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CAS-aided visualization in LATEX documents for mathematical education
1-18Views:27We have been developing KETpic as a macro package of a CAS for drawing fine LATEX-pictures, and we use it efficiently in mathematical education. Printed materials for mathematics classes are prepared under several constraints, such as "without animation", "mass printings", "monochrome", and "without halftone shadings". Because of these constraints, visualization in mathematical education tends to be unsatisfactory. Taking full advantages of LATEX and CAS, KETpic enables us to provide teaching materials with figures which are effective for mathematical education. The effects are summarized as follows:
(1) The plottings of KETpic are accurate due to CAS, and enable students to deduce mathematical laws.
(2) KETpic can provide adequate pictures for students' various interest. For example, when some students who understand a matter try to modify it, KETpic can give them appropriate and experimental figures.
(3) Even though CAS can draw 3D-figures beautifully and automatically, it is expensive for mass printings and the figures are sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are monochrome, but are richly expressive.
In this paper, we give various examples of LATEX-pictures which we drew by using KETpic. For instance, the picture which is used in order to explain the convergence theorem of Fourier series makes it easier for students to understand the idea that function series converge to another function. Also the picture of skeleton is endowed with clear perspective. KETpic gives us great potential for the teaching of combinatorial mathematics. Through these examples, we claim that KETpic should have great possibilities of rich mathematical expressions under the constraints above mentioned. -
Comment les enseignants en formation initiale utilisent les technologies informatiques dans leurs classes
187-208Views:29The research presented here deals with the way French pre-service teachers assimilate the working of technology tools and the effects on professional practice of integrating these tools into classes. We focused on the professional writings of pre-service teachers regarding the use of technology in their teaching. The results show that, besides official instructions, the motivations put forward by pre-service teachers who integrated technology in their classes are mainly their students' interest in computers and how powerful this tool is. They also show that in such an environment teachers tend to keep in the background and to leave the students to interact chiefly with the computer. We also noticed that the specificities of managing a classroom in computer environment are not taken into account unless they generate problems.
Résumé. La recherche présentée ici porte sur l'appropriation des outils informatiques par les enseignants français en formation initiale et les effets de leur intégration dans les classes sur les pratiques professionnelles. Nous avons pris comme objet d'étude des écrits professionnels, élaborés par ces professeurs stagiaires, portant sur l'utilisation des TIC dans leur enseignement. Les résultats obtenus font apparaître qu'outre les injonctions institutionnelles, les motivations invoquées par les stagiaires pour recourir à l'informatique concernent surtout l'attrait de leurs élèves pour l'ordinateur et la puissance de cet outil. Dans le cadre des usages en classe, nos résultats montrent que l'enseignant a tendance à s'effacer devant l'ordinateur, considéré comme l'interlocuteur privilégié de l'élève. Nous avons aussi pu constater que les spécificités de la gestion de la classe en environnement informatique ne sont prises en compte que lorsqu'elles se révèlent sources de problèmes. -
Blind versus wise use of CAS
407-417Views:7During my courses for mathematics major students I often use technology linked to the arising problems. In such cases I noted that some students were used to learn just some procedures, which made them able to solve (partially) some problems and when they got the result, they accepted it passively and did not relate it to the initial problem.
In this paper I outline a strategy and investigate some simple exercises about how to develop a critical attitude towards the results obtained by technology in an introductory course to CAS.
I believe that wise use of technology offers an effective method in teaching mathematics, without reducing the students' mental contribution. -
Live & Learn: When a wrong program works
195-208Views:26In this paper an interesting and surprising case study of my programming education practice is presented. This case underlines the importance of methods, standards and rules of thumb of the programming process. These elements of the programming technology can be taught well in education and they can guarantee the quality of the implemented programs. However the case described in this paper brings an anomaly when a programming standard is violated during the programming process and, although it should imply that the implemented program code works badly, the program works perfectly. This anomaly is caused by a typical implementation problem: the boundary and rules of the machine representation of numbers. This anomaly is going to be analyzed and the appropriate conclusions of our case study will be deducted. -
Herschel's heritage and today's technology integration: a postulated parallel
419-430Views:26During the early 20th century, advocacy of a range of mathematical technologies played a central part in movements for the reform of mathematical education which emphasised ‘practical mathematics' and the ‘mathematical laboratory'. However, as these movements faltered, few of the associated technologies were able to gain and maintain a place in school mathematics. One conspicuous exception was a technology, originally championed by the mathematician Herschel, which successfully permeated the school mathematics curriculum because of its:
• Disciplinary congruence with influential contemporary trends in mathematics.
