## Vol. 17 No. 1 (2019)

Published July 4, 2019

## ##issue.tableOfContents##

### Articles

• ##### The transition problem in Hungary: curricular approach
1-16
Views:
99

The curricular background of the transition problem from highschool to universty is analysed in Hungary. While students finish their mathematical studies successfully at highschool, pass their final exams, this knowledge seems to disappear at their first year at university. We investigate the mathematical knowledge expected by the Hungarian universities and compare it to expectations of the National Core Curriculum. Based on the levelling tests of four universities we created a seven problem test for highschool students containing very basic problems required both by the universities and the National Core Curriculum. We analyse the results of the test.

Subject Classification: D34, D35

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191
• ##### "On the way" to the function concept - experiences of a teaching experiment
17-39
Views:
58

Knowing, comprehending and applying the function concept is essential not only from the aspect of dealing with mathematics but with several scientific fields such as engineering. Since most mathematical notions cannot be acquired in one step (Vinner, 1983) the development of the function concept is a long process, either. One of the goals of the process is evolving an "ideal" concept image (the image is interrelated with the definition of the concept). Such concept image plays an important role in solving problems of engineering. This study reports on the beginning of a research aiming the scholastic forming of the students' function concept image i.e. on the experiences of a "pilot" study. By the experiment, we are looking for the answer of the following question: how can the analysis of such function relations be built into the studied period (8th grade) of the evolving process of the function concept that students meet in everyday life and also in engineering life?

Subject Classification: D43, U73

• ##### Infimum problems derived from the proofs of some generalized Schwarz inequalities
41-57
Views:
52

We define f(a;b)(r) = ar + b/r for all a, b, r Є R with r > 0. And, for some subsets A of R, we determine FA_+ (a; b) = inf (r Є A_+) f(a,b) (r) ; where A_+ ={r Є A : r > 0}. The above in ma are mainly motivated by the proofs of some recent generalized Schwarz inequalities established by the present authors.

Subject Classification: I35

• ##### Square root in secondary school
59-72
Views:
91

Although in Hungary, for decades, the calculation method of the square root of a real number is not in the mathematics curriculum, many of the taught concepts and procedures can be carried out using different square root finding methods. These provide an opportunity for students in secondary school to practice and deepen understand the compulsory curriculum. This article presents seven square-root- nding methods, currently teachable in secondary schools.

Subject Classification: A33, A34, F53, F54

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100
• ##### Trigonometric identities via combinatorics
73-91
Views:
47

In this paper we consider the combinatorial approach of the multi-angle formulas sin nΘ and cos nΘ. We describe a simple "drawing rule" for deriving the formulas immediately. We recall some theoretical background, historical remarks, and show some topics that is connected to this problem, as Chebyshev polynomials, matching polynomials, Lucas polynomial sequences.

Subject Classification: 05A19

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137
• ##### Balanced areas in quadrilaterals - Anne's Theorem and its unknown origin
93-103
Views:
57

There are elegant and short ways to prove Anne's Theorem using analytical geometry. We found also geometrical proofs for one direction of the theorem. We do not know, how Anne came to his theorem and how he proved it (probably not analytically), it would be interesting to know. We give a geometric proof (both directions), mention some possibilities – in more details described in another paper – for using this topic in teaching situations, and mention some phenomena and theorems closely related to Anne's Theorem.

Subject Classification: G10, G30

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212
• ##### Report of Meeting Researches in Didactics of Mathematics and Computer Sciences: February 1-3, 2019 Stúrovo, Slovakia
105-129
Views:
129

The meeting Researches in Didactics of Mathematics and Computer Sciences was held in Sturovo, Slovakia from the 1st to the 3th of February, 2019. It was organized by the Doctoral School of Mathematical and Computational Sciences of University of Debrecen. The 63 participants – including 17 PhD students – came from 7 countries, 22 cities and represented 36 institutions of higher and secondary education. There were 4 plenary, 42 session talks and 7 poster presentations in the program.