Van Hiele Levels and Achievement in Secondary School Geometry

Abstract

Prerre Van Hiele and Dina Van Hiele-Geldot developed a model of thinking geometry in late 1950's. The model is applied for identifying the student’s level of thinking, designing the instruction for their particular stage and assists them to advance to the next level. A survey study was designed and carried out by the researcher to explore the secondary level students. Students Van Hiele level and its relationship examination of mathematics. Five schools were selected from sarlahi district of Nepal by using simple random sampling method 150 students of grade x and 5 mathematics teacher from the selected schools participated in this study. Adapted version of Van Hiele geometry test (VGHT) was used as a main toll for the data collection. Students are assigned different Van Hiel levels according to their performance on VGHT. Likewise second tool was school examination in mathematics (SEM) which was meant to be constructed. Administered and scored by the teachers of the respective school. Thus student’s achievement in mathematics was obtained from school’s archival record. Furthermore, an interview schedule for teacher was developed to get their reflection about the VHGT. Students performance on VHGT was analyzed and they are assigned various Van Hiele level mainly according to Usiskin (1982) "3 out of 5" modified Van Hiele level determination scheme. The result form this study indicated that many of students who participated in the research have a weak conceptual understanding of geometric concepts. 47.33%, 22%, 20%, and 10% of the total students were at the level 0 (Pre-cognition) level 1 (visual), level 2 (analysis) and level 3 (informal deduction) respectively. No students were found to be thinking at level 4 (Rigor) The scores obtained by students on VHGT and SEM were correlated and correlation coefficient was found to be r =0.87. The result indicated that there was a significant strong

positive correlation between the advancement of the Van Hiele's level of understanding geometry and achievement in geometry. Also mathematics teacher form those participating schools expressed their unfamiliarity with Van Hiele theory. These results were found to be consistent with those of previous similar studies in UK, USA, Nigeria and South Africa. The hierarchical nature of the Van Hiele's model has significant implication for teaching geometry. It is suggested that educators responsible for teaching geometry. It is professional in charge of teacher training programs incorporate the principle upon which the Van Hieles model is based into instructional and curricular design. The finding of this study also highlight the necessity of aligning geometry syllabus and geometry instruction with the Van Hiele levels of geometric thinking as well as the use appropriate and correct language in geometry teaching and problem solving.