The Quality of the Student's Mathematical Proofs as a Function of Classroom Assessment A Qualitative-Quantitative Analysis

Abstract

In this quasi-experimental study mathematical proof writing is views as a problem-solving activity success at which requires adequate knowledge of relevant mathematical content and logical rules of inference, familiarity with heuristic proof-writing techniques, metacognitive skills, and positive effects 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 students’ mathematical proofs and selected affective variables such as attitudes towards mathematics, motivation, self-confidence, mathematics anxiety, and test anxiety.

Two intact undergraduate classes of fifty-one (51) students in Linear Algebra at the University of the Philippines Visayas Main Campus in Miag-ao, Iloilo during the Second Semester, 2002-2003, constituted the sample for the study. The traditional and learner-centered classroom assessments were randomly assigned to the control and experimental groups, respectively.

Each member of the experimental (LCA) and control (TA) groups wrote proofs for seven propositions which were scored blind by two raters using 4-point criteria (key mathematical understanding, logical validity, mathematical communication, and clarity and simplicity) specified in a researcher-constructed anaholistic proof-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 profs.