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Investigation of Van Hiele Geometric Thinking Levels within Item Response Theory Perspective
Last modified: 2017-03-30
Abstract
Van Hiele model in learning geometry was propounded to describe students geometric thinking both in elementary and secondary level in 1950s and have been commonly accepted and used in the literature. The model proposes five hierarchic levels (recognition, analysis, ordering, deduction, and rigor); and asserts that students need to be taught proper to their level in order to learn the concept. Hence, level determination in students’ geometric thinking is an important issue. For this purpose, different tests were developed in the literature. In these tests, students’ level is determined with respect to the number of correct responses to the items measuring different levels. Fidan (2009) developed Turkish version of geometric thinking test (GTT) within Van Hiele perspective for elementary level. Test consists of 50 items related to mentioned 5 levels. The purpose of current study is to examine psychometric properties of GTT within item response theory (IRT) perspective and compare the information provided by classical test theory (CTT) perspective. Results indicates that test consists of single factor and fits to 3PLM. Item information and characteristic curves indicated that four items gives almost no information, while test in general gives information mostly in 1 theta level. Moreover, the chance values differs between 0.5 and 0.123, which indicates the probability of correct response by chance, is high. The item parameters will be explained in detail and the misleading conclusions related to students levels based on CTT will be discussed by comparing ability estimates based on IRT and level determined by CTT perspective