Introduction to the Special Issue on Perspectivesand Experiences on Mentoring Undergraduate Students in Research: Part II

Abstract

This issue is the second of a special PRIMUS two-part issue collecting articles on undergraduate research from experienced faculty mentors. We offer it as a valuable resource for faculty leading undergraduate research programs. This issue presents a collection of papers offering advice on a variety of specific topics important for leaders of undergraduate research programs. Issues of finding and designing appropriate and accessible research projects, assessing undergraduate research, and publicizing it in the media are addressed.     

The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching,Instruction, and Student Achievement

In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during mathematics lessons. Specifically, it focused on helping teachers (a) learn more mathematics, (b) understand how children learn math, (c) use formative assessment to develop insight into what specific students know and do not know, and (d) develop effective classroom instructional strategies that enable student problem solving. Participants included 105 fourth- and fifth-grade teachers teaching in 19 low-income schools within a single district. Teachers were randomly assigned within schools either to a “business as usual” control group or to receive the professional development. The training consisted of a week-long summer institute and four to six in-service days during the school year. The training was run by full-time trained associates. We find some limited evidence of positive impacts on teachers' mathematical knowledge for teaching, but no effects on instructional practice or student outcomes.     

数学实验方法的历史脉络

本文从数学实验的实践出发,拨正对数学实验的误识,运用历史分析、逻辑分析和实证性研究的方法,指出数学实验可分为观察推演法、统计抽样检验法(包括蒙德卡罗方法、生物数学方法、运筹实验法)、模型数值计算和随机模拟法等三大类,并考察每类方法的发展历史和认识论特点。     

对<矩阵对角占优性的推广及应用>一文的注记

指出了《矩阵对角占优性的推广及应用》(《应用数学学报》1989年第12期)一文中的一个错误，给出了ID与M-矩阵类的关系，进一步讨论了矩阵的特征值分布，拓宽了该文及有关文献的结果。     

计算数学专业硕士研究生培养方案的分析与比较

尽管我国计算数学研究生教育事业已得到快速发展,但目前仍面临许多的问题和挑战。本文选取32所高校的计算数学专业硕士点作为代表,从培养目标、研究方向、学习年限、培养方式、课程体系、学位论文等方面对全国该硕士点的培养方案作总结、分析及比较,了解各硕士点培养方案的异同及特点,将有助于改革该硕士专业的培养模式,提高培养质量,适应社会经济发展。     

民族地区高等数学教学探索与实践

文章通过分析影响民族地区高等数学教学质量的制约因素,准确把握少数民族学生思维特点,从加强数学语言教学、构建和谐教学模式、激发学生学习兴趣等方面对提高民族地区高等数学的教学质量进行了探索与实践。     

Designing for communication at work: A case for technology-enhanced boundary objects

In this article we conceptualise the challenges of communication between a mortgage company and its customers in terms of crossing boundaries between communities. Through an ethnographic study we first address the question: what are the challenges of communication between sales agents and customers of a mortgage company around mathematical artefacts? Insight into these challenges formed the basis for an intervention in which we designed technology-enhanced boundary objects (TEBOs) that were reconfigurations of problematic symbolic artefacts. Secondly, we ask what the sales agents learned from the intervention. The data suggest that the intervention with the TEBOs helped employees to develop a better understanding of the mathematics behind the mortgages they sold, and to improve communication with their customers.     

Dealing with ‘fragile identities’: resistance and refiguring in women mathematics students

Many learners may be successful in mathematics but nevertheless see themselves as existing only on the margins of the practice, or as lacking stability in it – in this sense, they have what can be called a fragile identity. Although this kind of relationship with mathematics is not limited to girls and women, they do appear to express such fragile identities more often or more readily. Drawing on qualitative and quantitative data from undergraduates in three English universities, this paper presents an analysis of the way in which university mathematics is differentially experienced by men and women, and of the part this may play in women’s ongoing narratives of self as mathematicians. It is suggested that some women resist traditional positionings in the mathematics world, drawing on local resources which enable a sense of agency as successful students and a refiguring of their relationships with mathematics.     

数学优秀课成长的基础、过程与方法

以分数为目标、对教学内容理解表面化和教学设计无基本章法是造成课堂教学平庸、低效的主要原因,因此在关注优秀课的表现形式与评价标准的同时,更应关注优秀课成长的基础、过程与方法。超越应试是优秀课的基本要求与历史使命;理解数学是教学设计与优秀课成长的基础,而好的教学设计框架则是优秀课成长的过程与方法。     

我国目前数学活动经验研究综述

数学活动经验是近几年数学课程改革研究的热点话题之一。我国数学教育研究工作者和实践工作者对数学活动经验的研究,目前主要集中在数学活动经验的内涵、类型、主要作用和教育价值、促进学生积累数学活动经验的教学策略等方面。未来研究应该注重清楚简洁地界定数学活动经验及其所包含的内容,研究、实践使学生获得并积累数学活动经验的策略,在研究、实验的基础上提出数学活动、数学活动经验的基本要求,积极开展实证性研究和评价研究等。