| Abstract |
The chain rule is a fundamental concept of calculus. However, it is an
inherently difficult concept for many students. The key reasons for difficulties
in learning chain rule include inadequate understanding of the concept of
function, unable to compose and decompose function, and weak in
memorizing the basic formula and rules of differentiation. Therefore, a
Changeable Function Cube (CF-cube) by filling a small box into medium box
concept is proposed as a learning and teaching chain rule platform. It used
the concept of visualization, recognizing and differentiating the composite
function gradually by putting the small function into the medium function.
Differentiation of composite function can be checked through decompose
function by differentiating of the medium function (applied to the small
function) and multiplying it times the differentiating of the small function. Six
cubes were inserted with the 12 forms of basic formulae of differentiation and
different function types including 5 forms of polynomial functions, 1 form of
exponentials functions, 1 form of natural logarithm functions, and 6 forms of
trigonometric functions. Three stages were conducted and were practiced for
5 weeks. Stages 1, 2 cubes embedded with basic formula functions were
rolled and students were asked to differentiate them. Stage 2, 4 cubes in 2
sizes embedded with selected family functions were rolled and students were
asked to compose functions and differentiate the composite functions and
finalize their differentiation by chaining together with differentiating of
decomposed function. Stage 3, 6 cubes consisted of 2 formula cubes and 4
function cubes were rolled and students were asked to complete and
differentiate composite functions. Stage 1 is helping students to recall and
enhance their memory of basic formula of differentiation. Stage 2 and 3 are
assisting students to improve their problem-solving skills through constructing
and differentiating composite functions and hence, deepen their
understanding of chain rule |