Designing worked examples for learning tangent lines to circles

Abstract

Abstract. Geometry is a branch of mathematics that deals with shape and space, including the circle. A difficult topic in the circle may be the tangent line to circle. This is considered a complex material since students have to simultaneously apply several principles to solve the problems, these are the property of circle, definition of the tangent, measurement and Pythagorean theorem. This paper discusses designs of worked examples for learning tangent line to circles and how to apply this design to an effective and efficient instructional activity. When students do not have sufficient prior knowledge, solving tangent problems might be clumsy, and as a consequence, the problem-solving activity hinders learning. According to a Cognitive Load Theory, learning occurs when students can construct new knowledge based on the relevant knowledge previously learned. When the relevant knowledge is unavailable, providing students with the worked example is suggested. Worked example may reduce unproductive process during learning that causes extraneous cognitive load. Nevertheless, worked examples must be created in such a way facilitate learning.

Cooperative learning implementation to improve an achievements of students on science competition

“…Several studies have been conducted (Triarini et al, 2017), in a study that examined the effect of cooperative learning on academic achievement on Senior high school students in the field of mathematics, he reported that there was a significant difference between the value of student achievement taught by cooperative and traditional methods (Retnowati, 2018). Students taught by cooperative methods show high grades.…”