Interrogation of Silent Features, Creative Reasoning and Function Sense for Graphing Functions

Abstract

Graphs and Graphing function are crucial aspects of understanding, yet this is troublesome to students.  This research paper offers a quite distinct way of thinking to help ease such difficulty.  It focuses on analyzing, connecting silent features of functions with the improvement of graphing skills and concepts of concavities, and increasing and decreasing phenomena.  Two methods were explored, examined and discussed, namely arithmetic silent feature and reasoning, and asymptotic silent feature and reasoning.  Data collected through interviews and observation were qualitatively analyzed.  The impact of learning such methods on enhancing graphing skills and on understanding concavity was remarkable.  Students enthusiastic involvement, and use of basic skills and previous knowledge helped them in the process of assimilating and accommodating concepts that were previously procedurally learned. So, their graphing skills were significantly enhanced. Based on the study results, the researcher recommends that such methods be part of teacher’s specialized pedagogical content knowledge the teacher could take into consideration and add to his/her repertoire for effective teaching and better outcomes.