The other participants in the whole class discussion, the nonpresenters, also have potential learning opportunities. In problem-centered learning, all students have either solved or attempted to solve the task. "Thus it is natural for them to compare and contrast their ideas with the presenter's explanation, or more accurately, their construction of the presenter's explanation ( Lo et al. 1991). Through the reflection on their explanation and the presenter's, opportunities for learning occur.
As educators move toward the twenty-first century, we are challenged by calls for change. What is advocated in this chapter is the construction of appropriate learning environments where problem-centered learning promotes the existence of potential learning opportunities. When teaching and learning middle school mathematics are approached as activities that allow middle school students to make sense of mathematical tasks, and construction of meaning is an individual activity that relies on social interactions, then learning environments are in contrast to many current practices.
The middle level child, a child in the midst of transition, is experiencing changes in her development. With this in mind, the teacher has to provide a learning environment where students "feel free to explore mathematical ideas, ask questions, discuss their ideas, and make mistakes" ( NCTM 1989). Through problem-centered learning such an environment can be maintained. Teachers can listen to students' ideas while encouraging the students to listen to each other's ideas. The learning environment's atmosphere can be created where many answers are accepted and explored. Moreover, students can be encouraged to seek a verification of their own answers and not search for a verification of a right or wrong solution from an outside authority. Through small group experiences and whole class discussions, students are provided the possibilities for potential learning opportunities. By being challenged in their thinking, students are afforded the opportunity to pull prior experiences and mathematical ideas together and to learn from these opportunities.
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