Investigating Structures of Knowing within Three Relational Constructs, Leading to Higher-Order Mathematical Thinking

Abstract

This paper considers three constructs that address different, yet complementary perspectives on student mathematical performance. The three constructs are the relationship between procedural and conceptual forms of knowledge by Hiebert and Lefevre (1986), the psychology of mathematical abilities in schoolchildren as researched by Krutetskii (1976), and the developmental construct of the SOLO model as devised by Biggs and Collis (1982, 1991). It will be appreciated how these constructs derive three different viewpoints of 'structures of knowing' in mathematics resulting in the possibility of transitional pathways to higher-order thinking. "In simplest terms, higher-order thinking measures include all intellectual tasks that call for more than information retrieval." (Baker 1990 p.7)