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Conjecturing and proof-writing in dy...

Frerking, Bonnie Giddens.

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Conjecturing and proof-writing in dynamic geometry.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Conjecturing and proof-writing in dynamic geometry./
作者:	Frerking, Bonnie Giddens.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 1994,
面頁冊數:	131 p.
附註:	Source: Dissertations Abstracts International, Volume: 56-10, Section: A.
Contained By:	Dissertations Abstracts International56-10A.
標題:	Mathematics education. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9507424

Conjecturing and proof-writing in dynamic geometry.
Frerking, Bonnie Giddens.

Conjecturing and proof-writing in dynamic geometry. - Ann Arbor : ProQuest Dissertations & Theses, 1994 - 131 p.

Source: Dissertations Abstracts International, Volume: 56-10, Section: A.

Thesis (Ph.D.)--Georgia State University, 1994.

This item must not be sold to any third party vendors.

Statement of the problem. This study examined the relationships among van Hiele levels, proof-writing achievement, and conjecturing by secondary geometry students. More specifically, this study attempted to identify the correlations between students' van Hiele levels and their abilities to make conjectures or between students' abilities to conjecture and their success in writing justifications or proofs. Methods. Two classes of 58 students were taught using the inductive conjecturing method. Students were given opportunities to conjecture about properties of geometric figures, using Geometer's Sketchpad or Geometric Supposer, and to justify their conjectures. The control class of 27 students was taught using the traditional deductive approach. Data collection included pretesting and post-testing with the Van Hiele Geometry Test (VHL) and the Entering Geometry Test (EG) to determine the students' van Hiele levels and their achievement of geometric concepts. The Cognitive Development and Achievement in Secondary School Geometry Proof Test and the Gwinnett Educational Management System Mathematics Test (GEMS) were used to collect post study data on students proof-writing abilities and achievement of geometry objectives. Data were collected on student abilities to conjecture and make justifications by using the Conjecturing Evaluation Instrument (CEI) and the Justification Evaluation Instrument (JEI). The Kolmogorov-Smirnov test for normality, the Cochran's C test for homogeneity of variances and the Kruskal-Wallis one way ANOVA were used to test the non-parametric data. The ANOVA was used to test the parametric, homogeneous data. Correlations were determined by the use of Spearman's r. Results. Correlation of students proof-writing abilities to achievement of geometry objectives, proof-writing achievement and abilities to write conjectures or justifications, and proof-writing abilities to post van Hiele levels were significant. Gains of van Hiele levels and entering geometry knowledge as well as differences in proof-writing abilities and achievement of geometry objectives were not significant. Conclusions. Abilities to conjecture and justify conjectures in a geometry class are directly related to proof-writing abilities. Achievement of geometry objectives is directly related to gain of van Hiele levels and to proof-writing skills. Scores on conjecturing and justification activities were affected by the design of the activity worksheets.Subjects--Topical Terms:

641129
Mathematics education.

Conjecturing and proof-writing in dynamic geometry.
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300 $a 131 p.
500 $a Source: Dissertations Abstracts International, Volume: 56-10, Section: A.
500 $a Publisher info.: Dissertation/Thesis.
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506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a Statement of the problem. This study examined the relationships among van Hiele levels, proof-writing achievement, and conjecturing by secondary geometry students. More specifically, this study attempted to identify the correlations between students' van Hiele levels and their abilities to make conjectures or between students' abilities to conjecture and their success in writing justifications or proofs. Methods. Two classes of 58 students were taught using the inductive conjecturing method. Students were given opportunities to conjecture about properties of geometric figures, using Geometer's Sketchpad or Geometric Supposer, and to justify their conjectures. The control class of 27 students was taught using the traditional deductive approach. Data collection included pretesting and post-testing with the Van Hiele Geometry Test (VHL) and the Entering Geometry Test (EG) to determine the students' van Hiele levels and their achievement of geometric concepts. The Cognitive Development and Achievement in Secondary School Geometry Proof Test and the Gwinnett Educational Management System Mathematics Test (GEMS) were used to collect post study data on students proof-writing abilities and achievement of geometry objectives. Data were collected on student abilities to conjecture and make justifications by using the Conjecturing Evaluation Instrument (CEI) and the Justification Evaluation Instrument (JEI). The Kolmogorov-Smirnov test for normality, the Cochran's C test for homogeneity of variances and the Kruskal-Wallis one way ANOVA were used to test the non-parametric data. The ANOVA was used to test the parametric, homogeneous data. Correlations were determined by the use of Spearman's r. Results. Correlation of students proof-writing abilities to achievement of geometry objectives, proof-writing achievement and abilities to write conjectures or justifications, and proof-writing abilities to post van Hiele levels were significant. Gains of van Hiele levels and entering geometry knowledge as well as differences in proof-writing abilities and achievement of geometry objectives were not significant. Conclusions. Abilities to conjecture and justify conjectures in a geometry class are directly related to proof-writing abilities. Achievement of geometry objectives is directly related to gain of van Hiele levels and to proof-writing skills. Scores on conjecturing and justification activities were affected by the design of the activity worksheets.
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