Articles

• Should we draw, or should we work with numbers? Investigating proportional reasoning among 5th to 7th graders

  1-28

  Ildikó Bereczki

  Csaba Csíkos

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  Proportional reasoning is an essential component of our everyday life and our mathematics studies. The rate of development in this area varies between age groups. In order to find out the level of students in Grades 5–7, we developed an online test. We consider it important to emphasize and support the use of visual representations in this subject, and therefore the tasks of the test on the eDia (Csapó & Molnár, 2019) interface have three types of input and output.We distinguish between ratios represented visually in the form of discrete quantities, ratios represented visually in the form of continuous quantities and ratios represented by text or numbers. Our study aimed to explore the differences between task types. Results indicate a representation-dependent developmental shift: in Grades 5–6, students perform best on tasks involving visual discrete quantities, whereas in Grade 7, performance increases markedly on text-text tasks. This suggests that visual representations function as an early scaffold, while later instruction strengthens symbolic processing.

  Subject Classification: Primary: 97C30; Secondary: 97D40, 97D60

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• Removing the burden of syntax: developing computational thinking and algorithmic skills of STEM students

  29-49

  Ádám Gulácsi

  Maria Csernoch

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  In higher education, solving programming exercises using a high-level programming language is a standard approach for developing computational thinking and algorithmic skills. However, this method has its limitations: learning the syntax of a high-level programming language puts an extra cognitive load on students, preventing them from focusing on problem-solving. Furthermore, computational thinking is not limited to programming: STEM students can benefit more from solving problems within their own discipline, in different environments. This practical article proposes a collection of unplugged, semi-unplugged and plugged-in alternatives that can be used to develop the computational thinking and algorithmic skills of students.

  Subject Classification: 97P99

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• Effect of social aspects of the classroom climate on Grades 3–6 students’ perceptions of the emotional classroom climate in primary school mathematics lessons

  51-76

  Ana Kuzle

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  Current research efforts highlight the significance of the social climate in the classroom. This climate influences not only students’ academic performance, motivation, engagement, and participation, but also their perception of the emotional classroom climate. However, little attention has been given to the effects of the various social aspects of the classroom climate on students’ perceptions of the emotional classroom climate. The present study addressed this gap by investigating aspects of the social classroom climate as possible explanatory factors of a positive, negative or ambivalent students’ perception of the emotional classroom climate in Grades 3–6 mathematics lessons. The secondary analysis of participant-produced drawings revealed that in drawings depicting a positive emotional classroom climate, the teacher provided assistance and made the lesson goals clear. Furthermore, the students talked to each other about mathematics. Conversely, in drawings depicting a negative emotional classroom climate, the teacher made behavioral requests, and negative student-student communication was present. Both the working method and the classroom seating arrangement did not seem to affect the perceived emotional classroom climate. The results are discussed in terms of their theoretical, and practical implications.

  Subject Classification: 97C20

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• Discovery as culture, not template: lessons from Hungary

  77-102

  Keren Dror

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  In this study, I investigate the structural adaptations necessary to implement Hungarian-style guided discovery in mainstream secondary school classrooms. During a six-week residency in Budapest, I observed classrooms, interviewed five Hungarian educators, and collected survey and interview data from students. My findings suggest that guided discovery in Hungary is less a fixed method and more a pedagogical culture, shaped by shared values, historical influences, and professional communities. While Hungarian educators praised its ability to foster deep thinking, student agency, and creativity, they also described challenges around pacing, assessment, and curriculum alignment. Structural supports such as flexible curriculum frameworks, professional networks, and differentiated assessment practices emerged as critical enablers of the method’s success. Student responses revealed both the promise of discovery-based instruction and the pressures it can create without sufficient scaffolding. I conclude that Hungarian-style guided discovery is not best understood as a replicable model, but as a set of values that evolve through professional dialogue and trial-and-error. Its meaningful implementation depends not on uniform procedures, but on the presence of cultural, institutional, and community structures that allow teachers to make it their own.

  Subject Classification: 97D40, 97D50, 97C30

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• Error analysis in teaching combinatorics: the development of prospective teachers’ confidence and problem-solving skills

  103-125

  Zoltán Paulovics

  Csaba Csapodi

  Zoltán Lóránt Nagy

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  This study investigates the pedagogical potential of error analysis in the teaching of combinatorics within mathematics teacher education. Building on previous research that highlights the role of incorrectly worked sample solutions in cognitive, metacognitive, and affective learning processes, we conducted a mixed-methods study with prospective mathematics teachers at Eötvös Loránd University. Quantitative results from Likert-scale questionnaires (n = 26) indicate that regular analysis of incorrectly worked solutions substantially enhanced participants’ self-confidence, strengthened their problem-solving skills, and positively shaped their attitudes toward future teaching practice. Complementary qualitative data, analyzed through grounded theory, revealed five interrelated categories – self-reflection and confidence, discernment, deeper understanding, methodological surplus, and combinatorial surplus – that together explain the mechanisms through which error analysis supports professional growth. The findings suggest that systematic analysis of conceptual errors not only improves problem-solving competence but also fosters self-confidence, self-reflection, and teaching-related attitudes. By comparing our emergent model of error-analysis thinking with Schoenfeld’s problem-solving framework, we argue that “discernment” constitutes a distinctive and central dimension of error-based learning. The study contributes both theoretically, by refining models of mathematical problem solving, and practically, by offering concrete recommendations for integrating error analysis into mathematics teacher education curricula.

  Subject Classification: 97C30, 97K20, 97D40, 97C70, 97C99

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• MTR framework for teaching model-based testing

  127-144

  Gábor Árpád Németh

  Máté István Lugosi

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  In the current article, it is presented how Model ≫ Test ≫ Relax (MTR), a free and open-source, extended finite state machine model-based testing framework can be used for education purposes. With the education-related features of MTR – such as graph visualizations, subsequence creation, test suite export – the students are able to understand the concept behind model-based testing, the working of different model conversion and test generation algorithms. With project works, the students use the MTR framework for the automatic test design of a simplified, small scale realworld example. The framework also provides a simulation script for comparing the complexities and fault detection capabilities of different test generation algorithms.

  Subject Classification: 68M15

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