An object-oriented approach to teaching mathematics for engineering and science students

It is suggested to teach mathematics for engineering and science students as exploration of mathematics-related classes. Similarity with classes and objects of object-oriented programming is demonstrated. In the framework of the suggested approach, each relatively self-contained unit of mathematics curriculum is assigned a data type and is considered a class. In such setting, a theorem proof may be viewed as an assignment of values to object properties. The approach augments the role of recognition of mathematical objects, their properties and methods （operations） and diminishes the value of comprehensive study of rigorous proofs. The approach emphasizes the importance of development of mathematical intuition and combines conceptual and operational approaches to teaching and learning mathematics. Prospective implementation assumes using of computer-based systems of formal proof.     

Analysis of studies of the effects of computer-assisted instruction on the mathematics performance of students with learning disabilities

The purpose of this study was to conduct a meta-study of computer-assisted instruction (CAI) studies in mathematics for students with learning disabilities (LD) focusing on examining the effects of CAI on the mathematics performance of students with LD. This study examined a total of 11 mathematics CAI studies, which met the study selection criterion, for students with LD at the elementary and secondary levels and analyzed them in terms of their comparability and effect sizes. Overall, this study found that those CAI studies did not show conclusive effectiveness with relatively large effect sizes. The methodological problems in the CAI studies limit an accurate validation of the CAI’s effectiveness. Implications for future mathematics CAI studies were discussed.     

提高留学生学习兴趣的离散数学实践教学探索

离散数学内容丰富、概念多、定理多、抽象性强,加上很多留学生的数学基础比较薄弱、理解能力差,因此部分留学生学习兴趣低、学习困难。为此,提出对留学生离散数学的教学进行改革。改革的主要内容包括添加应用性教学内容、引入实践环节、建设题库和改革考核方式等。教学实践表明,这些举措有效地提高了留学生学习离散数学的兴趣、减轻了学习难度,培养了学生应用所学理论解决实际工程问题的能力。     

Cyberbullying among college students with disabilities

Cyberbullying has received increasing attention in recent years. However, the majority of this research has focused on children in middle school and on neurotypical youth, to the omission of people with disabilities. The current study, however, examines cyberbullying as it occurs among college students with and without disabilities. Two hundred five students completed a survey examining their experiences with cyberbullying, along with measures of predictor and outcome variables theorized to be related to cyberbullying. The results revealed that, as with traditional bullying, students with disabilities are at particular risk for cyberbullying victimization. Predictors of victimization included traditional bullying victimization, Internet use, and the noticeability of the disability. Outcomes of cyberbullying victimization (e.g., low self-esteem, high depression) appear to be particularly pronounced for individuals with disabilities.     

Learning styles' recognition in e-learning environments with feed-forward neural networks

Abstract People have unique ways of learning, which may greatly affect the learning process and, therefore, its outcome. In order to be effective, e-learning systems should be capable of adapting the content of courses to the individual characteristics of students. In this regard, some educational systems have proposed the use of questionnaires for determining a student learning style; and then adapting their behaviour according to the students' styles. However, the use of questionnaires is shown to be not only a time-consuming investment but also an unreliable method for acquiring learning style characterisations. In this paper, we present an approach to recognize automatically the learning styles of individual students according to the actions that he or she has performed in an e-learning environment. This recognition technique is based upon feed-forward neural networks.     

数学与应用数学专业“C程序设计”教学改革探讨

"C程序设计"是数学与应用数学专业的一门基础课,目前该课程在这两个专业中的教学内容有很大的局限性。传统的教学模式基本上不考虑数学与应用数学的专业性,教学手段上还是以教为主,学为辅。根据数学与应用数学专业的特点,从教学内容、教学模式和教学手段等方面对"C程序设计"教学进行了改革。经学生实际学习情况验证,取得了较好的教学效果。     

An intelligent e-learning system based on learner profiling and learning resources adaptation

Taking advantage of the continuously improving, web-based learning systems plays an important role for self-learning, especially in the case of working people. Nevertheless, learning systems do not generally adapt to learners’ profiles. Learners have to spend a lot of time before reaching the learning goal that is compatible with their knowledge background. To overcome such difficulties, an e-learning schema is introduced that adapts to the learners’ ICT (Information and Communication Technologies) knowledge level. The IEEE Reference Model (WG 1) defined by the Learning Technology Standards Committee (LTSA) is extended and used for this purpose. The proposed approach is based on the usage of electronic questionnaires (e-questionnaires) designed by a group of experts. Through the automatic analysis of the learners’ responses to the questionnaires, all learners are assigned to different learner profiles. According to these profiles they are served with learning material that best matches their educational needs. We have implemented our approach in five European countries and the overall case study illustrates very promising results.     

