Representations and reasoning in 3-D geometry in lower secondary school. (English)

Tso, Tai-Yih (ed.), Proceedings of the 36th conference of the International Group for the Psychology of Mathematics Education “Opportunities to learn in mathematics education", PME 36, Taipei, Taiwan, July 18‒22, 2012, Vol. 2. Taipei: National Taiwan Normal University. 339-346 (2012).

Summary: A key question for research in geometry education is how learners’ reasoning is influenced by the ways in which geometric objects are represented. When the geometric objects are three-dimensional, a particular issue is when the representation is two-dimensional (such as in a book or on the classroom board). This paper reports on data from lower secondary school pupils (aged 12‒15) who tackled a 3-D geometry problem that used a particular representation of the cube. The analysis focuses on how the students used the representation in order to deduce information and solve the 3-D problem. This analysis shows how some students can take the cube as an abstract geometrical object and reason about it beyond reference to the representation, while others need to be offered alternative representations to help them ‘see’ the proof.