It is an experimental research on constructivist models of mathematics teaching (CMMT). The researcher redesigned the lesson plans for CMMT and demonstrated that the precise CMMT would bring up the critical ability of students and improve their mathematics achievement.After testifying the results of this research, the researcher found that the CMMT is quite doable in Taiwan and helpful for students to improve their logical and critical thinking of mathematics. In addition, this finding also proved that adapting CMMT would not lower down the grades of students in their mathematics examinations.Nevertheless, the researcher provided several recommendations to teachers, textbook editors and other researchers. Hopefully, these ideas would bring the attention to those experts in conducing certain measurement of mathematics.