• External currency in wider mathematical practice beyond the school.
• Adoptive facility of incorporation in classroom practice and curricular activity.
• Educational advantage of perceived benefits outweighing costs and concerns.
An analogous perspective is applied to the situation of new technologies in school mathematics in the early 21st century. At a general level, the cases of calculators and computers are contrasted. At a more specific level, the educational prospects of CAS and DGS are assessed. -
Application of computer algebra systems in automatic assessment of math skills
395-408Views:36Mathematics is one of those areas of education, where the student's progress is measured almost solely by testing his or her ability of problem solving. It has been two years now that the authors develop and use Web-based math courses where the assessment of student's progress is fully automatic. More than 150 types of problems in linear algebra and calculus have been implemented in the form of Java-driven tests. Those tests that involve symbolic computations are linked with Mathematica computational kernel through the Jlink mechanism. An individual test features random generation of an unlimited number of problems of a given type with difficulty level being controlled flat design time. Each test incorporates the evaluation of the student's solution. Various methods of grading can be set at design time, depending on the particular purpose that a test is used for (self-assessment or administrative exam). Each test is equipped with the correct solution presentation on demand. In those problems that involve a considerable amount of computational effort (e.g. Gauss elimination), additional special tools are offered in a test window so that the student can concentrate on the method of solution rather than on arithmetic computations. (Another obvious benefit is that the student is thus protected from the risk of frustrating computational errors). Individual tests can be combined into comprehensive exams whose parameters can be set up at design time (e.g., number of problems, difficulty level, grading system, time allowed for solution). The results of an exam can be automatically stored in a database with all authentication and security requirements satisfied. -
Teaching XML
317-335Views:32The author has been teaching XML at the Faculty of Informatics, University of Debrecen since the end of the nineties. This paper gives an overview of XML technology from an educators viewpoint that is based on the experience that the author has gained teaching XML over the years. A detailed description of the XML course is provided. Methodological issues are also discussed. -
Compositions of dilations and isometries in calculator-based dynamic geometry
257-266Views:32In an exploratory study pre-service elementary school teachers constructed dilations and isometries for figures drawn and transformed using dynamic geometry on calculators. Observational and self assessments of the constructed images showed that the future teachers developed high levels of confidence in their abilities to construct compositions of the geometric transformations. Scores on follow-up assessment items indicated that the prospective teachers' levels of expertise corresponded to their levels of confidence. Conclusions indicated that dynamic geometry on the calculator was an appropriate technology, but one that required careful planning, to develop these future teachers' expertise with the compositions. -
Shall we use one more representation? Suggestions about establishing the notion of recursion in teaching informatics in primary schools
209-229Views:27Among the most prominent developmental tasks of primary school education one finds increasing pupils' cognitive capacity with especial regard to observing, interpreting, coding and proving skills, which form an integral part of information and communication culture.
Info-technology (problem solving with the tools and methods of informatics), a subject matter within informatics, provides outstanding opportunities to reach the aims outlined above.
This study presents methodological ideas related to the subfield Algorithmization and data modelling of Info-technology. More specifically, it presents teaching methods to be applied while establishing the notion of recursion in grades 3–8 of primary education, and at the same time it also focuses on various realization possibilities of the prominent developmental tasks mentioned above. -
Synthesis of concurrent programs
301-317Views:34Students need a well defined method to be successful in the complex process of writing a concurrent program. In this paper we show a step by step method to create such programs. The method based on UML which has been thought to students during previous courses. UML provides standard and relatively simple tools to describe concurrent systems, and from the description the program can be derived.
