Designs of goal free problems for learning central and inscribed angles

Abstract

A mathematics problem solving is usually a non-routine problem that different contexts, concepts or uncommon procedures. There are many strategies to present mathematics problems: with a specific goal or without a specific goal. A problem solving with a specific goal asks students to answer the given question. While a problem without specific goal or goal free does not ask students to solve a specific question, but to solve as many unknown as possibly seen in the problem. According to a Cognitive Load Theory (CLT), mathematics problem in goal free format is more beneficial for students with low prior knowledge since it can reduce extraneous cognitive load. By completing goal free problems, students work forward from "what is known" to any possible move. As a result, students are more likely develop reasoning. Nevertheless, there are very few study of goal free problems in mathematics. Using the principles of CLT, this paper discusses how to design goal free problems, particularly for learning angles in circle: central and inscribed angles, which is considered a difficult topic for junior high schoolers. Furthermore, this paper also discusses how to implement this goal free problem in the real classroom.