Search

Search Results

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

  103-125

  Zoltán Paulovics

  Csaba Csapodi

  Zoltán Lóránt Nagy

  Views:

  0

  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

• Compositions of dilations and isometries in calculator-based dynamic geometry

  257-266

  Jack A. Carter

  Beverly J. Ferrucci

  Views:

  147

  In an exploratory study pre-service elementary school teachers constructed dilations and isometries for figures drawn and transformed using dynamic geometry on calculators. Observational and self assessments of the constructed images showed that the future teachers developed high levels of confidence in their abilities to construct compositions of the geometric transformations. Scores on follow-up assessment items indicated that the prospective teachers' levels of expertise corresponded to their levels of confidence. Conclusions indicated that dynamic geometry on the calculator was an appropriate technology, but one that required careful planning, to develop these future teachers' expertise with the compositions.

• On the psychology of mathematical problem solving by gifted students

  289-301

  Sandor M. Veres

  Views:

  186

  This paper examines the nature of mathematical problem solving from a psychological viewpoint as a sequence of mental steps. The scope is limited to solution processes for well defined problems, for instance, which occur at International Mathematical Olympiads. First the meta-mathematical background is outlined in order to present problem solving as a well defined search problem and hence as a discovery process. Solving problems is described as a sequence of elementary steps of the so called "relationship-vision" introduced here. Finally, non-procedural aspects of the psychology of problem solving are summarized, such as the role of persistence, teacher-pupil relationship, the amount of experience needed, self-confidence and inspiration at competitions.

• Die Stichprobe als ein Beispiel dafür, wie im Unterricht die klassische und die bayesianische Auffassung gleichzeitig dargestellt werden kann

  133-150

  Ödön Vancsó

  Views:

  167

  Teaching statistics and probability in the school is a new challenge of the Hungarian didactics. It means new tasks also for the teacher- and in service-teacher training. This paper contains an example to show how can be introduced the basic notion of the inference statistics, the point- and interval-estimation by an elementary problem of the public pole. There are two concurrent theories of the inference statistics the so called classical and the Bayesian Statistics. I would like to argue the importance of the simultaneously introduction of both methods making a comparison of the methods. The mathematical tool of our elementary model is combinatorial we use some important equations to reach our goal. The most important equation is proved by two different methods in the appendix of this paper.