Linking procedural and conceptual mathematical knowledge through CAL

Abstract

Despite its high educational relevance, relatively few CAL studies have examined whether their computer‐based treatments search for and/or utilise any potential link between procedural and conceptual mathematical knowledge. This paper summarises some of the findings of studies of this kind, explains how these knowledge types may be linked and proposes two constructivist CAL environments which enable a desired link.

The Analysis of the Relation between Eight-Grade Students’ Estimation Performance in Triangles with Their Teaching Style Expectations and Sources of Motivation

“…In these two approaches, students' believes about solving mathematical problems are affected in a negative way. Kadijevich and Haapasalo (2001) pointed out that understanding the relations between procedural and conceptual knowledge can be developed with learning activities. Not only the quality of teaching activity but students' attitudes towards learning also affect the speed of this association process.…”

Computing in Differential Equations with Mathematical Thinking Approach among Engineering Students

“…Therefore, they use procedural knowledge and reflect on the outcome, which is known as the developmental approach [13] .However, some researchers believe that conceptual knowledge enables the development of procedural knowledge. Educational approach is an instructional implication which focuses on building meaning for procedural knowledge before mastering it.…”

What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts

“…A surplus of literature that has established relationships between conceptual and procedural knowledge (Baroody et al, 2007;Carpenter, 1987;Davis, 2005;Hiebert & Lefevre, 1987;Kadijevich & Haapasalo, 2001;Rittle-Johnson, Siegler, & Alibali, 2001;Skemp, 2006) and many of those relationships have also been substantiated by research on student understanding of the calculus. For example, Clark et al (1997) studied first-year calculus students' understanding of the chain rule and its underlying structure to examine how students learn to use a mathematical rule with understanding.…”