Mathematical thinking and reasoning capacity play an important role in forming thinking skills and mathematical capacity. This article clarifies the manifestations of mathematical thinking and reasoning abilities of first-grade students. At the same time, we propose a number of measures to develop the mathematical thinking and reasoning capacity of first-grade students, to improve the quality of mathematics teaching in elementary schools, meet the requirements of innovative teaching methods, and improve the quality of comprehensive education.Mathematical thinking and reasoning capacity play an important role in forming thinking skills and mathematical capacity. This article clarifies the manifestations of mathematical thinking and reasoning abilities of first-grade students. At the same time, we propose a number of measures to develop the mathematical thinking and reasoning capacity of first-grade students, to improve the quality of mathematics teaching in elementary schools, meet the requirements of innovative teaching methods, and improve the quality of comprehensive education.