An investigation of the Van Hiele levels of thinking in geometry at the beginning of the ninth grade

Boone, Wilbert Arthur (1984) An investigation of the Van Hiele levels of thinking in geometry at the beginning of the ninth grade. Masters thesis, Memorial University of Newfoundland.

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    Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
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Abstract

This study was motivated by the controversy which exists over the approach to teaching geometry in grade nine. Which approach should be used to teach geometry at this grade level: inductive or deductive? This has been an issue of concern in Newfoundland and Labrador during the last five years. -- The main purpose of the study was to investigate the level of thinking of grade nine students in geometry at the beginning of the school year. A second important aspect of the study was related to the text materials used to teach the geometry strand in grade eight. Also, it was attempted to determine if the mental development of grade nine students in geometry in Newfoundland and Labrador differed from those of students in the United States. -- The sample consisted of 1 004 grade nine students at the beginning of the school year in Newfoundland and Labrador. However, 75 students were eliminated from the sample because they were repeating grade nine (46) or using an alternative textbook series (29). Consequently, 929 students were included for data analysis. -- The students were required to provide information relative to their grade last year, the textbook used to study geometry in grade eight, and placement in grade nine this school year: advanced, academic, or practical. This information was utilized in data analysis. -- The students were administered a modified version of the van Hiele Geometry Test. This test included four levels of multiple-choice questions: Recognition, Analysis, Ordering, and Deduction. There were five questions at each level for a total of 20 questions. -- The students were classified according to the van Hiele theory of mental development in geometry. Each student was assigned a level: Recognition, Analysis, Ordering, or Deduction. It was possible to classify 88.7 percent of the sample using a criterion of 3 out of 5 items correct at each level. When a criterion of 4 out of 5 items correct at each level was applied, it was possible to classify 95 percent into a van Hiele level. In the case of 3 out of 5, the majority of students were at the recognition and analysis levels of the van Hiele theory. In the case of 4 out of 5, the majority of students were at the recognition level or below recognition level. The major find of the investigation was that students at the beginning of grade nine are not prepared for deductive reasoning according to the van Hiele model. -- The second major conclusion related to the textbooks used to teach geometry in grade eight and the level of thinking of students at the beginning of grade nine. It was found that the level of thinking of students in geometry at the beginning of grade nine was independent of the textbook used for geometry instruction in grade eight when a criterion of 3 out of 5 was applied. However, a significant difference was found when the 4 out of 5 criterion was used. The level of thinking in geometry was dependent on the text used for geometry instruction. -- The third major conclusion related to homogeneous populations and levels of mental development in geometry. There was a significant difference in the level of mental development in geometry of grade nine students in Newfoundland and Labrador and those in the United States. The level of cognitive development in geometry was higher for students in the United States.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/7949
Item ID: 7949
Additional Information: Bibliography: leaves 60-62.
Department(s): Education, Faculty of
Date: 1984
Date Type: Submission
Library of Congress Subject Heading: Geometry--Study and teaching; Mathematical ability

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