Knowing how a mathematical theory developed improves a pupil's understanding of it. This is the conclusion of Dutch researcher Iris van Gulik, who investigated how the history of mathematics can help pupils to learn this subject.
Van Gulik developed two teaching methods in which a mathematical theory was taught based on the history of its development. Firstly for 13 to 15-year-old high school pupils, geometry was introduced by studying 17th-century Dutch surveying in small groups. Secondly 16 to 18-year-old high school pupils learnt about proofs in plane geometry by working in groups on the history of non-Euclidean geometry.
After the lessons had been completed, Van Gulik investigated the motivation of the pupils and their results, and the experiences of the teachers. The history of non-Euclidean geometry was particularly successful. The pupils acquired a deeper understanding and the teachers indicated that they found the subject challenging and inspiring. In addition to this the new teaching method led to a livelier learning process and higher motivation among the pupils.
The study of 17th-century surveying did not directly lead to a deeper understanding or a higher motivation among pupils. However the 14 to 15-year-old pupils responded more positively to the integration of history in mathematics lessons than the 13 to 14-year-old pupils. The practical assignment in the curriculum was experienced as positive. A particular disadvantage of this method was the use of many texts written in old Dutch. Moreover the cooperation between the teachers of mathematics and Dutch was better at some schools than at others.
The inclusion of historical sources in the teaching material for mathematics is definitely effective. However the extent to which such historical source materials need to be processed should be established. A detailed teacher's handbook for the teaching methods is also vitally important.
At the turn of the 20th century it was common practice to use the history of how mathematics developed as a starting point for teaching this subject. Systematically following the most important steps in the development of mathematics was considered to be the most natural and efficient way of learning the subject. A century later these opinions have become more nuanced and new teaching methods have made their debut. However there are clear parallels between the mistakes pupils make in learning a mathematical theory and the problems encountered during the theory's development.
Iris Van Gulik's research was funded by NWO.
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