A qualitative three phase research study was undertaken to explore the geometric thinking of Grade 6 teachers in the context of low performance of the Gauteng learners in the International Competitions and Assessments for Schools (ICAS) tests in 2006. The van Hiele theory of geometric thinking was used as a theoretical framework. Data was collected by means of document analysis, teachers responding in writing to ICAS items and task based interviews. This research shows that the ICAS items map very well with the National Curriculum Statement (NCS) Assessment Standards and the van Hiele levels. The mapping of the 82 geometry ICAS items to the (NCS) Assessments Standards and the van Hiele levels revealed that 59% of the ICAS items were at van Hiele level 2 across all grades and therefore accessible to the majority of the learners. The written responses conducted with 40 ACE teachers and the task based interviews conducted with six teachers indicate that the majority of teachers are not at the required level of geometric thinking as expected by the NCS Assessment Standards and the van Hiele levels. This finding has serious implications for classroom practice in the learning and teaching of geometry in primary schools. The challenge for teacher education is to take into consideration the relationship between language and the van Hiele levels; the use of van Hiele levels in the development of teachers’ geometric thinking and the possible use of the van Hiele levels in identifying, explaining and rectifying geometric misconceptions.

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The purpose of this study was to reveal and define the problems middle school mathematics teachers experienced in applying transformational geometry and the solutions they proposed to overcome these problems. A total of six elementary mathematics teachers (grades 5-8) in Ankara participated in the study. The data were collected by means of one-to-one interviews with the participants. The findings indicated that the participants&rsquo / problems divided into three parts. These problems were problems arising from teachers, problems arising from students and problems arising from resources. The participants expressed challenges in teaching due to lack of materials, textbooks, and visualization ability of teachers, classroom size, and time. According to the findings, rotation was the most problematic issue. The participants claimed insufficient technological materials were the reason of this problem. Participants did not feel confidence enough to implement transformational geometry especially in rotation since they lacked adequate training and support. The participants claimed that the Ministry&rsquo / s support should be increased, concrete and technological materials should be sufficient in number, and the duration of transformational geometry lesson should be increased.