Treatments and Conversions in Student Written Solutions to Wasan Geometry Problems

Cognitive difficulty arises from two types of cognitive processes: treatments; within the same, conversions; between different types of representational registers. Conversions are difficult since they ask for understanding of two representations. Direction and the choice of first register could be a threshold for the student. Wasan geometry is used as a thought provoker and pre service mathematics teachers' written solutions to those problems for usage of cognitive processes: treatments and conversions are analyzed by content analysis method of qualitative research. Descriptive data regarding number of conversions and treatments are given. As much as correct/partially correct answers, the relation between cognitive processes and answers were analyzed. Students' written answers to three Wasan geometry problems on tangent circles are qualitatively analyzed for specific examples of treatment processes and conversion processes. Neither problem type nor correct answer is a reason for the choice of representational registers. One treatment may be worth many conversions. More usage is related to students' conformity. Direction of the conversion may be misleading. None of the students stays in mono-functional registers. Top and lowest grade students use more treatments and conversions. Usage of more conversions is not related to success and result in less number of treatments.