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The Effects of Proof on Achievement and Reasoning Ability of Students in Geometry

出版	University of Connecticut, 1981
URL	http://books.google.com.hk/books?id=WSHHNwAACAAJ&hl=&source=gbs_api

註釋The programs in secondary school mathematics throughout the United States contain different structures and strategies for curricula and methodology. The role of proof in this broad spectrum varies according to the opinions of the authors of texts, curriculum specialists and teachers. The purpose of this study was' to attempt to answer the question: "What effects do the teaching of proof and the writing of proof by the learners have on the level of student achievement in geometry and the development of the reasoning ability of the learners?" The sample for this study consisted of 369 grade ten and grade eleven students who were enrolled in a geometry course at three public high schools in Massachusetts. These students were found in eighteen different classes, nine of#which were randomly assigned to form the experimental group and the remaining nine classes served as the control group. The experimental group was required to prove 50fo or less of all the theorems and exercises found in two units of geometry: parallel lines in a plane and and areas of polygonal regions. The control group was assigned to prove between 80{dollar} and 90{dollar} of the same group of theorems and exercises found in these two areas of the geometry curriculum. All of the subjects were administered three examinations that were written and field tested by the researcher. The Reasoning Inventory (Copyright 1978 by Charles Garabedian, Jr.) and the Parallel Lines Inventory (Copyright 1978 by Charles Garabedian, Jr.) were administered before the unit of parallel lines was taught, then the Area Inventory (Copyright 1978 by Charles Garabedian, Jr.) was administered prior to the study of the area unit. After the homogeneity between the experimental group and the control group was determined, it was then deemed appropriate to apply the AITOVA statistical procedure to the scores of each group. These scores were obtained from readministering each instrument at the conclusion of each of the two units of study. The purpose of the ANOVA procedure was to test 27 of the 33 hypotheses of this study. These hypotheses were stated to indicate that there existed no statistically significant mean difference between specific groups of the sample in relation to parallel lines achievement, area achievement and reasoning ability. The same scores were also subjected to the formula for the Pearson Product-Moment Correlation Coefficient which allowed for the testing of the remaining six hypotheses that dealt with significant relationships between geometry achievement and reasoning ability. The statistical results indicated that 19 of the 27 significant mean difference hypotheses were not rejected at the 0.05 level of significance. This was interpreted to suggest that the amount of proof required for geometry students produced no significant effect on achievement in geometry or on reasoning ability. Furthermore, the rejection of the remaining eight significant mean difference hypotheses indicated that there existed some limited female superiority with respect to reasoning ability and there also existed some limited experimental superiority with respect to reasoning ability. In addition, the rejection of the final six hypotheses revealed that there existed significant positive relationships between the reasoning scores and the parallel lines scores as well as between the reasoning scores and the area scores.