| This thesis presents a situation-theoretic account of middle school students' working with linear functions. To that end, the formal apparatus of situation logic was employed to describe a pair of students' stepwise progression through a series of tasks that required them to create the mathematical representations of a table, an equation, and a graph to describe a real-world situation in front of them. Students were videotaped; the transcription of the videos of their interaction forms the basis of the analysis. The thesis is concerned with the reference relations students established in their work, as well as the constraining relations which enable information flow between the different representations. The theoretical background is the situative perspective of cognition, which was developed by James Greeno and his research groups in the 1990s at Stanford University. The thesis lays out the overall conception and develops one element of the overall framework, namely, how to treat information from this presented situative perspective. Main points of the thesis are (a) a proposal of how to represent key concepts of situation theory in formal terms (context dependence, constraints), (b) a proposal of how to operationalize a Peircian semiotic analysis with situation logic, (c) a detailed account of relations employed between different representations, that is, of the coordination and lack of coordination between different representations, (d) as a special case of (c), a proposal for a formal treatment of numbers, as numbers are aligned with real-world situations that they ought to quantify. |
