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Some aspects of teaching the technology of designing and planning information systems in health care
131-144Views:100In 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. -
Manipulative bulletin board for early categorization
1-12Views:139According to various researchers categorization is a developmentally appropriate mathematical concept for young children. Classifying objects also relates to every day activities of human life. The manipulative bulletin board (MBB) served as a kind of auxiliary means for approaching categorization by young children. In this article we investigated the kind of MBB that pre-service early childhood education teachers constructed in order to involve children in tasks of categorization, as well as, the way children manipulated these boards in order to categorize items. The MBB, as teaching aids, facilitated the engagement of the children in different categorization processes. -
Some problems of solving linear equation with fractions
339-351Views:142The aim of this paper is to offer some possible ways of solving linear equations, using manipulative tools, in which the "−" sign is found in front of an algebraic fraction which has a binomial as a numerator. It is used at 8th grade. -
Decision based examination of object-oriented programming and Design Patterns
83-109Views:129On the basis of our examination experience of Design Patterns the existing interpretations and descriptions of Design Patterns do not realise a clear and understandable answer for their aims. The reason for this is that the existing interpretation of the object-oriented paradigms is used for their description and formulation. In order that clear answers could be found for the aims of using Design Patterns, a new conception of their interpretation has to be established. In order to create a new conception, we have to analyze object-oriented paradigms.
According to our new conception the object-oriented methodology is based on the elimination of decision repetition, thus sorting the decisions to class hierarchy, with the help of which the data structure and methodology of decision options can be determined by the subclasses of the given class. Sorting the decisions and decision options to a class and its subclasses only the first decision case will be executed, which will be archived and enclosed by instantiation of one of the subclasses. For the following decision cases the archived decision result can be used without knowledge of which decision option was used, so to say which subclass was instantiated, because it is enclosed by using the type of the parent class.
The aim of the object-oriented technology is the elimination of decision repetition, which can be realized by sorting the decisions. The derivations are the abstract definitions of decisions, so the derivations can be interpreted as decision abstractions. The Design Patterns offer recipes for sorting the decisions. With the help of the decision concept the aim of Design Patterns can be cleared and a more natural classification of Design Patterns can be realized. -
Comparison of teaching exponential and logarithmic functions based on mathematics textbook analysis
297-318Views:148Exponential and logarithmic functions are key mathematical concepts that play central roles in advanced mathematics. Unfortunately these are also concepts that give students serious difficulties. In this paper I would like to give an overview – based on textbook analysis – about the Hungarian, Austrian and Dutch situation of teaching exponential and logarithmic functions. This comparison could also provide some ideas for Hungarian teachers on how to embed this topic in their practice in another more "realistic" way. -
Analysis of the affective factors of learning mathematics among teacher trainees
225-254Views:134The Hungarian National Core Curricula gives primacy to the development of abilities and the practical application of knowledge. The task of the training programme is primarily to prepare teacher trainees for the teaching and educating profession. As teachers, they are going to plan, organize, help, guide, control and evaluate the learning of mathematics of individuals and groups of students from the age of 6 to 10 (12), and cultivate their mathematical skills, thinking and positive attitude towards any mathematical activities. In order to train educators who are able to meet the above requirements on high standard, it is necessary to update the teacher training programme based on the trainees' preliminary knowledge and motivation level.
The key to learn about the child's mind and achieve conscious development is the systematization of factual knowledge and methodological awareness. The modern, flexible approach to subject pedagogy, based on pedagogy, psychology and epistemology, qualifies trainees to educate learners who understand and like mathematics. Therefore, it is essential to develop the trainees' positive approach to mathematics and arouse their demand for continuous professional improvement. (Programme of the four-year primary school teacher training, 1995.)
