Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning

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.