THE DESIGN AND EVALUATION OF AN INSTRUMENT FOR ASSESSING MASTERY VAN HIELE LEVELS OF THINKING ABOUT QUADRILATERALS
THE DESIGN AND EVALUATION OF AN INSTRUMENT FOR ASSESSING MASTERY VAN HIELE LEVELS OF THINKING ABOUT QUADRILATERALS
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Date
1989
Authors
Crowley, Mary Lora Noffsinger
Advisor
Henkelman, James
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Abstract
The goal of this project was to create a 40 minute long
multiple-choice Instrument to assess an Individual's dominant level
of thinking, as described by the van Hiele model of the development
of geometric thinking, on the topic of quadrilaterals. The study
was composed of four stages: (a) Item development, (b) pl lot
testing, (c) field testing and (d) final testing. Initially 53
items were developed and reviewed by a panel of experts. The
revised Items were then administered to 14 pl lot study subjects,
and, subsequently, to 113 field test subjects, both groups ranging
in academic background from sixth grade to university. Item
analysis comparing these subjects' choices of level specific
responses and their dominant van Hiele level, as determined through
the Burger and Shaughnessy interview, resulted in the
identification of 19 items for the final Instrument, the van Hiele Quadrilateral Test. For scoring purposes, the items on the test
are considered as four subtests, with 4, 5, 6 and 4 Items
corresponding to Levels 1, 2, 3 and 4, respectively. The items
associated with Levels 2, 3 and 4 met alI the item analysis
criteria. Two interpretation schemes were identified.
The final instrument was administered to 50 subjects in ninth grade and 51 subjects in twelfth grade. Grade membership and performance on the Nova Scotia Achievement Mathematics Basic
Concepts Test were compared to subtest performance and to the
resulting mastery decisions. Chi squared statistics failed to
support the independence of grade membership and van Hiele level.
The correlation statistics, Φ, indicated that there was a weak
correlation between grade level and mastery of Levels 1 and 2, with
stronger statistics associated with Levels 3 and 4. Little of the
total variance in mastery designations (η2y1x) was attributed to
variance In grade level. Little to moderate variance (η2y1x) in
performance on the Achievement Tests was attributed to variance in, the van Hiele level assignments. Two types of criterion-referenced
reliability statistics, the agreement coefficient, Ρο, and Cohen's
Kappa, K, were also determined. These indices suggest that the
subtests do not yield consistent results for these subjects. Until
reliability can be established, the Instrument ls not appropriate
for determing van Hiele mastery levels. The implications of these
findings and suggestions for further research are considered.