Abstract
Various digital tools have been developed for different aspects of mathematics teaching and learning; however, classroom mathematical learning typically involves paper-and-pencil environments and incorporates other types of physical tools such as concrete manipulatives. Thus, to better integrate the use of digital tools into classrooms, it is crucial to examine the interrelated roles of digital and physical tools in enhancing students’ mathematical learning. In this chapter, we address this issue by examining mathematics education studies that employ or develop theoretical models to explore students’ intertwined use of physical and digital tools. We first consider some fundamental aspects of theoretical models and provide a brief overview of the literature in mathematics education, specifically the use of technology in mathematics learning. We then focus on three illustrative studies and summarize the major findings, namely: (i) the importance of certain kinds of continuities and discontinuities between physical and digital tools, (ii) the ongoing relevance of physical tools that have affordances complementary to those of digital tools, and (iii) the importance of task design and the teacher’s role. We conclude this chapter by suggesting productive directions for future studies, i.e., considering new digital tools and new theoretical perspectives.
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Notes
- 1.
The theory of didactical situation could potentially be beyond the domain-specific level because it has been extended to other fields of education.
- 2.
Although this classroom episode was originally not analyzed with these specific notations, we selected this episode because it provides a concise illustration of the analysis using these notations.
- 3.
This conjecture includes one exception, namely the case of n = 2; however, it seems that the students considered this conjecture for n > 2 as they examined x3–1, x4–1, and so on.
- 4.
The e-Pascaline was already created before the construction of the model depicted in Fig. 3, but the features of this model, e.g., the importance of continuities and discontinuities between tangible and digital artefacts, were considered from the outset of the development of the e-Pascaline (Maschietto and Soury-Lavergne 2013).
- 5.
The students were not familiar with the concept of the positive or negative size of an angle (i.e., anticlockwise or clockwise). In other words, they did not distinguish between ∠ABP and ∠PBA. Furthermore, in a Japanese context, the distinction between an angle and the size of the angle is often left unclear, and the term angle sometimes means the size of the angle. Thus, in this section, an angle also means the size of the angle in some cases.
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We would like to thank the section editors (Angelika Bikner-Ahsbahs and Heather Johnson) and anonymous reviewers for their comments that helped us improve this chapter.
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Komatsu, K., Fujita, T. (2023). Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning. In: Pepin, B., Gueudet, G., Choppin, J. (eds) Handbook of Digital Resources in Mathematics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-030-95060-6_9-1
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Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning- Published:
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DOI: https://doi.org/10.1007/978-3-030-95060-6_9-2
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Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning- Published:
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DOI: https://doi.org/10.1007/978-3-030-95060-6_9-1