Purpose: The purpose of this study is to investigate the effects of instructional methods based on Constructivist theory and cooperative learning on first-grade students' mathematical learning achievement and social awareness. Method: A natural sample of 30 children aged 6-7 years old was cluster-randomized into an experimental group. Mathematical Learning Achievement Tests and Social Awareness Assessment Scale were used to assess mathematical learning achievement and social awareness before and after 15 sessions of instruction based on Constructivist theory and cooperative learning. Results: 1) After a certain period of learning or training, the experimental group showed improvement in Mathematical Learning Achievement (M=20.6, SD=1.40). Compared to the pretest, there was a significant improvement in students' performance in the posttest (t (29) = 12.51, p < 0.05). 2) After a certain period of learning or training, the experimental group showed improvement in Social Awareness (M=16.5, SD=1.14). Compared to the pretest, there was a significant improvement in students' performance in the posttest (t (29) = 17.88, p < 0.05). Conclusion: The instructional methods based on Constructivist theory and cooperative learning can enhance first-grade students' mathematical learning achievement and social awareness.