### Abstract

The investigation of limits is at the heart of analysis at university. Accordingly, it is a worthwhile topic for transition courses. The present study engages upper secondary students in reinventing the definition of convergent sequences. Using a commognitive framework, the central development stages of the definition from experiential to abstract are empirically investigated in terms of activated secondary school discourses. The students' familiarity with secondary school discourses is critical, as it allows them to transition from grasping processes with metaphors towards grasping them as formal and abstract objects. For this, school objects act as intermediate steps. Further studies of transition courses should explicitly address the role of students' secondary notions as resources for reifying processes into abstract objects.

Original language | English |
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Title of host publication | Proceedings of INDRUM 2018: Second Conference of the International Network for Didactic Research in University Mathematics |

Editors | Viviane Durand-Guerrier, Reinhard Hochmuth, Simon Goodchild, Ninni Marie Hogstad |

Place of Publication | Agder |

Publisher | University of Agder and INDRUM |

Pages | 537-546 |

Number of pages | 10 |

Publication status | Published - 2018 |

Externally published | Yes |

Event | 2nd Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018) - Kristiansand, Norway Duration: 5 Apr 2018 → 7 Apr 2018 Conference number: 2 http://indrum2018.sciencesconf.org/ |

### Conference

Conference | 2nd Conference of the International Network for Didactic Research in University Mathematics (INDRUM 2018) |
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Abbreviated title | INDRUM 2018 |

Country | Norway |

Period | 5/04/18 → 7/04/18 |

Internet address |

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## Cite this

Schüler-Meyer, A. K. (2018). Defining as discursive practice in transition - Upper secondary students reinvent the formal definition of convergent sequences. In V. Durand-Guerrier, R. Hochmuth, S. Goodchild, & N. M. Hogstad (Eds.),

*Proceedings of INDRUM 2018: Second Conference of the International Network for Didactic Research in University Mathematics*(pp. 537-546). University of Agder and INDRUM. https://hal.archives-ouvertes.fr/hal-01849923