Mastering the ability for learning to learn is the most ambitious goal of modern educators. A distinction is made between two relatively independent components of this expertise: (a) the reflective component of the learning to learn ability that allows a person comprehend what knowledge and skills he or she lacks to act in the new situation; (b) the search component of the learning to learn ability that allows the learner to find the missing knowledge and appropriate it. The article deals with the reflective component of the ability to learn and the method to develop it within the El'konin-Davydov system of school education. This system has grown from the hypothesis that reflective thinking belongs to the zone of proximal development of children starting school. Within this system, psychological tools are developed for fostering those reflective potentials of the human mind that are left neglected or even suppressed under the school system prevailing today. Psychological and educational means of developing reflection in class are illustrated through the clinical analysis of dialogs on a math lesson in the first grade. The developmental outcomes of the El'konin-Davydov educational system are exemplified using the cases of tasks with missing data. By the diagnostical assessment of the forth graders, we have confirmed that when the content of education is radically changed, the reflective components of the ability to learn can be successfully developed as early as in the elementary school.