## Abstract

Student success in Mathematics is a global priority. Mathematics is a fundamental part of engineering programs in higher education, necessary for application in further engineering studies and yet often becomes a stumbling block for engineering students. Concerningly, even successful students frequently exhibit weak understanding of key mathematical concepts. The vector calculus course is known to be particularly challenging for students.

While much research has been done into students’ constructions of core concepts at school level, less has been done on advanced mathematical topics such as vector calculus, yet this important insight has the potential to impact curriculum and pedagogy and to inform relevant support. This research conducted at the University of Twente, the Netherlands and the University of Cape Town, South Africa will use the constructivist APOS (Action-Process-Object-Schema) Theory to explore how students mentally construct concepts such as partial derivatives, directional derivatives and double integrals. APOS theory is based on the hypotheses that individuals construct mental actions, processes, and objects and organise them in schemas to solve mathematical problems.

In this exploratory case study we attempt to explore and understand how our

students understand the limits of integration of double integrals, informing the design of our teaching of vector calculus to improve students’ understanding and ultimately increase success. Students will participate in an assessment, complete a survey and participate in individual interviews. APOS Theory can be used directly in the analysis of data. Although initially intended we were unable to use this opportunity to compare the mental constructions of the cohorts from the two different universities and it will be assigned to future research.

While much research has been done into students’ constructions of core concepts at school level, less has been done on advanced mathematical topics such as vector calculus, yet this important insight has the potential to impact curriculum and pedagogy and to inform relevant support. This research conducted at the University of Twente, the Netherlands and the University of Cape Town, South Africa will use the constructivist APOS (Action-Process-Object-Schema) Theory to explore how students mentally construct concepts such as partial derivatives, directional derivatives and double integrals. APOS theory is based on the hypotheses that individuals construct mental actions, processes, and objects and organise them in schemas to solve mathematical problems.

In this exploratory case study we attempt to explore and understand how our

students understand the limits of integration of double integrals, informing the design of our teaching of vector calculus to improve students’ understanding and ultimately increase success. Students will participate in an assessment, complete a survey and participate in individual interviews. APOS Theory can be used directly in the analysis of data. Although initially intended we were unable to use this opportunity to compare the mental constructions of the cohorts from the two different universities and it will be assigned to future research.

Original language | English |
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Title of host publication | Engaging, Engineering, Education |

Subtitle of host publication | Book of Abstracts, SEFI 48th Annual Conference University of Twente (online), 20-24 September, 2020 |

Editors | Jan van der Veen, Natascha van Hattum-Janssen, Hannu-Matti Järvinen, Tinne de Laet, Ineke ten Dam |

Place of Publication | Enschede |

Publisher | University of Twente |

Pages | 1022-1032 |

Number of pages | 11 |

ISBN (Electronic) | 978-2-87352-020-5 |

Publication status | Published - 2020 |

Event | 48th SEFI Annual Conference on Engineering Education, SEFI 2020 - Online, Enschede, Netherlands Duration: 20 Sep 2020 → 24 Sep 2020 Conference number: 48 https://www.sefi2020.eu |

### Conference

Conference | 48th SEFI Annual Conference on Engineering Education, SEFI 2020 |
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Abbreviated title | SEFI 2020 |

Country | Netherlands |

City | Enschede |

Period | 20/09/20 → 24/09/20 |

Internet address |

## Keywords

- Vector calculus
- APOS theory
- Mental constructions
- Student success