Strategies for mental solving of graphic tasks with functions, 3rd Lyceum students: Content analysis strategy of interviews with Data Analysis methods

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Published: Apr 22, 2024
Keywords:
Mental Mathematics Functions Solving Strategies Flexibility Correspondence Analysis Hierarchical Cluster Analysis Biplot Analysis Kriging Interpolation
Nikolaos Papafilippou
Aristotle University of Thessaloniki
https://orcid.org/0009-0003-3148-7229
Thomas Koutsos
Aristotle University of Thessaloniki
Angelos Markos
Democritus University of Thrace
George Menexes
Aristotle University of Thessaloniki
Abstract

In this study, a methodological scheme for using Data Analysis methods (AFC, HCA, Biplot Analysis, Kriging Interpolation) is presented and proposed for the processing of speech data, which were collected through a clinical interview from 42 3rd grade Lyceum students, regarding their responses to nine graphs of two functions (linear-constant or quadratic-constant or two-linear) and was asked to find mentally the result of their sum or difference. The analysis of the findings showed that the students, during the mental solution of tasks with functions, sometimes developed algebraic/parametric strategies, sometimes graphical/geometric and sometimes graphical/numerical or a combination of these. According to the main results of the work, the choice of strategy depends both on the characteristics of the student (knowledge, preferences, experience) and the nature of the task. In tasks with linear functions, the students chose point-by-point approaches, algebraic-numerical or a combination thereof, while in tasks with curves they chose holistic approaches, graphic-geometric. Also, students with better math performance showed a greater degree of flexibility in the strategies they used and had more success. Through AFC was highlighted, the contrast between the point-by-point approaches, algebraic-numerical strategies and the holistic approaches, graphic-geometric, as well as the contrast between the combined graphic/geometric-graphic/numerical and graphic/geometric-algebraic/parametric strategies. Ordinary Kriging spatial interpolation method was used to estimate and present the students' success rates in the strategies and the result of the interpolation in the form of a contour map was projected to the factorial level of the AFC.

Article Details
  • Section
  • Empirical studies
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