An investigation into the van Hiele levels of thinking in the geometry component of academic and advanced mathematics

Quick, David Chesley (1987) An investigation into the van Hiele levels of thinking in the geometry component of academic and advanced mathematics. Masters thesis, Memorial University of Newfoundland.

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Abstract

The purpose of this study was to examine the van Hiele level of thinking of students enrolled in academic and advanced mathematics courses, to determine their readiness for deductive reasoning and to make comparisons between these groups and a group tested in the United States. -- A sample of 17 schools was randomly selected from both urban and rural setting in the province of Newfoundland and Labrador. A sample of 561 students was chosen and administered a modified version of the van Hiele Level Test in October 1985 and again in October 1986. -- An analysis of the results indicated that at the beginning of level II the majority of students, 47.1 percent using the 3 of 5 criteria and 77.8 percent using the stricter 4 of 5 criteria, were not at a sufficient van Hiele level to begin the study of deductive geometry. Analysis of the posttest given in level III indicated an increase in the van Hiele level over level II. However, a large percentage of students, 38.5 percent using the 3 of 5 criteria and 64.1 percent sing the 4 of 5 criteria, were still below the necessary van Hiele level. -- Comparisons of the advanced and academic groups favored the advanced groups in both level II and III. They were at higher van Hiele levels than their academic counterparts. A comparison of van Hiele levels with a group tested by Usiskin in the United States favored the Newfoundland student for both the academic and advanced programs.

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