Revolution in mathematics teaching

Apprenticeship teaching in mathematics offers a new way of learning.

Video by Science Education Centre Luma

For a year now, the corridors of the Department of Mathematics and Statistics have been lined with blackboards which students and teachers crowd around. Groups of students are doing sums, sitting at tables covered with plastic sheets that you can write on. What is all this?

“The method is called Extreme Apprenticeship, or XA. It’s based on the idea that the best way to learn mathematics is to actually do the calculations,” says Thomas Vikberg, who is currently writing his doctoral thesis on the method.

Positive experiences enable learning

Traditionally, mathematics teaching at the University relies on lectures. However, it often occurs that the students, although they may pass the exams, lack the skills and knowledge needed for the next course. This was the reason for introducing XA, which is based on doing sums and problems instead of listening to lectures.

The hands-on work takes place in the Department’s “calculating room”, where course assistants and teachers help the students if they get stuck. The way the exercises are constructed, the students also learn the theory behind them. Moreover, the degree of difficulty increases little by little.

“Suddenly, the students realise they are able to solve complex mathematical problems,” says Vikberg. “It’s that kind of positive experience which enables effective learning.”

The method poses challenges for both students and teachers.

“The hardest thing is actually not to help the students too much,” says Vikberg. “As a teacher, you’d like to explain everything for the learners, but here you need to let them find out for themselves.”

Learning by doing on a major scale

The method was introduced in autumn 2011 in two of the largest basic courses in mathematics, involving hundreds of students. The students’ response has been generally positive. The inspiration was derived from the Department of Computer Science, where XA has been employed for a number of years already.

“Individual advice and learning-by-doing are clearly a trend at the university,” says Vikberg. “It’s the scope that makes our course unique: we offer individual teaching to hundreds of students.”

It is a challenge to make the system run sustainably with the resources at hand. The calculating rooms are open for most of the week, which increases the teaching costs.

“But just think of the cost of a lecture hall filled with 400 students who just don’t get it,” Vikberg comments.

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Text: Katja Bargum
Photo: Ari Aalto
Video: LUMA-centre
Translation: AAC Global
University of Helsinki, digital communications

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