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. However, not all learning occurs through problems. There is still a need to devote a series of lessons to a particular topic. Yet, it is helpful to have children encounter ideas multiple times in various contexts before they engage in a block of work. The curriculum will become more challenging because some ideas from more advanced situations are embedded.