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Examples of using new interactive technologies for filling the gaps in students knowledge

Ratusiński T., Kucio M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2011

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Vol. 16

313--320

EN

Many changes in the curriculum of mathematics have been made during a few last years. Frequent changes carry certain consequences. Pupils which finish high school may possess different knowledge in different years. This is because they may have various ranges of educational material (different from those of their older or younger colleagues). Additionally, some parts of school mathematical material are more difficult to learn than others. Unfortunately, sometimes teachers tend to treat them cursorily. The planimetry is such a specific field of mathematics which requires specific thinking and analysis. It is necessary to reduce such differences in knowledge and skills, to supplement lacks of knowledge of students of the first year mathematics study. It is necessary to use the suitable tools to do this quickly and effective. Utilization of interactive GeoGebra based simulations and visualizations may be helpful in such a situation. Perfect co-operation with the interactive white board and possibility of delivering didactic materials by Internet are their additional advantage. We will show examples of such materials relating to similarities in our presentation. They are a part of developing project - the course of geometrical transformations on the plane. It is addressed to students of the first year of mathematics study. However, these materials can be used at high school level during additional activities according to pupils interests.

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From mirror reflection to the concept of line symmetry on the plane

Jagoda E.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2007

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Vol. 12

233-243

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Próba zastosowania technologii informacyjnej na lekcjach matematyki w gimnazjum

Makiewicz M.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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2001

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z. 25 [190]

91-104

EN

This article presents the advantages of applying Information Technology in the work of a mathematics teacher in gymnasium. It distinguishes seven different types of computer software useful in solving maths problems. It combiningcontent of syllabus of "Mathematics 2001" with modern Information Technology in developing students' skills.

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The shadows

Cihlář J

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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1998

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Vol. 4

34-40

EN

In my short lecture I would like so sell you a few words about my experiences from experiments, in which I and my colleagues were interested in possibilities of the progress of lower secondary school pupils space-vision. Especially I would like to point out the method, were we use the theme of shadows. This theme was ordered into the didactical sequence of problems, some of them I will present there.

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Realistic Approach Towards Mathematics Teaching

Melichar J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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1998

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Vol. 4

58-62

EN

Currently four possible approaches are being presented in the methodology of mathematics teaching: 1. Mechanical - The mechanical approach towards teaching corresponds with understanding the teaching as a system of reactions. By means of drill we can programme the pupil as a computer towards exercising arithmetic, algebraic and geometrical operations and solving problems which can be classified according to certain signs and solved further according to certain patterns. 2. Structuralistic - The structuralistic approach towards teaching can l demonstrated by two examples: the traditional geometry organize on a basis of axiomatic construction and the so called modern mathematics based on a theory of sets and logic. For pupils a structured world of sets and relations has been created. 3. Empirical - The empirical approach comes out of the needs of practise and it is supposed to serve those needs. In the teaching process the experience of the pupils is used, but the pupils are not lead to systematic and rational utilization of this experience. 4. Realistic - The real stimuli from the constantly enlarging world oi the pupil are used as well. The pupil becomes a re-discoverer oi mathematics which stimulates and develops his ability. The realistic mathematics education (RME) comes out of the principle that teaching mathematics means constructing mathematics by the own steps of the pupils from informal approaches connected with reality towards something acceptable as formal mathematics.

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Investigation of routes on various grids

Kopka J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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1998

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Vol. 4

49-62

EN

Problems in the curriculum have existed since ancient times, if not earlier. For example, an Egyptian mathematical manuscript (the Ahmes Papyrus) consisting of a collection of problems, was written about 1650 B.C. This has not changed in nearly 4000 years. The central idea of problems has been a common to school mathematics historically and to school mathematics today. Traditionally, when we have spoken about problems we have meant word problems and especially so-called story problems. From our contemporary view, these are only one particular kind of problem. These are problems with the help of which we present pupils with a pseudo - real world. Through this type of problem we present students with a situation or a task and in the form of a question with a goal that the student must achieve. We can say that these are „goal - aimed" problems, or in contemporary terminology closed problems. We require that the student choose some previously learned algorithm (if he/she knows more than one), and with this perform a calculation. They are often placed at the end of a set of algorithmic exercises and with help of them we practise what we have just learned. In many countries today, as in our own, these problems are of central importance, and it is by solving such problems that we can assess the student. Here is a typical example of a story problem when we must calculate with fractions: Story problem: On a trip at the end of school year there were 25 pupils. 3/5 of them are girls. How many girls and how many boys participated in the trip? A great change occurred in the concept of the problem when we began to consider the relationship between the student and a problem. Reys et al. (1984) argued that „a problem involves a situation in which a person wants something and does not know immediately what to do to get it". In this explanation of a problem, it is very important that the pupil wants to achieve the goal. If for example, we give to our student the task of making a present for his/her mother for Mothers' Day, it is problem for him/her only if they want to do it (in this new approach).