On tasks that lead to praxeologies’ formation: a case in vector calculus
Résumé
A praxeology comprises a type of task, a technique to accomplish it, a discourse (technology) explaining this technique and a theory supporting this discourse. We consider a situation where a praxeology was presented to students in a lecture, but they discovered an alternative one while working on a routine exercise. This exercise was then followed by a more challenging question related to immediate results obtained by the students. We analyzed this student experience in view of Chevallard’s six steps of constructing a praxeology. We suggest that observing students’ work on standard exercises may give some productive and innovative ideas for the design of tasks that help students deepen their understanding and encourage theoretical justifications of their solutions. We also comment about possible effects of the explicit requirement to search for the most efficient solution on the formation of praxeologies by students.
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