The growth of robot technology has prompted growing interest in educational-support robots that assist in learning. Most of these studies report on collaborative learning between educational-support robots and healthy children. Meanwhile, the number of children in primary schools with diagnosed developmental disabilities (gray zone children) has increased in Japan. Gray zone children may have difficulty learning over long time periods. Moreover, gray zone children tend to receive peer teaching from healthy children in the school environment. Other symptoms of autism in children are low self-esteem and possibly depression. We expect that gray zone children will learn best by teaching another learner. Learning-by-teaching promotes self-esteem and improves the learning time. In a previous study, a robot that answered a question incorrectly and uttered “Please teach me” or similar statements provided a collaborative learning environment for the learning-by-teaching method. However, whether collaborative learning with this robot increases the learning time of gray zone children was not investigated. Therefore, the present study investigates whether gray zone children can improve their learning time in collaborative learning with a robot that prompts learning-by-teaching. The robot is designed to answer questions incorrectly and utter statements such as “Please teach me.” The robot is also designed to have learning capability. For example, the robot learns the methods of problem-solving from its human partner. Thus, when presented with a question that can be solved by a previously learned method, the robot can answer the question correctly. The experimental results suggested that the learning enhancement was driven by the robot’s initial incapacity to answer a question, and its requests for assistance by the gray zone child. Gray zone children engaged in collaborative learning with our robot spent more time learning than those working alone. Moreover, the gray zone children enjoyed the collaborative learning with our robot than the robot which always solves questions correctly and never solves questions correctly.