Creating Valid and Reliable Geometric Thinking Test Based on the First Three Levels of Van Hiele Theory

Geometry is one of the important subjects in mathematics which is related to students’ reasoning and thinking. Based on van Hiele theory a student must pass through five sequential and hierarchical discrete levels of geometric thinking to achieve a successful reasoning in geometry. Geometric thinking consists of problem solving and manipulating spatial images. The aim of the present study was to create a reliable and valid test to assess students’ level of geometric thinking based on van Hiele theory. The survey research was used and a test has been made by reviewing recent research and literature. The test includes 21 questions related to the levels of geometric thinking based on van Hiele theory. The geometry concepts in creating this test comprise: angle, triangle, square, rectangle, rhombus, parallelogram, trapezoidal and circle. Students who were studying in grades 4-8 in elementary and middle schools in 2009-2010 in Tehran were considered as a statistical population. By cluster sampling method 507 students were chosen. The test was taken from the sample consists of 162 students from grade four, 174 students from grade five, 85 students from grade six, 47 students from grade seven, and 39 students from grade eight. Content validity, construct validity (factor analysis), and item analysis including difficulty index, discrimination index, and Cronbach’s alpha for internal consistency of the test items were used to get the results. Five factors were realized by factor analysis as follow: properties of shapes from angle dimension, rotation, properties of shapes from right angle dimension, properties of shapes and angles, and the relationship between shapes.