First we give a brief introduction to the concurrent systems. This is followed by the description of the method, and finally we demonstrate the method on a small problem. -
Forming the concept of parameter with examples of problem solving
201-215Views:31Pupils are encountering difficulties with learning algebra. In order for them to understand algebraic concepts, particularly the concept of parameter it was decided by the teacher of mathematics and Information Technology to integrate the teaching of these two subjects. The aim of this study is to investigate whether, and to what degree, software can be useful in process of forming the concept of parameter. This longitudinal study was conducted in a junior high school (13-16 year old children) using different computer programs. -
Some aspects of teaching the technology of designing and planning information systems in health care
131-144Views:25In this article, we use the well-known ideas of technology in designing of new information systems in health care. We explain the principle that "making a health care application" "is more than writing a program", "it requires a strong co-operation and continuous contact" between the system analysts and users. The concept of the information system must contain the work of the whole system, which means that the planning and designing process should focus on the services, which really support the customer's functions. It has to be compatible with the earlier information systems based on several decade's experience. In this paper we use the most important elements of system theory. First of all we explain why it is important to take into account the behaviour of those, who operate the information system, and also their habits and way of thinking when planning then information system. We emphasise that it is importance to overview the whole information system and its functionality because it is a major aspect of the system planning.
This paper can be used in university courses especially in teaching SDM, SSADM, Martin, etc. technologies for information system analysts, program designers and programmers. -
Is it possible to develop some elements of metacognition in a Mathematics classroom environment?
123-132Views:89In an earlier exploratory survey, we investigated the metacognitive activities of 9th grade students, and found that they have only limited experience in the “looking back” phase of the problem solving process. This paper presents the results of a teaching experiment focusing on ninth-grade students’ metacognitive activities in the process of solving several open-ended geometry problems. We conclude that promoting students’ metacognitive abilities makes their problem solving process more effective.
Subject Classification: 97D50, 97G40
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Expressiveness of programming languages and environments: a comparative study
111-141Views:31In written and oral communication tools, the support of the understanding of our message have an important role: we can increase the expressiveness and the level of understanding of our topic by approaching it in several ways, i.e. in written methods by highlighting the important parts; in oral by changing tone and other elements of non-verbal communication. In this paper programming languages and developing environments are compared with each other in terms of their methods and their level of support to the solution of programming tasks.
There is a need to have these tools in programming and, of course, in teaching programming. What are the factors that define the distinctness and the legibility of a program? What are the basic principles which give an instrument in programmers' and students' hands in order to create a properly working program from already existing algorithms in the most efficient way? We search for the answers to these questions in this paper. -
Teaching of old historical mathematics problems with ICT tools
13-24Views:20The aim of this study is to examine how teachers can use ICT (information and communications technology) tools and the method of blended learning to teach mathematical problem solving. The new Hungarian mathematics curriculum (NAT) emphasizes the role of history of science, therefore we chose a topic from the history of mathematics, from the geometry of triangles: Viviani's Theorem and its problem field. We carried out our teaching experiments at a secondary school with 14-year-old students. Students investigated open geometrical problems with the help of a dynamic geometric software (GeoGebra). Their research work was similar to the historical way. -
Mathematische Bildung im Klagenfurter Doktorand(inn)enkolleg
67-84Views:30In 2003 we set up a programme for PhD-studies ("Doktorand(inn)enkolleg") at the University of Klagenfurt which should promote and support PhD-studies in the field of mathematics education.Within this programme it is worked on the topic "general mathematics education" from different perspectives.
