Probing Students’ Levels of Geometric Thinking in Geometry and Their Enacted Example Space Function

Abstract

The study explored the pre-service secondary Mathematics teachers’ levels of geometric thinking in geometry and their enacted example space function while they were exposed to van Hiele model instruction. The findings of the study reveal that most of the students were functioning at the recognition level in plane geometry and the highest geometric thinking level manifested prior to their exposure to van Hiele model is the informal deduction level. The evidences based on the study show that students’ example space function from various phases of instruction does not depend on their levels of geometric thinking that they had in plane geometry. Students with various levels of geometric thinking were able to generate quality examples across phases of instruction. Evidences likewise support the claim that van Hiele model assists students’ development of their example space function. Prior to the instruction misconception on properties of prism was evident among students. After the instruction, the breadth and the depth of understanding in relation to properties of prism was evident based on the quality of examples they provided. The most dominant geometric thinking level after students’ exposure to the van Hiele model instruction is also the recognition level.