Abstract: With implementation of the strategy of invigorating China through science and education, the urgent need to cultivate high-level scientific research and application talents has put forward higher requirements for the reform and development of basic mathematics and science education. In this paper, focusing on the innovative scientific thinking, the analysis and description of the motion of rigid body in theoretical mechanics of physics specialty is taken as an example, and the spatial thinking embodied in abstract concepts of vector is combined with linear space in linear algebra to show and analyze how to carry out cross-integrated mathematical and science education in basic theory courses. The teaching practice of combining theoretical mechanics with linear algebra is carried out, and the problems existing in the current basic mathematics and science education are analyzed in detail. The reform of cross-integrated mathematics and science education is explored, including teaching contents, assessment methods, online and offline classroom constructions, etc. It is thus recommended to implement deeply cross-integration teaching philosophy, advocate to guide students understanding deeply the basic mathematical and science concepts and principles, change their passive acceptance of thinking habits, and stimulate their professional interest and self-cultivation awareness of original innovation ability.

Key words: rigid body, linear transformation, cross-integrated mathematics and science education, scientific thinking