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• The use of different representations in teaching algebra, 9 th grade (14-15 years old)

  29-42

  Eszter Árokszállási

  Views:

  136

  Learning 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.

• Conversion between different symbolic representations of rational numbers among 9th-grade students

  29-45

  Gábor Torma

  József Kosztolányi

  Views:

  197

  Our 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

• Cooperative learning in teaching mathematics: the case of addition and subtraction of integers

  117-136

  Ileana Mate

  Views:

  103

  In the course of teaching and learning mathematics, many of the problems are caused by the operations with integers. My paper is a presentation of an experiment by which I tried to make the acquisition of these operations easier through the use of cooperative methods and representations. The experiment was conducted in The Lower-Secondary School of Paptamási from Romania, in the school year 2009-2010. I present the results of the experiment.

• Illustrated analysis of Rule of Four using Maple

  383-404

  György Maróti

  Views:

  107

  Rule 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.