Identifying the van Hiele levels of geometric thinking in seventh-grade students through the use of journal writing

The purpose of this study was to implement the van Hiele model of geometry in the seventh grade of a public school and determine if the levels of knowing, determined by the van Hieles, could be identified in a classroom setting. The study investigated the observed subjects\u27 entry levels of geometric knowing, whether those entry levels were consistent with those identified by Pierre and Dina van Hiele and in the Brooklyn College Study, whether journal entries could be used to identify the van Hiele levels of thinking within the context of a classroom setting, and the five phases that van Hiele believes are necessary for progression from one level of thought to another. Seventy-eight subjects, from three ability level groups, participated in the 15 sessions of the study. Each session included time for the individual student to record initial responses to questions and to explain relationships and share responses. This study was designed to determine if a classroom investigator could follow the steps outlined by The Project at Brooklyn College, and identify the van Hiele levels of thinking using the Module descriptors. The students in this study kept their own records which were read and interpreted by the investigator. A second reader validated the findings. It was found that it is possible to correlate the van Hiele levels of thinking in the classroom setting with findings of The Project at Brooklyn College. Sixty-eight percent of the subjects in Class A remained at Level 0, identifying shapes by appearance, while 32% of the subjects made progress toward Level 1 where properties were included. For Class B, 10% remained at Level 0, 70% made progress toward Level 1 and 20% had some movement toward Level 2, where informal arguments were presented. Class C had 6% in Level 0, 73% in Level 1 and 21% showing movement toward Level 2. Finally, as suggested by the van Hieles, one must continually pass through the five phases of learning to move from one level to the next. This was affirmed in the clinical setting in the Brooklyn College Study and reaffirmed in this classroom study