What’s there in an n? Investigating contextual resources in small group discussions concerning an algebraic expression
Elisabeth Rystedt, Cecilia Kilhamn and Ola Helenius
This small-case study combines a content related and a dialogical approach, in an in-depth analysis of how three 12-year-old pupils in a video recorded small group discussion construe the meaning of the letter n in an algebraic expression. The findings indicate that the pupils used a rich variety of contextual resources in their sensemaking attempt. They also tried out a wide range of interpretations of the letter indicating that their conception of an algebraic letter was rich but unstable and that the dialogue was instrumental in helping them move from primitive to more advanced interpretations. In addition to previously known difficulties of understanding letters as variables, we found that the meaning of the communicative convention ”expressed in n” proved an obstacle, and conclude that learning mathematics is as much about learning a specific communicative genre as learning about mathematical objects and relationships.
Elisabeth Rystedt got a licentiate degree in September 2015 and this article is a part of her thesis. As a PhD student she was a member of the The Graduate Research School in Educational Sciences at the University of Gothenburg. Today she is working 50% at the National Center for Mathematics Education (NCM) and 50 % as a teacher educator at the University of Gothenburg. Her research interest concerns how pupils understand introductory algebra.
Cecilia Kilhamn is a Dr of Philosophy in Mathematics Education and works as a lecturer and teacher educator at the University of Gothenburg. She is also a mathematics education researcher with an interest in classroom research in primary and lower secondary school.
Ola Helenius has PhD in mathematics and is a researcher and deputy director at the National Centre for Mathematics Education at the University of Gothenburg. Some of his current research interests include neuroscience perspectives on learning mathematics, socio-cultural perspectives on preschool mathematics and mathematics curriculum design research.