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12 septembre 2020
- handle: 10670/1.zi38mv
- hal: hal-03113955
info:eu-repo/semantics/OpenAccess
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Transition to and across university mathematics Teaching and learning of analysis and calculus Topology Concept image Intuitive models.Sujets proches
Schoolteaching Didactics School teaching Pedagogy Instruction Continuous functions ContinuumCiter ce document
Laura Branchetti et al., « Continuity of real functions in high school: a teaching sequence based on limits and topology », HAL-SHS : sciences de l'éducation, ID : 10670/1.zi38mv
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It is well known that students have difficulties with the concept of continuity, specifically on points of discontinuity, and concepts like limits and infinity. In Italian textbooks, the continuity of functions is usually defined using limits, while an intuitive characterization of continuous functions is proposed without providing the students with formal tools to use it, like “the graphs of continuous functions can be drawn without lifting the pencil out of the paper”. Limits are one of the most complex subjects to learn and are usually introduced in an algorithmic way, without a true comprehension of the subject. We argue that introducing the definition of continuous functions using limits is problematic and we designed and tested a teaching sequence to investigate the potentiality of including a topological approach in high school.