University mathematics students' perception of proof and its relationship to achievement Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/8910jz16f

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  • The focus of this study was junior-level mathematics students' perception of proof and its relationship to achievement. The following problems were investigated: 1) nature of perception of proof of undergraduate mathematics students who have enrolled in Advanced Calculus; 2) relationship between students' perception of selected aspects of proof and their achievement in Advanced Calculus; and 3) relationship between measures of perception of proof and achievement in Advanced Calculus. Twenty versions of a questionnaire, each containing six items, were administered randomly to 47 students in Advanced Calculus. The questionnaire items measured selected aspects of students' perception of proof. Student responses to the questionnaire were evaluated and put into response categories by three judges. An interview script was developed based on the results of the written questionnaires and a pilot study involving undergraduates with a similar backround as those in the study. The script assessed students' subjective perception of the nature of mathematical proof, degree to which students enjoy proof, and amount of confidence students have in their ability to construct proofs. Eight follow-up interviews were conducted. They were taped, analyzed, and categorized into an inductively developed category system. Achievement data were obtained from student performance on tests and homework assignments. It was the total number of points accumulated by each student. The following hypotheses were tested: 1) The correlation between total score obtained on the written questionnaire and achievement in Advanced Calculus for class A is not significantly different than the same correlation for class B. 2) There is no significant proportion of variation in achievement that is associated with perception of proof. 3) There is no association between achievement in Advanced Calculus and perception of the aspects of proof addressed by each situation on the written questionnaire. Data were analyzed using 2x2 contingency tables, correlation coefficient, and qualitative analysis of interviews. From these analyses the following conclusions were drawn: 1) the nature and role of hypothesis in mathematics is misunderstood by at least a large minority of junior-level mathematics students; 2) a significant proportion of variation in achievement is associated with perception of proof. Several recommendations for research and practice were discussed.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2013-07-22T16:10:31Z (GMT) No. of bitstreams: 1 LewisSM1987.pdf: 1173146 bytes, checksum: 0b989b8bd42d7c0fd0b40e6ead6702fb (MD5)
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  • description.provenance : Submitted by Kim Stowell (ksscannerosu@gmail.com) on 2013-06-12T22:27:19Z No. of bitstreams: 1 LewisSM1987.pdf: 1173146 bytes, checksum: 0b989b8bd42d7c0fd0b40e6ead6702fb (MD5)
  • description.provenance : Made available in DSpace on 2013-07-22T16:10:31Z (GMT). No. of bitstreams: 1 LewisSM1987.pdf: 1173146 bytes, checksum: 0b989b8bd42d7c0fd0b40e6ead6702fb (MD5) Previous issue date: 1986-08-06

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