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.     

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。     

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.     

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.     

针对本科生的演化算法教学探讨

演化算法是一种自然启发式全局优化算法,其鲁棒性、高效性、全局搜索能力和隐并行性好等特点,使其成为计算机领域的一个研究热点。为了能使本科生对演化计算方法有所了解,并对今后的工作或研究生学习有所帮助,有必要为计算机专业的本科生开设演化计算课程。文章结合在本科生教学中的心得,对如何开展本科生演化算法教学进行了探讨。     

留学生数据库原理全英文教学探索与实践

在我国高等教育国际化背景下,留学生全英文教学已经成为留学生教育的重要组成部分。在留学生数据库原理全英文课程的教学过程中,为了提高教学质量,对教材选取、教学内容的组织安排、教学方法、教学手段和实践教学环节进行了初步探索,并取得了理想的教学效果。文章对所取得的教学经验进行了归纳总结,以期能够对从事计算机专业留学生全英文教学的同行有所帮助。     

The graf system: An interactive graphic system for teaching mathematics

GRAF is a software package developed to visualize real functions of the form y = f (x) of x = x (t), y = y (t). It also allows the study of rotations, translations, enlargements, compositions of functions and so on. The user is given uniform and easy interaction possibilities with the package. GRAF is written in the BASIC language and run on a Tektronix 4051 graphic desktop computer. This package has been developed for didactical application, particularly in high schools. It has been tested with students in many mathematic courses.     

Learning effects of CAI on college students

The purpose of this study was to determine if college students learn better when using lecture/CAI than by using the conventional lecture method, when the material presented is very visually oriented. The subjects consisted of 28 students enrolled in a freshman level computer science course that is required for their major. Students were randomly assigned to one of two groups. Both groups received the same lecture. The control group was presented examples in class by the professor aided by transparencies. The treatment group was presented the same examples using a computer tutorial, without teacher intervention. As was indicated on the pre-test, the two groups demonstrated remarkably similar results in the amount of prior knowledge of the subject area. There was no significant difference between the two groups in the amount of learning that took place, as shown by the results of the post-test. There was, however, a considerable difference in time spent on the task. The examples took much longer for theprofessor to present to the control group than it took the treatment group to absorb the interactive examples on individual computers. The majority of the students who were in the treatment group (lecture and computer examples) indicated that they preferred the computer tutorial to having examples presented by the instructor.