LEARNING GOAL-FREE PROBLEMS: COLLABORATIVELY OR INDIVIDUALLY?

Abstract

Goal-free is a learning strategy to present a problem without specific questions, in contrary to a goal-given problem. This research examined the goal-free effects during mathematics collaborative learning measured by cognitive load ratings and transfer performance. An experiment was conducted in authentic mathematics classrooms employing a factorial design with 2 problem presentations (goal-free vs. goal-given problems) ´ 2 learning environments (collaboratively vs. individually) using a Geometry topic. This consisted of four consecutive phases: introductory, acquisition, near and far transfer tests. 111 seventh graders (Average: 12.8 y.o.) who were novices, participated voluntary. The findings showed that students who learned by goal-free problems had significantly higher far-transfer scores than when the goal was given. Interestingly, in the acquisition phase, the students in goal-free problems experienced significantly higher cognitive load than their counterparts. Further, it was found that overall, individuals scored significantly higher in a far-transfer test than those who learned collaboratively; however, during the acquisition phase individuals experienced significantly higher cognitive load than collaborative learning. No pattern of interaction effects was indicated. Overall, it was concluded that goal-free problems may be learned either collaborativelly or individually. Nevertheless, the goal-free problems stimulated higher cognitive load during learning, which seemed to have a positive influence.

Keywords

• goal-free problems
• cognitive load
• collaborative
• mathematics