Journal of Research and Advances in Mathematics Education
Volume 6 Issue 1 January 2021

The effectiveness of goal-free problems for studying triangle similarity in collaborative groups

Purnama, Pratama Wahyu (Unknown)
Retnowati, Endah (Unknown)

Article Info

Publish Date
16 Dec 2020


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.

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Journal Info





Education Mathematics


JRAMathEdu (Journal of Research and Advances in Mathematics Education) is open-access and peer-reviewed scholarly online journal managed by Department of Mathematics Education, Universitas Muhammadiyah Surakarta and published by Muhammadiyah University Press (MUP). The journal is published twice a ...