In the first part of this paper intentions, the fields of work and the form of organisation are briefly demonstrated. The second and main part considers in detail the work in one of the four fields of work, and finally, the third and last part presents some experiences with regard to the contents as well as general ones. -
Analogous programming with a template class library
135-152Views:43In this paper, a template class library and its usage can be read. The classes of the library contain the C++ code of the algorithm of programming theorems. This library supports the implementation of the programs that are planned by analogous programming but the primary aim of its usage is to introduce the object-oriented programming style to show how a reusable code can be written with inheritances, overriding virtual methods, composition of objectcs and template parameters. -
Report of the conference "Connecting Tamás Varga’s Legacy and Current Research in Mathematics Education": November 6-8, 2019, Budapest, Hungary
5-8Views:88On the occasion of the 100th anniversary of the birth of the Hungarian mathematics educator, didactician and reform leader Tamás Varga, a conference on mathematics education has been organized in November 2019 and held at the Hungarian Academy of Science.
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Building a virtual framework to exploit multidisciplinary project workshops – peaks & pits
147-164Views:14Multidisciplinary project work in connection to industry is highly favoured at University education, since it prepares students to envision their spectrum of profession, to be able to participate in production projects in co-operation with partners out of campus, and learn to communicate between disciplines. An effctive combination presumes selection of right partners, set-up of proper virtual platform to bridge time, space, and diffrences in working styles. The set-up process requires several phases of design-based research proofing the melding process to produce a productive workshop that is sustainable. The paper describes the review of literature, the platform and set-up established, a first phase in bridging Art and Computer Science through the description of MOMELTE project, a critical evaluation in order to learn from mistakes, and a new list of design principles to improve the next phase of the workshop process. -
A first course in computer science: languages and goals
137-152Views:17The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the university level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specific language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends C++ as the most appropriate language. An appendix provides a sample syllabus. -
The "Teaching Mathematics and Computer Science" Journal logo's mathematical background
55-65Views:3In the present contribution we give an elementary technology for drawing the geodesics, paracycles and hypercycles on the pseudosphere. -
Facilitating class attendance to improve student achievements
77-90Views:29Many studies have revealed that attendance is strongly associated with students' achievements, and have proposed different strategies to improve students' attendance. However, there are few studies investigating how to efficiently take students' attendance – the key component to improve students' attendance. Taking attendance manually is inefficient since it will consume part of the limited class time. This paper describes the design and the implementation of an online attendance system that is currently used in classes at West Virginia University and California University of Pennsylvania. Examples of the system are provided online. Implementation codes of the system are shared, which can be used to teach computer science courses such as Web Programming or Client-Server Script Languages. -
Introductory Computer Programming Courses in Mathematics Curriculum
19-30Views:110We present the results of surveys and curricular research on introductory computer programming courses that are required or recommended for mathematics degrees at U.S. colleges and universities. Our target schools were those with populations between 5,000 and 20,000 undergraduate students. A key result is a synopsis of programming languages in use in these introductory courses with Java, Python and C + + holding the top three spots. We found that 85% of the 340 schools in our pool require or recommend an introductory programming course as a component of a mathematics degree. Furthermore, most of these introductory programming courses are taught by faculty outside of the mathematics department. These results indicate that mathematics faculty value computer programming and should be actively involved in setting learning outcomes, incorporating skills and concepts learned in introductory programming courses into subsequent mathematics courses, and determining programming languages in use.
Subject Classification: 97D30, 97P20, 97P40
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Development of classification module for automated question generation framework
89-102Views:27Automatic question generation is in the focus of recent researches which includes bordering disciplines like education, text mining, knowledge-engineering. The elaborated system generates multi-choice questions from textbooks without using an external semantic database. One of the base modules of the system is the classification module defining the extracted word. This paper describes modules of the framework including a detailed analysis of the classification part. We show the operability of the elaborated system through a practical test. -
Mobile devices in Hungarian university statistical education
19-48Views:77The methodological renewal of university statistics education has been continuous for the last 30 years. During this time, the involvement of technology tools in learning statistics played an important role. In the Introduction, we emphasize the importance of using technological tools in learning statistics, also referring to international research. After that, we firstly examine the methodological development of university statistical education over the past three decades. To do this, we analyze the writings of statistics teachers teaching at various universities in the country. To assess the use of innovative tools, in the second half of the study, we briefly present an online questionnaire survey of students in tertiary economics and an interview survey conducted with statistics teachers.
Subject Classification: 97-01, 97U70, 87K80