In our research we are looking for ways of ascertaining the starting parameters which have influence on the planning of the studies of mathematics and subject pedagogy. In this article we introduce a questionnaire by the means of which we collected information on the trainees' attitude and its changing towards mathematics. With the help of the analysis of the answers we paint a picture of the ELTE TÓFK (Eötvös Loránd University, Faculty of Elementary and Nursery School Teacher's Training) third year students' attitude to the subject, and we compare it to the tendencies noticed in the mass education. The energy invested in learning is influenced by the assumption of the relevance and importance of the subjects. Therefore we considered it also our task to reveal. Besides the students' attitude toward mathematics and their assumption about their own competence we have collected data also on their performance in the subject. Summarising the research results we show the advantages of the questionnaire, and summarise the observations which would indicate need for methodological changes in the mathematics teacher training. -
A proposed application of Monte Carlo method in teaching probability
37-42Views:131Pupils' misconception of probability often results from lack of experience. Combining the concept of probability and statistics, the proposed application is intended for the teachers of mathematics at an elementary school. By reformulating the task in the form of an adventure, pupils examine a mathematical problem, which is too difficult for them to solve by combinatorial method. By recommending the simulation of the problem, we have sought to provide pupils with valuable experience of experimenting, recording and evaluating data. -
Analyse d’obstacles lies a la notion de fonction reciproque
43-61Views:77L'article présente une réflexion sur les difficultés éventuelles des étudiants au cours de l'étude des fonctions réciproques. Nous nous intéressons à l'enseignement de cette notion dans le cadre de la transition entre le lycée et la première année d'université en France. L'article résume la façon de présenter de nos jours le concept de fonction réciproque dans le curriculum français. Nous présentons des propositions d'enseignement issues de quelques travaux de recherche anglophones. Cela nous permet de mettre en lumière l'existence d'obstacles dans l'apprentissage et de difficultés dans l'enseignement de cette notion. -
A role of geometry in the frame of competencies attainment
41-55Views:138We discuss aspects of the Education Reform from teaching to educational system. In this context we recognize some problems in recognition of some competencies that students need to achieve and we present how we have developed the measurement method of spatial abilities and problem solving competence. Especially, we investigate how students use spatial visualization abilities in solving various problems in other mathematical course. We have tested how students use their spatial abilities previously developed in geometry courses based on conceptual approach to solve a test based on procedural concept in Mathematical Analysis course. -
A new approach for explaining Rhind's Recto – and its utility in teaching
337-355Views:107The Recto is a table in the Rhind Mathematical Papyrus (RMP) of ancient Egypt containing the unit fraction decompositions of fractions 2/n (3 ≤ n ≤ 101, n odd). To the question how (and why) the decompositions were made, there exists no generally accepted answer. The fact that in some other sources of Egyptian mathematics decompositions different from those in Recto exist makes the problem more difficult.
Researchers normally try to find the answer in some formulas by which the entries of the table were calculated [see e.g. 1, 42]. We are convinced that the correct answer is not hidden in formulas but in the characteristics of Egyptian mathematics namely those of fraction and division concepts. To study them is important not only from historical point of view but also from methodological one: how to develop fraction concept and how to make division easier. -
From Newton’s fluxions to virtual microscopes
377-384Views:148The method of fluxions was originally given by Newton among others in order to determine the tangent to a curve. In this note, we will formulate this method by the light of some modern mathematical tools: using the concept of limit, but also with hyperreal numbers and their standard parts and with dual numbers; another way is the use of virtual microscopes both in the contexts of classical and non standard analysis. -
Illustrated analysis of Rule of Four using Maple
383-404Views:117Rule of Four, as a basic didactic principle, was formulated among the NCTM 2000 standards (see [14]) and since then it is quoted by numerous books and publications (see [4], [9], [12]). Practically we can say it is accepted by the community of didactic experts. The usage of the Rule of Four, however, has been realized mainly in the field of calculus, in fact certain authors restrict the wording of the principle to the calculus itself (e.g. [3]).
Calculus is a pleasant field, indeed. A sequence of values of a function provides us with example for numeric representation, while the formula and the graph of the function illustrate symbolic and graphical representations, respectively. In the end by wording the basic features of the function on natural language we gain textual representation.
This idyllic scene, however, becomes more complex when we leave the frame of calculus. In this paper we investigate the consequences of the usage of Rule of Four outside calculus. We discuss the different types of representations and show several examples which make the multiple features of representation evident. The examples are from different fields of mathematics and are created by the computer algebra system Maple, which turns out to be an excellent tool for illustration and visualization of the maim features of mathematical objects.
Next we introduce the concept of basic representation and rational representation, which is considered as the mathematical notion of "didactic usable" or "didactic rational" representation. In the end we generalize the notion of numeric representation, which leads us a more widely usable didactic principle which can be considered as a generalization of Rule of Four. -
Self-regulated learning in mathematics lessons at secondary level
139-160Views:70Self-regulation is a prerequisite to be able to set goals and to find suitable ways to reach them. Furthermore, it is an important ability which affects different areas of every day’s life. In educational context, self-regulation is often linked to self-regulated learning. The concept of self-regulated learning as well as key terms related to this topic such as problem-solving and modelling tasks will be discussed, while an emphasis lays on the role of the teacher. In this paper, a study on the attitudes of mathematics teachers towards self-regulated learning is presented. It focuses on teachers’ assessment of the possibility and limitations of self-regulated learning in mathematics lessons. It can be observed that most of the surveyed teachers try to incorporate self-regulatory processes in their teaching, but encounter difficulties related to various factors, such as their students, framework conditions, and the time required for such learning processes.
