Open-ended Mathematical Problems In Middle Schools

Open-ended Mathematical problems were used in mathematics teaching since 1970s. Compared to traditional close-ended problems, their givens may not be complete;their solutions may not be definite. These properties could give students opportunities to attack them from different aspects, to get various solutions, and to share their solutions. In this process, the students are active explorer of new knowledge. Therefore, Open-ended Mathematical problems have been recommended for use in mathematics teaching as useful supplement to traditional mathematical problems in math textbooks. Researchers in the field of mathematics education often treat open-ended mathematical problems as a model of mathematics teaching. They have discussed the definitions, classifications and merits of open-ended problems. However, very little work has been done to teach open-ended mathematical problems as a special kind of problems so as to achieve the most efficiencies.In this thesis, we first give a definition of open-ended problems, then classify them from the formal and formless perspectives, and finally discuss how to use them in teaching practice based on constructivism theory, students' cognitive development and several teaching principles.