Abstract
Similarity is a topic in Geometry which investigates similar elements of a plane. This topic has a high complexity that generates cognitive load in working memory. A deep understanding of the concept is needed to solve similarity problems. Based on cognitive load theory, learning by goal-free problems is suggested since it can minimize cognitive load. This research examined the effectiveness of presenting similarity inquiries using goal-free problems for learning by collaboration. Using a factorial design: 2 presentation techniques (goal-free vs. goal-given problems) x 2 groupings (collaborative vs. individual) in authentic classrooms, the experiment consisted of four consecutive phases: introductory, learning phase, retention test, and transfer test. One-hundred eleven eighth-graders from four classrooms in a junior high school in Yogyakarta, Indonesia, served as research participants. The findings showed that students who were learning using goal-free problems possessed significantly higher scores of retention and transfer tests, as well as experience lower cognitive load during both tests. On the contrary, it was found that studying individually yielded a significantly higher transfer score than studying collaboratively. Since there was no interaction effect, it may be concluded that goal-free problems can be effective for either collaborative or individual learning.
Highlights
Problem-solving is the major goal and focus of mathematics instruction (Schoenfeld, 2016)
The findings showed that students who were learning using goal-free problems possessed significantly higher scores of retention and transfer tests, as well as experience lower cognitive load during both tests
Research design The study examined the effectiveness of goal-free problems using a factorial design: 2 presentation techniques x 2 groupings
Summary
Problem-solving is the major goal and focus of mathematics instruction (Schoenfeld, 2016). Problem-solving is a skill that should be improved among students in learning mathematics (Retnowati, Ayres, & Sweller, 2010). Problem-solving is typically used for problems with a high level of complexity. Geometry is one of the materials in mathematics with high complexity (Irwansyah & Retnowati, 2019). The triangle similarity is a topic in Geometry, which requires students to investigate similar elements of a plane. Triangle similarity might be categorized as a complex material because it requires a minimum of four steps to finding a solution. The first step is the identification of the corresponding sides and problems. The second step is making equations from the corresponding sides. The step is solving equations, and the final step is finding the solutions of the problems (Tasari, 2011:18-23).
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More From: JRAMathEdu (Journal of Research and Advances in Mathematics Education)
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