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RESEARCH PRODUCT

Reasoning with paper and pencil: The role of inscriptions in student learning of geometric series

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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. This study is an attempt to document and analyse how students are using inscriptions in reasoning and learning about geometric series. Following a sociocultural perspective on learning and development (Rogoff, 1990; Saljo, 2005; Wertsch, 1998), it is important to study students’ actions and use of artifacts in problem-solving settings to gain insight into how they appropriate mathematical concepts and modes of reasoning. The focus of the present study is on how students rely on and use the specific type of cultural tools that we refer to as inscriptions when engaging in mathematical problem solving. Inscriptions are understood as artifacts such as graphs, drawings, and mathematical symbols used for cognitive, communicative, mathematical, and problem-solving purposes in interactional settings1. The inscriptions may appear in text books, they may be made by the teacher for instructional purposes, or they may be self-made by learners while engaging in problem solving.