00000ctm a22000003a 4500 UP-8027390931313810131 Buklod 20260218115405.0 m |o d | ta 100615s2008 xx d r |||| u| (iLib)UPVIS-00016558223 upv-gl LG 996 2008 M38 Z35 Zamora, Lourdes A. Callanta The quality of student's mathematical proofs as a function of classroom assessment a qualitative-quantitative analysis Lourdes A. Callanta-Zamora. [s.l.] University of the Philippines Open University 2008. 245, [32] l. Dissertation (Ph.D. Mathematics) -- U.P. Open University, 2008. In this quasi-experimental study mathematical proof writing is viewed as a problem solving activity success at which requires adequate knowledge of relevant mathematical content and logical rules of inference, familiarity with heuristics prof writing techniques, metacogniitive skills, and positive affects towards self and mathematics. The extent to which two types of classroom assessment - traditional (TA) and learner-centered (LCA) - provided these cognitive and affective requisites is described on the basis of a quantitative and qualitative analysis of their effects on the quality of stdents' mathematical proofs and selected affective variables such as attitudes towards mathematics, motivation, self-confidence, mathematics anxiety, and test anxiety. Each member of the experimental (LCA and control (TA) groups wrote proofs for seven propositions which were scored blind by two rates using a 4-point criteria (key mathematical understanding, logical validity, mathematical communication, and clarity and simplicity) specified in a researcher-constructed anaholistic proff writing rubric. The proofs were also qualitatively assessed to determine the nature and extent of the subjects' understanding of the key mathematical content and identify logical fallacies committed as well as instances of inappropriate use of language, mathematical terminology and notation. The long-term effects of classroom assessment on proof quality were determined through a comparison of the mean index values obtained by the two groups in all criteria indicators, including the frequencies of manifestations of validity, soundness, consistency, and fallacious reasoning in these proofs. Four categories of learning difficluties encountered by the TA and LCA groups in relation to proof writing, were identified and addressed: (a) difficulty with the form and substance of a proof, (b) difficulty in understanding a proof for a theorem or theoretical exercise, (c) difficulty in understanding the key content and their relationships in a proof, and (d) difficulty or confusion with associated mathematical terminology and notation. The comparison of the mean index values obtained by both groupsfor the different criteria measures, as well as the frequencies of manifestations of validity, soundness, consistency, and fallacious reasoning in their proofs reinforce the above findings. Moreover, as a result of their learning experiences in the course, the LCA subjects more significantly liked mathematics and regarded it as their most favorite subject in school, and felt more challenged to solve difficult problems in mathematics. On the other hand, the TA subjects' experiences resulted in a significant reduction of their level of frustration with their previous learning of mathematics, a greater interest to know more about the subject and preference to discuss and learn mathematics with others, and a better understanding of geometry and trigonometry than algebra, along with increased levels of test anxiety and discomfort when dealing with numbers and mathematical symbols. UPVIS UPV-GL LG 996 2008 M38 Z35 Thesis