Written Meta-Cognition and Procedural Knowledge.

Abstract

The ability to express one's mathematical thoughts in writing and computational proficiency can be viewed as reflecting different aspects of an individuals ' understanding of mathematics. Computational proficiency is the primary means used by educators to assess student's understanding of mathematics and thus in the mathematics classroom cognitive development is measured for the most part through students' ability to apply their procedural knowledge in a problem solving environment. In contrast, in written mathematics one's thoughts are not so much involved with the application of procedural knowledge as with reflection upon the concepts and procedures themselves. In this art icle we analyze the relationship between an individual's ability to apply their procedural knowledge and the ability for meta-cognitive reflection and conceptual thought during written mathematics, with writing exercises designed in accordance with the framework for conceptual development of Sfard. (Sfard,1992,1994) and graded according to the scoring rubric set forth in Countryman. (Countryman,1992) This teaching research was done at a community college with students enrolled in the remedial courses of elementary algebra and basic mathematics who frequently displayed difficulties with computational exercises.