The purpose of this paper is to consider the teaching program that applies Vygotsky's theories of teaching and learning to children who have Puerto Rican backgrounds. In the program, Hedegaard and Chaiklin developed the approach of "radical-local teaching and learning". The approach was based on Vygotsky's idea of "spontaneous concepts" and "scientific concepts", and it attempted to combine children's local knowledges with general concepts from subject-matter disciplines. Through the teaching program, the children acquired the research methods and formulated core models. This paper describes the teaching-learning processes.