Identifying and fostering higher levels of geometric thinking

Abstract

Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7 %) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is at the first level whereas 4.3 % of students are at the zero level. Only 1.4 % of students reached the second level of geometric thinking. Students had the most difficulty with the use of appropriate geometric language, so a teaching approach to improve mathematical language was created, in an attempt to accelerate the transition to a higher level of geometric thinking. The teaching approach that proved successful was based on the use of different materials, concrete experiences, promoting the use of appropriate geometric language and motivation of students.