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Classification and Mathematical Thinking: Tinkering with Classification Games in a Constructionist Environment

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Abstract

Classification is a complex process that involves scientific concepts and higher-order mental processes such as abstraction, generalization, and pattern recognition. Even though it is an important competence for understanding the world, dealing with data and information, and solving complex problems, the education system embeds just its simplest operations and only in very early schooling. This study examines six middle school students’ activities as they play, modify, and redesign two Tetris-like classification games on the mathematical concepts of number sets and angle in an online authoring system called Sor.B.E.T (Sorting Based on Educational Technology). The qualitative data analysis of students’ dialogues aimed to bring in the foreground the classification processes students applied and the way these processes were entangled with the development of meanings and ideas on the mathematical concepts embedded in the games. According to the results, the play and modding of the two classification games enabled the development of higher-order classification processes such as objects’ properties comparison, properties discrimination, and classes’ encapsulation. They also supported meaning-making processes and triggered discussions about abstract mathematical notions, such as the concept of angle in various typical mathematical or physical contexts and the concept of number sets, the boundaries of each one, and the relationships among them through exploration and learner-generated exemplification.

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Data Availability

The transcribed data of audio recordings and interviews have been decoded so that there are no data on student identity, and they are stored in secured servers of the NKUA. Parts of them can be provided after a request and a justification of use to the authors. The data are currently available in the Greek language, but parts can be translated if necessary.

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Acknowledgements

The Sor.B.E.T. application was designed by Prof. Kynigos, director of the Educational Technology Lab-NKUA. The prototype version of Sor.B.E.T. was developed by the Master student Eleftheria Giama as part of her Master’s thesis. The second version was developed with the contribution of the PhD student Maria-Stella Nikolaou and the post-doc researcher Marianthi Grizioti. We would also like to thank the PhD student Katia Schiza and the Master student Joanna Arampatzi for their contribution to the design of the two math games.

Funding

This research has received funding from the European Union’s Horizon Europe Framework Programme for Research and Innovation under the Grant Agreement No. 101060231 (Exten.D.T.2 - Extending Design Thinking with Emerging Digital Technologies)

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Authors and Affiliations

  1. Educational Technology Lab, Department of Educational Studies, School of Philosophy, National and Kapodistrian University of Athens, Athens, Greece

    Chronis Kynigos, Marianthi Grizioti & Maria Latsi

Authors
  1. Chronis Kynigos
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  2. Marianthi Grizioti
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  3. Maria Latsi
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Contributions

The authors confirm contribution to the paper as follows: study conception and design: Chronis Kynigos; study implementation and data collection: Marianthi Grizioti, Maria Latsi; analysis and interpretation of results: Marianthi Grizioti, Chronis Kynigos; draft manuscript preparation: Chronis Kynigos, Marianthi Grizioti, Maria Latsi. All authors reviewed the results, made suggestions and modifications, and approved the final version of the manuscript.

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Correspondence to Chronis Kynigos.

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There is no conflict of interest in the current research. The software (SorBET) that is used is open source and freely available.

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Kynigos, C., Grizioti, M. & Latsi, M. Classification and Mathematical Thinking: Tinkering with Classification Games in a Constructionist Environment. Digit Exp Math Educ 9, 508–529 (2023). https://doi.org/10.1007/s40751-023-00131-8

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