Our goal in this article is to discuss the importance of problems in early childhood education for the child's development and engagement with the mathematics existing in childhood culture. Our assumption is that an important task for young children's education is to create a democratic and critical environment, in which multiplicity of perspectives is celebrated, along with diversity of concepts and practices, with movement between imaginary and real worlds. In light of this, the goal of this article is to defend a perspective for curriculum and for the role of the mathematics educator, promoting the learning of mathematics through problem solving in early childhood years. In order to discuss and illustrate this perspective we describe the pedagogical practices of two teachers who teach 4- and 5-years-olds, who create for their students an environment rich in problem solving and investigations. In both classrooms, all children individually succeeded in sharing their unique solutions and new knowledge constructed as a result of their inquiries. The experience provides evidence that problem solving affords children the opportunity to raise conjectures, to discuss possibilities and to draw conclusions, even if partial ones, that are then vetted by the group as the authors share their solutions. In this way, the work with problem solving nurtures cooperative learning and promotes the exploration of a diversity of ideas. (author abstract)