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Teaching of financial mathematics using Maple
289-301Views:210The paper deals with the application of computer algebra system Maple in teaching of financial mathematics. In the Czech Republic financial mathematics is included in the curricula of grammar and secondary school. Therefore, this subject is also taught at pedagogical faculties. Most concepts of financial mathematics are difficult to understand for students. In the paper we show the ways of facilitation understanding these concepts using tools of Maple. The main result is in preparing special maplets which enable interactive studying of the principles of such concepts. Each of these maplets deals with particular financial problem from real life, e.g. mortgage credit, consumer credit, credit card etc. -
Teaching centroids in theory and in practice
67-88Views:212The main aim of this paper is to present an inquiry-based professional development activity about the teaching of centroids and to highlight some common misconceptions related to centroids. The second aim is to emphasize a major hindering factor in planning inquiry based teaching/learning activities connected with abstract mathematical notions. Our basic problem was to determine the centroid of simple systems such as: systems of collinear points, arbitrary system of points, polygons, polygonal shapes. The only inconvenience was that we needed practical activities where students could validate their findings and calculations with simple tools. At this point we faced the following situation: we have an abstract definition for the centroid of a finite system of points, while in practice we don't even have such systems. The same is valid for geometric objects like triangles, polygons. In practice we have triangular objects, polygonal shapes (domains) and not triangles, polygons. Thus in practice for validating the centroid of a system formed by 4,5,... points we also need the centroid of a polygonal shape, formed by an infinite number of points. We could use, of course, basic definitions, but our intention was to organize inquiry based learning activities, where students can understand fundamental concepts and properties before defining them. -
The background of students' performance
295-305Views:122The question to which we were seeking was: how can we reveal the students' strategies and mental process by following their work precisely and by finding out what correlation these have with their efficiency. Our aim was to understand the factors behind of students' achievement. We tried to follow up the process of problem solving by looking at the number of wrong turnings. -
Examining relation between talent and competence through an experiment among 11th grade students
17-34Views:151The areas of competencies that are formable, that are to be formed and developed by teaching mathematics are well-usable in recognizing talent. We can examine the competencies of a student, we can examine the competencies required to solve a certain exercise, or what competencies an exercise improves.
I studied two exercises of a test taken by students of the IT specialty segment of class 11.d of Jedlik Ányos High School, a class that I teach. These exercises were parts of the thematic unit of Combinatorics and Graph Theory. I analysed what competencies a gifted student has, and what competencies I need to improve while teaching mathematics. I summarized my experience about the solutions of the students, the ways I can take care of the gifted students, and what to do to the less gifted ones. -
Examples of analogies and generalizations in synthetic geometry
19-39Views:114Teaching tools and different methods of generalizations and analogies are often used at different levels of education. Starting with primary grades, the students can be guided through simple aspects of collateral development of their studies. In middle school, high school and especially in entry-level courses in higher education, the extension of logical tools are possible and indicated.
In this article, the authors present an example of generalization and then of building the analogy in 3-D space for a given synthetic geometric problem in 2-D.
The idea can be followed, extended and developed further by teachers and students as well. -
Interactive web portals in mathematics
347-361Views:212Many of the recent problems in higher education (less contact seminars, the heterogeneity and the increasing number of our students) call for new instructional methods. At University of Szeged we have developed a mathematical web portal which can offer a solution for such problems among the changing circumstances. This freely available, easy-to-use web-surface supports interactive mathematical problem-solving and student self assessment. Our computer program cooperates with a lot of free software (computer algebra systems, formula parsers, converters, word processors). WebMathematics Interactive has been available for the public since June 2002 on its web page http://wmi.math.u-szeged.hu. -
Consequences of a virtual encounter with George Pólya
173-182Views:200The consequences of a virtual encounter with George Pólya as a teacher are recorded. An instance of his influence on my mathematical thinking is recounted through work on one of the problems in one of his books.
Subject Classification: 01A99, 11A05, 97-03, 97D50
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Conversion between different symbolic representations of rational numbers among 9th-grade students
29-45Views:288Our research involved nearly 800 ninth-grade secondary school students (aged 14-15) during the first weeks of the 2023/2024 school year. Less than 40% of students solved the text problems related to common fractions and percentages correctly. In terms of student solutions, pupils showed a higher success rate when the text of the problem contained common fractions, and the solution had to be given as a percentage. In this case, the success rate of switching between different symbolic representations of rational numbers (common fraction, percentage) was also higher. Observation of the methods used to solve also suggests that the majority of students are not flexible enough when it comes to switching between different representations.
Subject Classification: 97F80, 97D70
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Synthesis of concurrent programs
301-317Views:86Students 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. -
CALIBRATE and CAS/DGS resources
267-279Views:105The CALIBRATE project was initiated by the EU with the goal of expanding the use of ICT in education by increasing the amount of available learning resources via resource exchange. Although CAS/DGS can be used to easily create high quality learning resources which are also easily adaptable across national boundaries, such resources are difficult to find at CALIBRATE portals. We believe that this is due to CAS/DGS still being rather exotic to most of the people as well as with the common problem of finding existing appropriate resources. A possible solution is for CALIBRATE portals to properly equip existing and forthcoming CAS/DGS resources with suitable metadata and to provide some integration with CAS/DGS tools, enabling both beginners and power users to create and exchange CAS/DGS resources. -
Fostering engineering freshmen’s shifts of attention by using Matlab LiveScript for solving mathematical tasks
1-14Views:241We designed an experimental path including a summative assessment phase, where engineering freshmen are involved in solving mathematical tasks by using Matlab LiveScripts. We analyzed the students’ answers to a questionnaire about their perceived impact of the use of Matlab on their way to solve mathematical tasks. The main result is that students show shifts of attention from computations to other aspects of problem solving, moving from an operational to a structural view of mathematics.
Subject Classification: 97U70, 97H60
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