Van Hiele Levels and Achievement in Secondary School Geometry
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Faculty of Education
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.
Description
Keywords
Secondary School Geometry, Van Hiele Levels