Prof. Luis Radford - Laurentian University, Canada
On algebraic thinking
In this presentation I draw on the history of mathematics, semiotics, and mathematics education research to deal with the problem of elementary algebraic thinking. I suggest that two distinctive interrelated features of algebraic thinking are: (1) its peculiar way to deal with unknown quantities, and (2) the specific culturally and historically evolved modes of representing/symbolizing the unknown quantities and their operations. While the first feature refers to the analytic manner in which calculations are carried out with known and unknown quantities, the second feature refers to the constraints and affordances of the diverse semiotic systems (e.g., pre-alphanumeric, alphanumeric, graphic) through which unknown quantities are conceptualized and represented. These two distinctive features of algebraic thinking allow us to better understand the students’ legendary difficulties in the learning of algebra and provide us with clues to tackle the specifics of task design. Some videotaped classroom excerpts will serve to illustrate the main ideas of the presentation.