Constructivism-based visual instructions for students learning the concept of a continuous function at a point

Abstract

The concept of a continuous function at a point involves a key calculus idea, to help students learn about the content in calculus. Therefore, developing a learning environment where students can independently build concepts and related knowledge when learning this topic is crucial. Previous studies show challenges for teachers in designing lessons, however, there exist fewer number of studies discussing effective solutions to support teachers. This study fills this gap through the exploration of constructivism based visual instructions. This study employed an action research methodology involving 12 pre-service teachers at Sai Gon University, organized into three stages namely identifying issues when teaching the lesson of "a continuous function at a point", exploring solutions, and finally discussing the best application. The findings demonstrated that using visual models in teaching helped students understand and verify hypotheses, reject wrong ones, and construct new knowledge about the continuous function at a point in an effective way. Four perspectives-numerical, graphical, linguistic, and algebraic-were used during the teaching process to solve the challenge of learning the concept of a continuous function at a point.