The Effect of Arrow Diagrams on Achievement in Applying the Chain Rule

Abstract

In this study the effectiveness of an arrow diagram which can help students apply the Chain Rule was investigated. Different variations of this diagram were used as mnemonic devices for applying the Chain Rule. For the investigation two instruments were developed, diagnostic test and post-test. The diagnostic test was developed to determine the students' difficulties with the Chain Rule and to create matched groups. It was administered to 76 students taking the Advanced Calculus Course. By matching according to the results of the diagnostic test, the sample of 24 pairs of subjects is obtained. The results of the post-test, administered after the teaching program, indicated that the arrow diagram had positive effects on applying the Chain Rule.

From human activity to conceptual understanding of a mathematical concept

“…For the two functions f and g, the composite function or the composition of f and g, is defined by (f×g)(x)=f(g(x)). Despite the importance of the chain rule in differential calculus and its difficulty for students, the chain rule has been studied in mathematics educational research (Clark et al, 1997;Gordon, 2005;Uygur & Ozdas, 2007;Webster, 1978). Students' difficulties included the inability to apply the chain rule to functions and also with composing and decomposing functions (Clark et al, 1997;Cottrill, 1999, Hassani, 1998.…”

Full journal

“…For the two functions f and g, the composite function or the composition of f and g, is defined by (f×g)(x)=f(g(x)). Despite the importance of the chain rule in differential calculus and its difficulty for students, the chain rule has been studied in mathematics educational research (Clark et al, 1997;Gordon, 2005;Uygur & Ozdas, 2007;Webster, 1978). Students' difficulties included the inability to apply the chain rule to functions and also with composing and decomposing functions (Clark et al, 1997;Cottrill, 1999, Hassani, 1998.…”