Since performance assessment was introduced in Korea in the middle of 1990, many problems which include its definition, characters, methods and scorings etc., raised in mathematics education worlds. Therefore this paper presents the theoretical background of performance assessment in mathematics education. Contemporary teaching and loaming theories reject stimulus-response theory which emphasizes outcome. Performance assessment emphasizes the assessment which reveal learning process and various strategies. And it bases on constructivism and socio-cultural perspective. This paper presents paradigms which guide the roles and purposes of assessment. The paradigms include conventional paradigm, constructivist paradigm and critical paradigm. There is a close correlation between constructivist paradigm and performance assessment. Assessment has to grasp the development of present and the possibility of development of future of the students. Performance assessment must be fixed the new paradigm of education for this purpose.