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In which way is thinking dependent on the situational context? How is information transferred between different co-existing representations of the same situation? In this book, these questions are explored in the context of middle school students working with linear functions. Conceptual understanding and reference are discussed in a Peircian semiotic framework. A detailed, formal analysis based on situation calculus goes deeply into the questions of linkages between representations, the meaning of numbers, and the informational content of different mathematical representations. The study shows how our reasoning can be dependent on the present perceived situation, and how this may hinder us to reason backwards like understanding how a table we created from an observation relates back and represents that very observation. This has implications for modeling in particular and education and transfer in general.

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Gertraud Benke is an Assistant Professor at the University of Klagenfurt, Austria. She has been working as a linguist and educational researcher in the field of mathematics and natural science education.

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