Perhaps the most powerful aspect of this work is devoting substantial amounts of time to having children share their thinking in class. It requires the one who is sharing to translate thoughts into words that make sense to others. It is also important for the listener, who may hear a different strategy or representation, validate the thinking of another student, or compare the efficiency of various strategies. These students learn both ways of reasoning and mathematics content during these discussions. Teachers, who had been using this approach, wrote their views of children and mathematics and some guiding principles about teaching mathematics as a result of their work with problem-centered learning.
Children have a wide variety of resourceful ways of thinking from immature to highly complex.
Children want challenge in their mathematical tasks and problems. Children develop more power the longer they are involved in such work. Less mature children eventually show great growth, although this may not occur quickly. Children eventually work on problems for extended periods of time. A problem-centered approach changes both the content of the curriculum as well as how the curriculum is organized.