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Task reformulation as a practical tool for formation of electronic digest of tasks
1-27Views:154Creative thinking as well as thinking itself is being developed at active learning-cognitive activity of students. To make mathematic matter a subject of interest and work of students at classes, it is efficacious to submit it in a form of tasks. The tasks may be set up in a purposeful system of tasks by means of which reaching the teaching goals in the sense of quality and durability of gained knowledge may be more effective. A suitable means for presentation of tasks with their characteristics (as e.g. didactic function and cognitive level) as well as task systems themselves is an electronic digest of tasks as a database. The analysis of textbooks and digests of tasks commonly used at schools in Slovakia shows that they do not include all the types of tasks necessary for setting up complete (in the sense of didactic functions) task systems. One of the most important methods used for formation of the missing tasks is reformulation of tasks. The individual strategies of task reformulation are explained in details on examples in this article. -
Examining continuity/discontinuity of a function by using GeoGebra
241-257Views:199The possibility to visualize the things with the help of today's dynamic software (GeoGebra being one of them), enables the students to see and explore mathematical relations and concepts that were difficult to be presented in the past, prior to the state-of-the-art technologies. In methodological sense, the contribution of this paper lies in the presentation of a set of visualizations designed to help students better understand and explore the basic calculus concepts such as continuity at a point, to examine discontinuity at a point, to display discontinuities and the relations between continuity and differentiability of single variable functions. In technical sense, this paper presents creative GeoGebra applets which offer new possibilities that could be of a vital importance for the future development of e-learning of College mathematics. -
Comparative geometry on plane and sphere: didactical impressions
81-101Views:65Description of experiences in teaching comparative geometry for prospective teachers of primary schools. We focus on examples that refer to changes in our students' thinking, in their mathematical knowledge and their learning and teaching attitudes. At the beginning, we expected from our students familiarity with the basics of the geographic coordinate system, such as North and South Poles, Equator, latitudes and longitudes. Spherical trigonometry was not dealt with in the whole project. -
Teaching model-based testing
1-17Views:1832Different testing methodologies should play an important role in the education of informatics. In the model-based testing (MBT) approach, the specification of the system is described with a formal model. This model can be used to revise the correctness of the specification and as a starting point for automatic test generation. The main problem with MBT is however, that there is a huge gap between theory and practice and that this approach has a high learning curve. To cope with these problems, current paper shows, how the MBT approach can be introduced to students through a small scale example.
Subject Classification: P50
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"Upperview" algorithm design in teaching computer science in high schools
221-240Views:156In this paper we are going to present a teaching/learning method and suggest a syllabus that help the high school students look at the algorithm design strategies from a so called "upperview": greedy, backtracking, divide and conquer, dynamic programming. The goal of the suggested syllabus is, beyond the presentation of the techniques, to offer the students a view that reveals them the basic and even the slight principal differences and similarities between the strategies. In consensus with the Comenius principle this is essential, if we want to master this field of programming ("To teach means scarcely anything more than to show how things differ from one another in their different purposes, forms, and origins. ... Therefore, he who differentiates well teaches well."). -
Mapping students’ motivation in a problem oriented mathematics classroom
111-121Views:230This research focuses on mapping students’ motivation by implementing problem-solving activities, namely how the problem-oriented approach affects the students’ commitment, motivation, and attitude to learning. As a practicing teacher, the author faced difficulties with motivation and sought to improve her practice in the form of action research as described in this paper. Based on the literature, the author describes sources of motivation as task interest, social environment, opportunity to discover, knowing why, using objects, and helping others. The author discusses the effect of problem-oriented teaching on the motivation of 7th-grade students. In this paper, the results of two lessons are presented.
Subject Classification: 97C20, 97D40, 97D50, 97D60
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Differentiated instruction not only for Mathematics teachers
163-182Views:299The aim of differentiated development in a heterogeneous group of learners (DDHG) is to reduce school leaving without education, using an adaptive and innovative teaching-learning environment and using the most effective strategies, methods and techniques. Furthermore, this strategy helps in developing skills for learners and building cooperation between learners in heterogeneous classes through the use of the special, status-management educational procedure, and finally its strength is to sort the status ranking among learners, and to change the social structure of the class. Our goal is to figure out how to share best practices with teachers. One of the effective ways to renew teaching practice is through further training for teachers. As a trainer of the Logic-based subprogram of the Complex Basic Program (CBP) the author of the paper has experienced how well logic-based and decision-making strategies work in other subjects as well as in mathematics.
