Student enrichment in mathematics: A case study with first year university students (in IJMEST)
Harry Wiggins, Johann Engelbrecht, Ansie Harding
Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)
How do we teach a mixed ability class? It’s not easy. Teaching to the middle bores some and leaves others behind.
A student enrichment programme was developed at the University of Pretoria.
5 activities worked on by 22 students who were invited to join the programme. They could consult the lecturer or each other. Designed using inquiry-based learning principles. Feedback by a survey, and 4 students were interviewed.
Enthusiasm: 10% neutral, the rest said they enjoyed the project.
“I don’t see the point of you coming to study if you don’t want to challenge yourself to become better.”
Self-activity. 82% worked alone. “You don’t always rely on a lecturer, just do your own stuff…”
Depth of understanding: Student got to experience complex numbers as more than just learning the algebra.
Personal growth: Students could immediately share the knowledge they gained when the rest of the class covered complex numbers.
No marks, just for enrichment.
Appreciation: 79% said the project changed their view of mathematics. “I feel honoured when lecturers share their passion with students. It makes me enjoy the subject and classes more.”
Take home message: There is not much enrichment at university level. When tasks are not challenging enough, not enough chemicals needed for learning are released (Stepanek, 1999).
How guided were the activities? 1st on polynomials, used Geogebra, had a document on complex numbers they had to read and answer questions, e.g. what is the most interesting question on complex numbers you have seen. Last 2 activities were challenging – draw sibling curves without software. Last question making conjectures and try to prove them.
Sibling curves: If you have a polynomial with complex roots, how do you represent the roots? A polynomial of order n will have n sibling curves. Links to complex numbers.
Facebook wasn’t used much, mostly the enrichment group used the internet and the lecturer.
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