is the world's most comprehensive and longest-running abstracting and reviewing service in pure and applied mathematics. The database contains more than 3.6 million bibliographic entries, starting from the 18th century. The presentation during the DMV/GAMM meeting gave a short introduction to the search engine with emphasis on selected fields of applied mathematics. This is a shortened version of the talk without details about the database itself. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A comprehensive theory of representation for mathematics education

Representation is a difficult concept. Behaviorists wanted to get rid of it; many researchers prefer other terms like “conception” or “reasoning” or even “encoding;” and many cognitive science resarchers have tried to avoid the problem by reducing thinking to production rules.There are at least two simple and naive reasons for considering representation as an important subject for scientific study. The first one is that we all experience representation as a stream of internal images, gestures and words. The second one is that the words and symbols we use to communicate do not refer directly to reality but to represented entities: objects, properties, relationships, processes, actions, and constructs, about which there is no automatic agreement between two persons. It is the purpose of this paper to analyse this problem, and to try to connect it with an original analysis of the role of action in representation. The issue is important for mathematics education and even for the epistemology of mathematics, as mathematical concepts have their first roots in the action on, and in the representation of, the physical and social world; even though there may be a great distance today between that pragmatical and empirical source, and the sophisticated concepts of contemporary mathematics.     

Trends in researching the socioeconomic influences on mathematical achievement

We introduce the topic of socioeconomic influences on mathematical achievement through an overview of existing research reports and articles. International trends in the way the topic has emerged and become increasingly important in the international field of mathematics education research are outlined. From this review, there is a discussion about what appears to be neglected in previous work in this area and how the papers in this issue of ZDM provide information about some of these neglected areas. The main argument in this article is that socioeconomic influences on mathematical achievement should not be considered as a taken-for-granted fact that is accepted uncritically. Instead, it is suggested that the relationship between multiple socioeconomic influences and various understandings of mathematical achievement are historically contingent ways of understanding exclusions and inclusions in mathematics education practices. Research is not simply “evidencing” the facts of these relationships; research is also implicated in constructing the ways in which we think about these. Thus, mathematics education researchers could devise more nuanced approaches for understanding the social, political and historical constitution of these relationships.     

Design,Concepts, and State of the Art of the swMATH Service

In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context.     

Researching how professional mathematicians construct new mathematical definitions: a case study

In this work, we study the mathematical practice of defining by mathematics researchers. Since research is an important part of many professional mathematicians, understanding how they do research is a necessary step before thinking about future researchers’ undergraduate and postgraduate education. We focus on the defining process associated with the generalization of existing definitions as a way of constructing new ones. Data of this qualitative study come from a case study whose subject is a mathematics researcher in the area of differential geometry. We have interviewed this researcher and collected her research documents. From our analysis of the data, we have identified four phases in the defining process (Finding an opportunity to generalize an existing concept, Proposing a new definition, Justifying that the new definition is valid and Continuing the chain of definitions), which we will describe in detail in Section 4.     

Language and communication in mathematics education: an overview of research in the field

Within the field of mathematics education, the central role language plays in the learning, teaching, and doing of mathematics is increasingly recognised, but there is not agreement about what this role (or these roles) might be or even about what the term ‘language’ itself encompasses. In this issue of ZDM, we have compiled a collection of scholarship on language in mathematics education research, representing a range of approaches to the topic. In this survey paper, we outline a categorisation of ways of conceiving of language and its relevance to mathematics education, the theoretical resources drawn upon to systematise these conceptions, and the methodological approaches employed by researchers. We identify four broad areas of concern in mathematics education that are addressed by language-oriented research: analysis of the development of students’ mathematical knowledge; understanding the shaping of mathematical activity; understanding processes of teaching and learning in relation to other social interactions; and multilingual contexts. A further area of concern that has not yet received substantial attention within mathematics education research is the development of the linguistic competencies and knowledge required for participation in mathematical practices. We also discuss methodological issues raised by the dominance of English within the international research community and suggest some implications for researchers, editors and publishers.     

