What does research say?
The following ‘Levels of geometric thought model’ (modified van Hiele levels by Clements and Battista 1992) divides the learning of geometry into particular levels thus giving you a tool with which to analyse particular activities.
- Reys et al. (2012) state that at the primary school level, many experiences with geometry fail to go past level 1 (the visual stage), when they should really be moving towards the next 2 levels in both primary and secondary school. As such, Vitale, Swart, and Black (2014) point out that “a potential pitfall of the instructional application of stage-based models [such as the van Hiele model] is the imposition of artificial boundaries on student activities – e.g. unnecessarily delaying rigorous tasks for younger students or overlooking necessary visuo-spatial tasks for older students (p. 232).
- Further to this, “in school-based tasks young children often apply informal labels such as “slanty”, “pointy”, or “skinny” to describe common shapes (Clements, Swaminathan, Hannibal & Sarama, 1999, as cited in Vitale et al., 2014, p. 232). Whilst we as educators want to encourage children to be descriptive, doing it at the detriment of children being able to recognise ‘defining’ features of shapes is not a desired outcome.
- Hu, Ginns & Bobis (2015) conducted a study that looked at the influence of tracing worked examples on students ability to solve problems in geometry (regarding parallel lines and angles). Their findings "indicate that learning of geometry principles by novices may be enhanced substantially by the simple addition of explicit instructions to trace elements of instructional materials" (p. 92). Although it would be unwise to generalise given that the study was not dealing with shapes explicitly, given that parallel lines are a feature of many basic shapes these findings may still have some relevance.