Reasoning with Paper and Pencil: The Role of Inscriptions in Student Learning of Geometric Series

The purpose of this article is to analyse how students use inscriptions as tools for thinking and learning in mathematical problem-solving activities. The empirical context is that of learning about geometric series in a small group setting. What has been analysed is how students made use of inscriptions, self-made as well as those provided by text books and teachers, and the role these inscriptions played in the coordination of students' learning/communication. Through the use of inscriptions (made on the chalkboard and with paper and pencil), the students externalised their thinking while engaging in mathematical reasoning on the topic of geometric series. The inscriptions were significant as anchor points for arguments in the ongoing discussions. Three main issues are highlighted: (a) how the inscriptions used contribute to the process of appropriation, (b) how the students use inscriptions to externalise and clarify their ideas and attempts at meaning-making, and (c) how the inscriptions are conducive to closing the gap between the original problem as given in the text book and the mathematisation necessary. It is argued that inscriptions, through their material nature, play a decisive role in learning mathematical reasoning. (Contains 3 figures and 5 notes.)