Mathematics,manifest: a review of Mathematics: the Winton Gallery at the Science Museum

Mathematics: the Winton Gallery strives, like any exhibition concerning mathematics, to make meaningful contact between the abstruse realms of mathematics and the viewing audience. Unlike many other exhibitions, this is here accomplished by displaying a rich range of objects that demonstrate the essential role of mathematics in the world by emphasizing connections to the viewers’ existing cognitive environments. Through a focus on the ways that mathematical work affects and informs our human world, the exhibition succeeds in connecting a mathematical way of thinking with the lives of the viewing public in a complex and profound way, in exchange for their efforts and attention. While an approach which places the interweave of life and mathematics at its centre may invite worries about the representation of pure mathematics or whether such a strategy insulates the viewer from an understanding of ‘real’ mathematics, what this exhibition does is to offer a sense of the mind-set that underscores mathematical work. By revealing the implications of this mode of thought, the exhibition encourages the audience to understand their own lives and world in a more mathematically-oriented way, while also encouraging them to understand mathematics in terms of the ways their human world is already formed.     

Gender justice,human rights and measurement in the mathematics classroom

In line with international trends, the new South African mathematics curriculum implores mathematics educators to realize a pedagogy in their classrooms that is more practical, activity-oriented, and connected to their learners' lives. Drawing on data from a larger study that explores theory–practice relations in mathematics education, this paper shows how such progressive practices, when interpreted with respect to the teaching of measurement which required learners to use different measuring instruments for measuring the school grounds in learning about length and perimeter, were found to be deeply gendered. In two different contexts of an ‘African' township school and a predominantly ‘Indian' suburban school, girls in a grade 6 mathematics classroom faced direct sexism as they struggled to take the opportunity to participate in the activity and learn how to measure – an important mathematical competence and everyday knowledge and skill. The article analyses the data with reference to the human rights imperatives of the new national curricula and approaches to addressing disadvantage and discrimination for girls in mathematics classrooms.     

Mathematics professional development as design for boundary encounters

This theoretical paper examines a process for researchers and teachers to exchange knowledge. We use the concepts of communities of practice, boundary encounters, and boundary objects to conceptualize this process within mathematics professional development (MPD). We also use the ideas from design research to discuss how mathematics professional development researchers can make professional development the focus of their research. In particular, we examine the question: How can MPD be conceptualized and designed around research-based knowledge in ways that promote knowledge exchange about students’ mathematics and mathematics learning among researchers and teachers to improve the practices of both the research and the teaching communities? We propose that MPD is a premier space for researchers and teachers to exchange knowledge from their communities, impacting both researchers’ and teachers’ practices without reducing the importance of either.     

Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its availability in classrooms also provides opportunities for positive changes to teaching and learning. Very many examples are documented in the professional and research literature, and in this paper we organize them into 10 types. These are displayed in the form of a ‘pedagogical map’, which further classifies them according to whether the opportunity arises from new opportunities for the mathematical tasks used, change to interpersonal aspects of the classroom or change to the point of view on mathematics as a subject. The map can be used in teacher professional development to draw attention to possibilities for lessons or as a catalyst for professional discussion. For research on teaching, it can be used to map current practice, or to track professional growth. The intention of the map is to summarise the potential benefits of teaching with technology in a form that may be useful for both teachers and researchers.     

Visualisation and proof: a brief survey of philosophical perspectives

The contribution of visualisation to mathematics and to mathematics education raises a number of questions of an epistemological nature. This paper is a brief survey of the ways in which visualisation is discussed in the literature on the philosophy of mathematics. The survey is not exhaustive, but pays special attention to the ways in which visualisation is thought to be useful to some aspects of mathematical proof, in particular the ones connected with explanation and justification.     

