## Abstract

We focus on a ‘typical’ task in which students have to give a functional generalisation in algebraic form of a growing sequence of spatial structures. We analyse the contribution of this task to a coherent knowledge of functions. Despite a plethora of research about misconceptions and the teaching of functions, little is known about the overall growth of students’ understanding of functions throughout schooling. We aim to map the development of students’ understanding of concepts which contribute to understanding functions in two different curriculum systems: the UK and Israel. The research uses a survey

instrument that was developed in collaboration with a group of teachers and the task for this paper is one of six that span several routes to understanding functions. Our data appears to contradict some other studies as well as to suggest conjectures about how students' willingness to use covariational reasoning depending to some extent on task features.

instrument that was developed in collaboration with a group of teachers and the task for this paper is one of six that span several routes to understanding functions. Our data appears to contradict some other studies as well as to suggest conjectures about how students' willingness to use covariational reasoning depending to some extent on task features.

Original language | English |
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Title of host publication | Proceedings of the 8th British Congress of Mathematics Education |

Editors | S. Pope |

Place of Publication | Nottingham |

Publisher | British Society for Research into Learning Mathematics |

Chapter | 2 |

Pages | 17-24 |

Number of pages | 8 |

State | Published - Apr 2014 |

Externally published | Yes |

### Publication series

Name | Proceedings of the 8th British Congress of Mathematics Education 2014 |
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Publisher | British Society for Research into Learning Mathematics |

ISSN (Electronic) | 1463-6840 |