The identification,implementation, and evaluation of critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities

Critical user interface design features of computer-assisted instruction programs in mathematics for students with learning disabilities and corresponding implementation guidelines were identified in this study. Based on the identified features and guidelines, a multimedia computer-assisted instruction program, ‘Math Explorer’, which delivers addition and subtraction word problem-solving instruction for students with learning disabilities at the early elementary level, was designed and developed. Lastly, usability testing was conducted to assess whether Math Explorer was well-designed in terms of the interface for students with learning disabilities. Given the results of the usability testing, this study corroborated the fact that the critical user interface design features and guidelines in mathematics computer-assisted instruction programs would be essential for facilitating the mathematical learning of students with learning disabilities. Implications for practice and future research were discussed.     

离散数学教学改革研究

离散数学的教学目的是培养学生的抽象思维和缜密概括能力,文章分析了离散数学课程教学过程中存在的一些实际问题,探索面向应用能力培养的教学改革,在关注理论知识应用的同时,注重知识之间的内在联系,促使学生认识到严谨的逻辑思维、高度的抽象思维以及形式化表示在计算机科学发展过程中的作用.该教学改革可以有效地培养和提高学生理解和运用...     

离散数学中的分层次实验教学研究

从离散数学的实验教学现状出发,分析了进行分层次实践教学的必要性,研究了分层次教学的原则、实验设计原则、实验设计思路,实验设计内容,实验具体实施和考核方案,最后进行了成果分析。实践教学证明,在离散数学课程中进行分层次教学有利于培养学生的动手能力和创新精神。     

基于建构主义的离散数学教学探讨

将建构主义理论应用于离散数学的教学实践中,在教师课前准备、课堂授课和学生课后复习等环节作了有益的尝试。教学实践表明,在建构主义理论指导下的教学方法能够有效地提高学生的学习兴趣,加深他们对课程内容的理解。     

Extended muSIMP/muMATH for teaching and learning mathematics

muSIMP is described by its authors (David Stoutemyer and Albert Rich, of the Soft Warehouse, Honolulu. Hawaii) as a “surface language” for muLISP. The latter is one of their earlier products, a LISP interpreter and development system for microcomputers.muSIMP has a very different syntax from LISP, although in other respects it is effectively the same language. A “conventional mathematics” appearance is clearly helpful to users. muSIMP offers f (x, y, z) where LISP would require (f x y z), for example, and the assignment “A: B + C 1 D;” is obviously nearer to most mathematics students' experience than the LISP equivalent, “(SETQ A (PLUS B(TIMES C D)))”.muMATH is a large library of muSIMP function and variable definitions. It permits the user to carry out symbolic algebraic operations including algebraic simplification, logarithmic and trigonometric expansion, equation solving, vector and matrix manipulation, differentiation, integration, limits and summation. All of this software can be extended as required by the user, so that new rules for differentiating or integrating can be added, for example.muSIMP does not, as sold, possess graphics capability, XSIMP, the author's extended version of muSIMP, for the RML 380Z (CP/M system) includes all the Research Machines Level 2 graphics functions, retaining a correspondence of names and order of parameters. XSIMP also contains a full floating-point arithmetic package, with the four arithmetic operations complemented by exponential, logarithmic, trigonometric and square root functions. Functions have also been provided in XSIMP for making BDOS and BIOS calls to CP/M.     

Real-time imaging-based assessment model for improving teaching performance and student experience in e-learning

Multimedia is an essential and integral part of electronic learning (e-learning). In this study, teaching performance and student learning experience are measured using real-time multimedia processing tools and techniques for the e-learning paradigm. Visual attention and visual engagement analysis are performed using two developed algorithms. Video lectures are recorded and delivered to students in e-learning pedagogical setup, which are examined for the visual attention and visual engagement of the student and teacher, respectively. Proposed methodology integrates the assessment on both student and teacher ends. Multimedia processing of video lectures for teaching performance produces scoring dataset. The same methodology on student end for visual attention is used to investigate student experience. These types of datasets then reduced to time-based datasets from the image-based dataset. Correlation and association of both datasets provide the opportunity to relate both student experience and teaching performance as well as to move forward to create content that is more useful. Computational performance of the developed algorithms is compared using different video lectures with their processed frames per second, which is analyzed as per their corresponding bins. Mean, max, and median of the processed frames of all the processed videos are also compared.     

Software development of interactive microcomputer programs used in teaching mathematics: A case history

This paper presents the experience of using microcomputers in the teaching of mathematics to undergraduates at Paisley College of Technology. The production of software for use by students has been a sizeable undertaking and the paper presents an account of the software development programme whose first stage was a formative and experimental period on which was based the specification of the software developed in the second stage. The definition and development of software tools for interactive programs to be used in mathematics teaching has been found to be of prime importance in producing the required software in a relatively efficient manner.     