Subject Classification: 97D10
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Understanding the spatiotemporal sample: a practical view for teaching geologist students
89-99Views:121One of the most fundamental concept of statistics is the (random) sample. Our experience – acquired during the years of undergraduate education – showed that prior to industrial practice, the students in geology (and, most probably, in many other non-mathematics oriented disciplines as well) are often confused by the possible multiple interpretation of the sample. The confusion increases even further, when samples from stationary temporal, spatial or spatio-temporal phenomena are considered. Our goal in the present paper is to give a viable alternative to this overly mathematical approach, which is proven to be far too demanding for geologist students.
Using the results of an environmental pollution analysis we tried to show the notion of the spatiotemporal sample and some of its basic characteristics. On the basis of these considerations we give the definition of the spatiotemporal sample in order to be satisfactory from both the theoretical and the practical points of view. -
Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS
363-376Views:134Calculus concepts should have been taught in a carefully designed learning environment, because these concepts constitute a very important base for almost all applied sciences. The integral, one of the fundamental concepts of Calculus, has a wide application area. This paper focuses on constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of a CAS.
In this study, a semi-structured interview was carried out. In this interview, we tried to construct the disk method formula.
The levels of constructing the disk method formula in this study are:
• Introducing the concept: evaluating the volume of an Egyptian pyramid.
• Evaluating the volume of a cone obtained by revolution (using Maple worksheet).
• Designing their own ring and evaluating its price (using Maplet).
In this study, the interview has been presented as a dialog between teacher and students. When we look at feedback from students, we see that such a teaching method effects students in a positive way and causes them to gain conceptual understanding directed towards the concepts of approximation and volume. -
On a special class of generalized conics with infinitely many focal points
87-99Views:108Let a continuous, piecewise smooth curve in the Euclidean space be given. We are going to investigate the surfaces formed by the vertices of generalized cones with such a curve as the common directrix and the same area. The basic geometric idea in the background is when the curve runs through the sides of a non-void triangle ABC. Then the sum of the areas of some triangles is constant for any point of such a surface. By the help of a growth condition we prove that these are convex compact surfaces in the space provided that the points A, B and C are not collinear. The next step is to introduce the general concept of awnings spanned by a curve. As an important example awnings spanned by a circle will be considered. Estimations for the volume of the convex hull will be also given. -
Professional Competence in science education
129-137Views:52The article begins with a brief introduction aimed at sensitizing the reader to the perception of a trend in Mathematics and Computer Science Education publications towards empirical studies. Contrary to the stated trend, the characterization of Professional Competence is intended to serve as the guiding concept for the paper. The role of Professional Competence is discussed in various areas incorporating context-relevant publications in consecutive chapters. The discussion starts with the area of material development, covering Educational Standards and ends with Didactic Principles.
Subject Classification: 97xxx, 94xxx
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Kompetenzstreben und Kompetenzerwerb: Funktionale didaktische Fördermöglichkeiten durch Differenzierung und Individualisierung
1-52Views:130As a first glimpse of specific research endeavours the most important components of competence motivation are discussed in relation to didactical questions of gaining competence by inner differentiation and individualization: self-efficacy, optimal challenge, intrinsic motivation, exploration needs, internal attribution, self-determination motivation, defense of self-worth, self-concept, and achievement motivation. In this sense "competence" means ever changing standards of self-regulation of an individual interacting with the various cognitive and emotional demands of his/her environment.
In fulfilling these requirements a prototypical example of inner differentiation in mathematics instruction is given. This didactical elaboration is available as a selfinstructing unit in Hungarian and German language within the "Electronic periodical of the Department of Methodology of Mathematics" which can be reached under http://mathdid.inhun.com. -
Arithmetic progressions of higher order
225-239Views:157The aim of this article is to clarify the role of arithmetic progressions of higher order in the set of all progressions. It is important to perceive them as the pairs of progressions closely connected by simple relations of differential or cumulative progressions, i.e. by operations denoted in the text by r and s. This duality affords in a natural way the concept of an alternating arithmetic progression that deserves further studies. All these progressions can be identified with polynomials and very special, explicitly described, recursive progressions. The results mentioned here point to a very close relationship among a series of mathematical objects and to the importance of combinatorial numbers; they are presented in a form accessible to the graduates of secondary schools. -
Veranschaulichung der Lehrstoffstruktur durch Galois-Graphen
217-229Views:159In this article we compare the process diagram with the Galois-graph, the two hierarchical descriptions of the curriculum's construction from the point of didactics. We present the concrete example through the structure of convex quadrangles. As a result of the analysis it is proved that the process diagram is suitable for describing the activity of pupils, still the Galois-graph is the adequate model of the net of knowledge. The analysis also points out that in teaching of convex quadrangles the constructions of curriculum based only on property of symmetry and only on metrical property are coherent. Generalizing concept is prosperous if the pupils' existing net of knowledge lives on, at most it is amplified and completed. Teaching of convex quadrangles in Hungarian education adopts this principle.
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