The relationship between teachers’ instructional practices and their learners’ level of geometrical thinking
Keywords:Geometry, Van Hiele theory, instructional practice, level of thinking, mathematics
This case study describes and investigates the instructional practices of Grades 1 to 5 teachers and the levels of geometry thinking of the learners, according to the Van Hiele model, with a view to determining whether there is a match between the instructional practice and the learners’ level of thinking. The instructional practices of the teachers were observed and analysed, and their learners’ levels of geometry thinking were accessed through a Van Hiele test. The results suggest that there is not a simple relationship between the phases of learning, as described by Crowley in 1987, and geometric development in terms of the Van Hiele levels. It is, however, possible to explain the geometric development to a limited extent in terms of the Van Hiele levels of the observed teaching activities. Although the presence of activities on an appropriate level does not guarantee growth in terms of the Van Hiele model, the absence thereof results in stagnation. The instructional practices in primary schools in all Grades should span geometry experiences on all the levels, because the previsualisation level and Van Hiele Level 1 thinking are still evident up to Grade 5.