NEWTON: An Interactive Environment for Exploring Mathematics

We have developed a unique computational environment for use in teaching introductory mathematics. Our system, calledNewton, runs on Macintosh computers and consists of a user-friendly interface to the symbolic mathematics package Maple, supplemented by an extensive library of our own Maple code. Formulas are easily constructed and modified, appearing like those in textbooks; multiple windows allow users to see and work with several formulas at once. Formulas, graphs, and text can be intermixed in collapsible sections on worksheets. Users do not interact with Maple directly and need know nothing of Maple's syntax and command structure. Mathematical operations are selected from menus, with the added bonus that this makes it possible to document solutions. Originally designed for use in conjunction with the two semester introductory calculus sequence, the system has been extended for multivariate and vector calculus, linear algebra, numerical analysis, and differential equations.     

Architecture for Mathematics: The School of Mathematics at Città Universitaria in Rome

One obvious aspect of the relationship between architecture and mathematics is the nature of the actual places designed by architects for the mathematical community. The School of Mathematics of the Città Universitaria was designed by Giò Ponti. Claudio Presta examines Ponti’s design to see how architecture can create an appropriate space for doing mathematics. What is the meaning, if there is one? What are the motives that drove the architect to create a building expressly for the School of Mathematics and not a simple/complex building in which the School could simply be housed? Ponti provides an answer by following the shape of the Greek theater for one part of the building, while the dimensions of the other part tend towards the Golden Section.     

Using the Unfamiliar to Problematize the Familiar: The Case of Mathematics Teacher In-Service Education

Abstract

Schoenfeld's theory of teaching (Schoenfeld, 1998 Schoenfeld, A. H. 1998. Toward a theory of teaching-in-context. Issues in Education, 4(1): 1–94. [Crossref] , [Google Scholar], 1999 Schoenfeld, A. H. 1999. Models of the teaching process. Journal of Mathematical Behavior, 18: 243–261.  [Google Scholar]) describes, explains, and predicts teacher practice and, more specifically, teachers’ decision-making processes, in terms of their knowledge, beliefs, and goals. On the basis of this theoretical model of the teaching process, we designed a workshop with the purpose of providing mathematics teachers with analytical tools with which to reflect upon their own practice. Two rounds of this workshop were implemented with teacher leaders and mathematics educators. Participants collectively watched videotapes of teaching practices that included examples of a range of teacher decisions and actions. The tapes served as stimuli for both spontaneous and guided conversations about teacher knowledge, goals, and beliefs. Initially, two main kinds of comments predominated: evaluative and research oriented. As the workshops progressed, a third and potentially more productive mode of analysis of teacher practices evolved. We briefly describe the design of the workshops, their implementation, and the main “watching modes” and comments. It appears that teachers and researchers can be induced to think about why other teachers (and perhaps themselves) make particular instructional moves, and that they can engage substantially with the roles of knowledge, goals and beliefs in shaping instructional choices.     

The Calculus of Relations as a Foundation for Mathematics

A variable-free, equational logic $\mathcal{L}^\timesA variable-free, equational logic based on the calculus of relations (a theory of binary relations developed by De Morgan, Peirce, and Schr?der during the period 1864–1895) is shown to provide an adequate framework for the development of all of mathematics. The expressive and deductive powers of are equivalent to those of a system of first-order logic with just three variables. Therefore, three-variable first-order logic also provides an adequate framework for mathematics. Finally, it is shown that a variant of may be viewed as a subsystem of sentential logic. Hence, there are subsystems of sentential logic that are adequate to the task of formalizing mathematics. This paper is an expanded version of a talk given by the author at the Special Session on Automated Reasoning in Mathematics and Logic, held March 8–10, 2002, at the Georgia Institute of Technology, during the Joint Southeastern Section MAA/Southeast Regional AMS Meeting. The session was organized by Johan G. F. Belinfante.     

Education Research as Analytic Claims: The Case of Mathematics

ABSTRACT

Despite widespread calls for evidence-based research in education, this strategy has heretofore generated a surprisingly small return on the related financial investment. Some scholars have suggested that the situation follows from a mismatch between education as an assumed field of study and applied empirical research methods. This article's analysis of evidence-based recommendations in mathematics education is based on a critique that evidence-based research recommendations for classroom practice simply advance analytic claims that are conceptually connected to the particular practice under investigation.     