Subject Classification: 97D40
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New style in teaching word processing
417-426Views:135Teaching word processing is confined to looking through some menus and showing some functions of a word processor program, although technology presents just a small part of forming layouts. This fact causes that people who are writing documents spend a lot of time by trying to form, e.g., title pages or inner pages.
The present paper deals with a design of an online course on word processing that fits better the needs of many users. The online course is designed for teaching (LA)TEX by leading the students to the technical issues of the typesetting system through layout and grammar rules: demonstrates the most important basic recommendations of typography and grammar rules through samples, and shows how to program the currently displayed layout in the (LA)TEX programming languages. This methodology suits better the common working habit, and can be a useful help in word processing documents. -
Supporting the theory of math didactic using knowledge-measuring questions and analysis of the solutions
1-16Views:191New or rediscovered results presented in this paper are the results of the analysis of the problem sets used in the two-tier system secondary school final examination in mathematics, a system that was introduced in Hungary in 2005.
Many of the revealed problem arise in connection with misunderstanding the text of the problems. Causes of misinterpretation can be either that the text is lacking some important information, or that it should be interpreted not in word-to-word manner.
Theses and their argumentations presented here refer partly on the new types of problems (tests, non-standard mathematical contents), and partly on improvement of learning-teaching process in topics of equations and approximations. -
Forming the concept of parameter with examples of problem solving
201-215Views:153Pupils 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. -
The use of different representations in teaching algebra, 9 th grade (14-15 years old)
29-42Views:167Learning Algebra causes many difficulties for students. For most of them Algebra means rote memorizing and applying several rules without understanding them which is a great danger in teaching Algebra. Using only symbolic representations and neglecting the enactive and iconic ones is a great danger in teaching Algebra, too. The latter two have a primary importance for average students.
In our study, we report about an action research carried out in a grade 9 class in a secondary school in Hungary.The results show that the use of enactive and iconic representations in algebra teaching develops the students' applicable knowledge, their problem solving knowledge and their problem solving ability. -
Constructing the disk method formula for the volume obtained by revolving a curve around an axis with the help of CAS
363-376Views:163Calculus 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. -
Overview of the accessibility of webpages, related research, advantages, guidelines and recommendation
233-262Views:212The essay aims to provide a survey of web accessibility, introduce the relevant research results along with describing the advantages of obstacle free webpages. Furthermore, I will attempt to promote the awareness of the significance of accessibility and equal access to information in case of educational webpages especially in the higher education sphere. My primary audience are educational policy makers and leaders of higher education institutions along with in-service teachers who regularly use webpages during their daily work with students struggling with various impairments. The article's focus is expanded onto the relevant professional and legal background, the most important accessibility principles in addition to discussing the tools assuring accessibility and the presentation of best practices for web developers elaborating the electronic learning environments for higher education institutions. -
Maximum and minimum problems in secondary school education
81-98Views:191The aim of this paper is to offer some possible ways of solving extreme value problems by elementary methods with which the generally available method of differential calculus can be avoided. We line up some problems which can be solved by the usage of these elementary methods in secondary school education. The importance of the extremum problems is ignored in the regular curriculum; however they are in the main stream of competition problems – therefore they are useful tools in the selection and development of talented students. The extremum problem-solving by elementary methods means the replacement of the methods of differential calculus (which are quite stereotyped) by the elementary methods collected from different fields of Mathematics, such as elementary inequalities between geometric, arithmetic and square means, the codomain of the quadratic and trigonometric functions, etc. In the first part we show some patterns that students can imitate in solving similar problems. These patterns could also provide some ideas for Hungarian teachers on how to introduce this topic in their practice. In the second part we discuss the results of a survey carried out in two secondary schools and we formulate our conclusion concerning the improvement of students' performance in solving these kind of problems. -
Mathematical gems of Debrecen old mathematical textbooks from the 16-18th centuries
73-110Views:102In the Great Library of the Debrecen Reformed College (Hungary) we find a lot of old mathematical textbooks. We present: Arithmetic of Debrecen (1577), Maróthi's Arithmetic (1743), Hatvani's introductio (1757), Karacs's Figurae Geometricae (1788), Segner's Anfangsgründe (1764) and Mayer's Mathematischer Atlas (1745). These old mathematical textbooks let us know facts about real life of the 16-18th centuries, the contemporary level of sciences, learning and teaching methods. They are rich sources of motivation in the teaching of mathematics. -
Some problems of solving linear equation with fractions
339-351Views:184The 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. -
Interdisciplinary Secondary-School Workshop: Physics and Statistics
179-194Views:169The paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing.
Subject Classification: F90, K90, M50, R30
