Effective learning requires that people reflect on their thinking processes after experiencing failure in problem-solving and that they acquire knowledge to use in the next problem-solving task. However, previously researchers have pointed out that some learners cannot reflect appropriately on their mistakes. The present study focused on the quality of the lessons in the use of the metacognitive learning strategy called "lesson induction", in order to examine the kind of knowledge learners acquire after problem-solving failure. A criterion was developed to enable an evaluation of the quality of the lessons induced. Middle school students (8th graders at 1 school: 86 boys, 73 girls) took a lesson-induction task and then completed a questionnaire. The data analysis examined the relationship between the quality of the lessons and the students' academic performance, and compared the quality of the lessons with an evaluation by mathematics teachers. The results indicated that the new criterion may be useful for capturing the quality of the lessons induced. The results from the evaluation of the quality of the lessons suggested that the students may have had difficulty analyzing their own mistakes and extracting knowledge that would be useful for problem-solving transfer. Furthermore, the results of the analysis of the relationship between the quality of the lessons and the students' characteristics suggested that a learning belief that emphasizes deep cognitive processing, such as deep understanding or failure utilization, may be related to inducing high quality lessons.