The quality of evidence in tablet‐assisted interventions for students with disabilities

The purpose of this review is to weigh the evidence of the effectiveness of tablet‐assisted instructions (TAIs) at improving academic outcomes of students with disabilities. An extensive search process with inclusion and exclusion criteria yielded a total of 17 studies to be included in the present study: three group design studies and 14 single‐subject design studies. The quality indicators proposed by Gersten et al. ( 2005 ) and Horner et al. ( 2005 ) were applied to evaluate the methodological rigour of TAI studies and their feasibility to be considered evidence‐based. Results revealed that (a) most group design studies provided little information about the intervention agent and equivalence of groups across conditions, (b) the social validity of using tablets for students with disabilities was strongly established across all single‐subject design studies and (c) procedural fidelity in assessment and intervention implementation was inadequately addressed in group design studies. Although this review suggests that TAI used in single‐subject design studies can be a potentially evidence‐based practice for students with disabilities, there still remains to be established whether the group design studies can be considered evidence‐based, because of the lack of methodological rigour in group design studies. Finally, implications for future directions and practical ideas are discussed.     

Structured derivations: a unified proof style for teaching mathematics

Structured derivations were introduced by Back and von Wright as an extension of the calculational proof style originally proposed by E. W. Dijkstra and his colleagues. Structured derivations added nested subderivations and inherited assumptions to this style. This paper introduces further extensions of the structured derivation format, and gives a precise syntax and semantics for the extended proof style. The extensions provide a unification of the three main proof styles used in mathematics today: Hilbert-style forward chaining proofs, Gentzen-style backward chaining proofs and algebraic derivations and calculations (in particular, Dijkstra’s calculational proof style). Each of these proof styles can now be directly presented as a structured derivation. Even more importantly, the three proof styles can be freely intermixed in a single structured derivation, allowing different proof styles to be used in different parts of the derivation, each time choosing the proof style that is most suitable for the (sub)problem at hand. We describe here (extended) structured derivations, feature by feature, and illustrate each feature with examples. We show how to model the three main proof styles as structured derivations. We give an exact syntax for structured derivations and define their semantics by showing how a structured derivation can be automatically translated into an equivalent Gentzen-style sequent calculus derivation. Structured derivations have been primarily developed for teaching mathematics at the secondary and tertiary education level. The syntax of structured derivations determines the general structure of the proof, but does not impose any restrictions on how the basic notions of the underlying mathematical domain are treated. Hence, the style can be used for any kind of proofs, calculations, derivations, and general problem solving found in mathematics education at these levels. The precise syntax makes it easy to provide computer support for structured derivations.     

注意力迁移的联合平衡领域自适应

目的 现有的图像识别方法应用于从同一分布中提取的训练数据和测试数据时具有良好性能,但这些方法在实际场景中并不适用,从而导致识别精度降低。使用领域自适应方法是解决此类问题的有效途径,领域自适应方法旨在解决来自两个领域相关但分布不同的数据问题。方法 通过对数据分布的分析,提出一种基于注意力迁移的联合平衡自适应方法,将源域有标签数据中提取的图像特征迁移至无标签的目标域。首先,使用注意力迁移机制将有标签源域数据的空间类别信息迁移至无标签的目标域。通过定义卷积神经网络的注意力,使用关注信息来提高图像识别精度。其次,基于目标数据集引入网络参数的先验分布,并且赋予网络自动调整每个领域对齐层特征对齐的能力。最后,通过跨域偏差来描述特定领域的特征对齐层的输入分布,定量地表示每层学习到的领域适应性程度。结果 该方法在数据集Office-31上平均识别准确率为77.6%,在数据集Office-Caltech上平均识别准确率为90.7%,不仅大幅领先于传统手工特征方法,而且取得了与目前最优的方法相当的识别性能。结论 注意力迁移的联合平衡领域自适应方法不仅可以获得较高的识别精度,而且能够自动学习领域间特征的对齐程度,同时也验证了进行域间特征迁移可以提高网络优化效果这一结论。     

Doing online research involving university students with disabilities: Methodological issues

Changes in how disability is understood have determined an increase in the number of people with disabilities who study at university. Several studies have aimed to investigate the experiences of students with disabilities. However, one difficulty in these studies is that very different types of disability (e.g., reading disabilities as compared to motor disability) are grouped together under the broad label of “students with disability”. Recently, the increase in access to computers and technology has made it possible to distribute questionnaires through the Internet and reach a higher number of participants; however, the use of online questionnaires for conducting research on the experiences of students with disabilities poses theoretical, methodological and ethical challenges to the researcher. Some of these issues are common to questionnaires conducted both online and offline; others, however, are typical of online studies. Here we will review these problems and their consequences in terms of research validity, along with some possible solutions that may minimize the risks of harming the privacy of participants, losing responses, and biasing data.