Bridging the Gap Between the Derivatives And Graph Sketching in Calculus

Abstract

Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained to sketch the graph. Nevertheless, the students face great difficulties in achieving this goal; and fail to relate the results obtained in the analysis and their representation in a graph. Their performance is thus negatively affected eventually. To overcome this cognitive gap, an innovative board game named Graph Puzzle (GP) is developed. It is intended to function as a manipulator to facilitate students in comprehending the inter-related algebraic, symbolic, and graphic representation of a function under the applications of derivatives, forming the corresponding procedural and conceptual knowledge. To measure the effectiveness of this board game, 84 undergraduate students who took this calculus course were given pre- and post-test before and after the learning session. An ANCOVA test conducted reveals a significant difference (F (1, 81) = 12.182, p = 0.001) between pre and post-test score in solving polynomial functions, whereas students’ performance in solving rational functions indicates no meaningful difference (F (1, 81) = 0.04, p = 0.841) of post-scores between control and treatment groups. From this standpoint, it is shown that GP has the potential to serve as a solution to the difficulties faced on graph sketching in calculus, particularly when dealing with polynomial functions.
 
 Keywords: Visualization, Calculus, Embodied learning, Game-Based Learning, Graph Sketching