A social perspective on technology-enhanced mathematical learning: from collaboration to performance

This paper documents both developments in the technologies used to promote learning mathematics and the influence on research of social theories of learning, through reference to the activities of the International Commission on Mathematical Instruction (ICMI), and argues that these changes provide opportunity for the reconceptualization of our understanding of mathematical learning. Firstly, changes in technology are traced from discipline-specific computer-based software through to Web 2.0-based learning tools. Secondly, the increasing influence of social theories of learning on mathematics education research is reviewed by examining the prevalence of papers and presentations, which acknowledge the role of social interaction in learning, at ICMI conferences over the past 20 years. Finally, it is argued that the confluence of these developments means that it is necessary to re-examine what it means to learn and do mathematics and proposes that it is now possible to view learning mathematics as an activity that is performed rather than passively acquired.     

Geometric dissections now swing and twist

Conclusion  With their visual and kinetic appeal, hinged dissections and their design techniques will continue to play a role in mathematical recreation and education. They also invite substantive research in mathematics and computer science. Hinges are the simplest of linkages, permitting only relative rotation between connected pieces; with hingeability we address issues of transformation of objects which have wider relevance. In addition to the problem of generality discussed briefly in the introduction, there is the search for algorithms: procedures for determining whether a given dissection is hingeable, and for finding effectively a plan of motion that carries the hinged pieces from one of the figures to the other.     

Mathematics education research, its nature, and its purpose: A discussion of Lester's paper

This commentary discusses the framework for mathematics education researchers outlined in Lester's (2005) paper. The author reacts to (a) Lester's concern about the current political forces in the U.S. to define scientific research in education rigidly, and offers a possible reason—apart from political ideology—for the emergence of hese forces; (b) recapitulates lester's outline and model for theory-based research in mathematics education, and intereprets Lester's paper as a call to the MER community to respond to the current political forces that (inappropriately) shape our field and (c) addresses the role of mathematical context in MER, a topic absent from the paper's narrative.     

The role of the researcher’s epistemology in mathematics education: an essay on the case of proof

Is there a shared meaning of “mathematical proof” among researchers in mathematics education? Almost all researchers may agree on a formal definition of mathematical proof. But beyond this minimal agreement, what is the state of our field? After three decades of activity in this area, being familiar with the most influential pieces of work, I realize that the sharing of keywords hides important differences in the understanding. These differences could be obstacles to scientific progress in this area, if they are not made explicit and addressed as such. In this essay I take a sample of research projects which have impacted the teaching and learning of mathematical proof, in order to describe where the gaps are. Then I suggest a possible scientific programme which aspires to strengthen the research practice in this domain. Eventually, I make the additional claim that this programme could hold for other areas of research in mathematics education.     

多传感器分布式检测和估计融合

随着科学和工业的发展,信息科学领域涌现出许多应用数学科学问题,这些问题的研究拓宽和加速了基础数学理论的研究.另一方面,基础数学理论的进展以及在信息科学领域的成功应用也促使了工业领域的蓬勃发展.数学与其他学科的相互渗透已成为当今应用数学的主要特点之一,如在2010年ICM(国际数学家大会)上有2个分别关于控制和图像科学的1小时大会报告、7个关于"Mathematical Aspects of Computer Science"的特邀报告和8个关于"Mathematics in Science and Technology"的特邀报告.多源信息融合是数学和信息科学结合的一个重要研究方向.本文主要考虑其中两类基本问题:多传感器检测融合和估计融合,主要创新点包括:(1)对一般传感器观测相关条件下的多传感器分布式检测融合系统,获得同时搜索最优传感器律和最优融合律的高效算法;(2)对失序观测、错误观测和异步观测多传感器分布式估计融合系统,给出统一的全航迹(不仅仅校正当前状态估计)全局最优估计融合公式和算法;(3)对有偏不确定系统估计融合提出极小化Euclid误差准则,并基于多传感器和多算法估计融合获得极小化Euclid误差的抗偏估计高效算法.     

国内外数学文献的产出分析——数学各分支上文献分布的比较研究

通过对国内外数学文献产出的统计分析,将国内外数学文献按各分支的分布状况做了量化描述,比较了国内外数学发展趋势的异同,以及各分支上研究人员的集中情况和产出情况,从而反映出我国数学研究工作的一些特点。