Since the mathematics curriculum reform suffers many criticisms. These issues arise from some misconceptions of constructivism. First purpose of this paper is to explore the paradigms of constructivism and each of their beliefs in learning. The second purpose is to clarify these problems in mathematics education. The major findings of this paper are as fallows: 1. To improve the top-down model in mathematics education. 2. It's necessary to understand what differences between teachers' values and their positions. 3. To overemphasize the position of radical constructivism in math learning. 4. To rethink the importance of basic skills in mathematics. 5. It's important for teacher's subject matter knowledge.