IT相关专业离散数学教学研究（英文）

离散数学作为一个和连续数学不同的领域一直在IT中扮演重要角色。离散数学的教学被认为是IT教学中不可分割的部分。然而,由于各学校情况不同,面向IT学生的离散数学教学仍存在一些挑战。文章介绍一所美国大学针对IT专业本科生的不同背景和需求进行教学设计以满足教学目标,期望这些经验能对其他学校相关课程的设计有所帮助。     

3D 创客教育与高中信息技术教学融合探索

实施全面的新课改以后,我国的教育模式在不断发生改变。针对现在信息技术教学中存在的问题和固定的教 学模式的问题,3D创客教育与高中信息技术教学相融合的教学方法开始流行起来。通过以往的教学经验,结合学生的学习特 点,为学生打造一个个性化的多元化教学课堂。3D创客教育的提出,对高中信息技术教学具有一定的指导意义。     

Mathematica软件在中学数学教学中的应用实践

在不断强调提高学生素质，拓广学生知识面，加强学生实践能力的课程改革过程中，现代教育技术与数学教学的整合引起了不少从事数学教育工作者的研究兴趣。随着数学软件的成熟，使得计算机技术与数学教学结合更加密切。     

土壤中重金属污染源辨识的数学模型

建立了基于坐标旋转下高斯分布函数的土壤表层重金属污染物点源扩散模型,并利用MATLAB中的非线性极小拟合方法得到模型参数,进而求得污染源的具体位置。以2011年高教社杯全国大学生数学建模竞赛A题数据为例,计算结果表明,旋转后的高斯分布函数拟合精度显著提高,从而为准确探究污染源及位置提供了新的途径。     

数学教育中的多媒体计算机网络

多媒体计算机的出现,给教育教学带来了无限生机。计算机辅助教学已成为当今教学改革的核心。多媒体计算机辅助数学教学,有助于突破教学难点,使教学形式多样化,进而提高教学效益。计算机辅助数学教学中应处理好人机和谐关系、媒体互促关系和主导与主体的关系。     

对高校服装设计专业教育教学的反思

由于受到"艺术至上论"和"技术至上论"两种不良教学思想的影响,使得我国高校服装设计教育出现毕业学生综合素质较差,学生知识结构单一,设计思路狭窄,与社会实际需求脱节现象严重等等弊端,我们要不断深刻反思,加以改进。     

A Study of Voice-Recognition Software as a Tool for Teacher Response

Voice-recognition technology (VRT) promises ease of use in responding to student writing, but its impact on writing processes and the quality of teacher commentary is unclear. This article details the results of a study undertaken to evaluate the effectiveness of VRT in responding to student writing. Over the course of two semesters, in response to texts written by students in his first-year college composition course, one of the authors composed 58 end comments, alternating between two methods of composition: typing on a keyboard and dictating directly into text by means of VRT. While his writing processes in the respective modalities differed dramatically, particularly in terms of revision, the quality of the resulting texts appeared roughly the same: A detailed content analysis of the comments, using Richard Straub and Ronald Lunsford's (1995) typology, revealed significant variation in only 1 of 25 variables, measured as a proportion of total words. Meanwhile, students surveyed indicated they found few differences between the typed and dictated comments in terms of their usefulness, clarity, and tone. These findings, along with a comparison of time on task and user impressions of the two modalities, indicate that VRT represented a valuable tool for producing end comments that the user was able to dictate fluently, but that the technology was ineffective for the limited editing and revising attempted within the design of the study.     

浅谈多媒体技术在高中数学教学中的运用

随着信息技术的不断发展,运用多媒体技术进行教学当前已经比较普遍.文章分析了高中数学学科的特点以及在高中数学学科中运用多媒体技术进行教学的作用并简要分析了运用这项技术获得好的教学效果的途径.     

西部高校艺术设计专业特色办学的思考

西部高校艺术设计专业办学应该转变传统的效仿观念,从地域文化、发展空间、发展机遇三方面所具有的办学优势出发,探索适合自己的独特办学思路。通过"学研产"相结合实现优秀人才的培育,通过开办特色专业促进地方经济的发展,通过学习研究民间美术实现地域文脉的传承。     

Exploring digital fiction as a tool for teenage body image bibliotherapy*

This article reflects on the findings of the interdisciplinary ‘TransForm’ project, which ran between 2012 and 2014 and aimed to explore how reading and writing digital fictions (DFs) might support young women in developing frameworks for more positive thinking regarding their body image. The project comprised the following stages: (1) a review and compilation of DFs thematising and/or problematising female corporeality; (2) a series of cooperative inquiries with 3 groups of young women (aged 16–19 years) over a period of 5 weeks, examining participants’ responses to a selection of the previously compiled DFs, as well as the challenges these young women face in relation to body image and (3) an interventionist summer school in which participants aged 16–19 explored body image issues via writing DFs. This article reports on the main observations and findings of each stage, and draws conclusions for future research needs in this area.