  Learning to derive subgoals reduces the gap between experts and students and
makes students prepared for future problem solving. Researchers have explored
subgoal labeled instructional materials with explanations in traditional
problem solving and within tutoring systems to help novices learn to subgoal.
However, only a little research is found on problem-solving strategies in
relationship with subgoal learning. Also, these strategies are under-explored
within computer-based tutors and learning environments. Backward
problem-solving strategy is closely related to the process of subgoaling, where
problem solving iteratively refines the goal into a new subgoal to reduce
difficulty. In this paper, we explore a training strategy for backward strategy
learning within an intelligent logic tutor that teaches logic proof
construction. The training session involved backward worked examples (BWE) and
problem-solving (BPS) to help students learn backward strategy towards
improving their subgoaling and problem-solving skills. To evaluate the training
strategy, we analyzed students' 1) experience with and engagement in learning
backward strategy, 2) performance, and 3) proof construction approaches in new
problems that they solved independently without tutor help after each level of
training and in post-test. Our results showed that, when new problems were
given to solve without any tutor help, students who were trained with both BWE
and BPS outperformed students who received none of the treatment or only BWE
during training. Additionally, students trained with both BWE and BPS derived
subgoals during proof construction with significantly higher efficiency than
the other two groups.
