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  • Solution of an open reality based word-problem in two secondary schools
    143-156
    Views:
    78

    This survey through an open reality based word problem is intended to assess - in two secondary schools in Komárom (Hungary) and in Komarno (Slovakia, Hungarian name: Révkomárom) in grade 10 - the ability of students to realize openness of a task. The comparison is justified by the fact that the language of teaching is Hungarian in both secondary schools, but with different curricula. This survey is related to the Content Pedagogy Research Program by the Hungarian Academy of Sciences. It is preceded by several surveys with a word problem (Pocket Money) of the third author and led by her between 2012 and 2015, and within that project in 2017 within a large sample test, among about 1500 students and university students in Hungary (?, ?) (?, ?). In our research we wanted first to assess how openly work students in two schools of the two cities mentioned in solving the same task. The answer to this question was similar to the large sample test results, so most of the students worked in a closed way, when solving this word problem. So we went on and tried to explore how students thought about their own solution given to this task, through mixed-type interviews.

    Subject Classification: 97D70, 97F90, 97D50, 97M10

  • How do secondary school students from the Kurdistan Region of Iraq understand the concept of function?
    221-244
    Views:
    100

    The study investigates secondary school students' understanding of the concept of function. The paper focuses on three main aspects: students' ability to define the concept of function; students' ability to recognize different representations of function; and students' ability to convert between different representations. A test was developed to assess the three main constructs of the study and administered to 342 students in secondary schools in the Kurdistan Region of Iraq. According to the results, students have diffculties in recognizing different representations of function and conversion between them. Connections between different parts of the test may provide hints on educational challenges of how to appropriately teach functions.

    Subject Classification: 26Bxx, 97D60

  • Square root in secondary school
    59-72
    Views:
    71

    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

  • An examination of descriptive statistical knowledge of 12th-grade secondary school students - comparing and analysing their answers to closed and open questions
    63-81
    Views:
    33

    In this article, we examine the conceptual knowledge of 12th-grade students in the field of descriptive statistics (hereafter statistics), how their knowledge is aligned with the output requirements, and how they can apply their conceptual knowledge in terms of means, graphs, and dispersion indicators. What is the proportion and the result of their answers to (semi-)open questions for which they have the necessary conceptual knowledge, but which they encounter less frequently (or not at all) in the classroom and during questioning? In spring 2020, before the outbreak of the pandemic in Hungary, a traditional-classroom, “paper-based” survey was conducted with 159 graduating students and their teachers from 3 secondary schools. According to the results of the survey, the majority of students have no difficulties in solving the type of tasks included in the final exam. Solving more complex, open-ended tasks with longer texts is more challenging, despite having all the tools to solve them, based on their conceptual knowledge and comprehension skills. A valuable supplement to the analysis and interpretation of the results is the student attitudes test, also included in the questionnaire.

    Subject Classification: 97K40, 97-11, 97D60

  • The tools for developing a spatial geometric approach
    207-216
    Views:
    31

    Tamás Varga writes about the use of tools: "The rational use of tools - the colored bars, the Dienes set, the logical set, the geoboard, and some other tools - is an element of our experiment that is important for all students, but especially for disadvantaged learners." (Varga T. 1977) The range of tools that can be used well in teaching has grown significantly over the years. This paper compares spatial geometric modeling kits. Tamás Varga uses the possibilities of the Babylon building set available in Hungary in the 1970s, collects space and flat geometry problems for this (Varga T. 1973). Similarly, structured kits with significantly more options have been developed later, e.g. ZomeTool and 4D Frame. These tools are regularly used in the programs of the International Experience Workshop (http://www.elmenymuhely.-hu/?lang=en). Teachers, schools that have become familiar with the versatile possibilities of these sets, use them often in the optional and regular classes. We recorded a lesson on video where secondary students worked with the 4D Frame kit. We make some comments and offer some thoughts on this lesson.

    Subject Classification: 97G40, 97D40

  • Some Pythagorean type equations concerning arithmetic functions
    157-179
    Views:
    39

    We investigate some equations involving the number of divisors d(n); the sum of divisors σ(n); Euler's totient function ϕ(n); the number of distinct prime factors ω(n); and the number of all prime factors (counted with multiplicity) Ω(n). The first part deals with equation f(xy) + f(xz) = f(yz). In the second part, as an analogy to x2 + y2 = z2, we study equation f(x2) + f(y2) = f(z2) and its generalization to higher degrees and more terms. We use just elementary methods and basic facts about the above functions and indicate why and how to discuss this topic in group study sessions or special maths classes of secondary schools in the framework of inquiry based learning.

    Subject Classification: 97F60, 11A25

  • A computational thinking problem-thread for grade 7 students and above from the Pósa method
    101-110
    Views:
    65

    Lajos Pósa has been developing his “learning through discovery” (Győri & Juhász, 2018) method since 1988. His weekend math camps are focused on fostering problem-solving skills and high-level mathematical-thinking skills in gifted students from grades 7 to 11. One of the core aspects of the method is the structure of the problems, all problems are part of a complex, intertwined, and rich network. In this article we analyze a computational thinking problem-thread and its role in the camps’s network of problems (Gosztonyi, 2019), and show some aspects of the method. The insights gained using this method can be useful in other contexts. The possible adaptation of the method to secondary and high schools is briefly discussed as well.

    Subject Classification: 97D40