Students gain knowledge only from the teacher's explanation and student books, so students have not been able to develop their critical thinking skills became the aims for this research to 1) explain the differences in critical thinking abilities of experimental and conventional group students; 2) the differences in critical thinking abilities of male and female students, and 3) interaction using mathematics learning model on students' critical thinking skills. The type of research used is the factorial design treatment by level 2x2 methods. In both classes, samples were applied with different treatments. The population is all second-grade students of SDN Sungai Geringging. Sampling was done by using the multistage random sampling technique. The data analysis technique used descriptive statistics to analyze and to describe the research data, and the inferential descriptive to analyze with a two-way ANOVA test. The research resulted that there are (1) differences in the critical thinking abilities of the experimental group students with the conventional group students of class II SD in Sungai Geringging; (2) differences in the critical thinking abilities of male and female students of class II SD, and (3) there is an interaction using the mathematical inquiry learning model on students' critical thinking skills of class II SD in  Sungai Geringging.