Abstract
Advanced mathematics is a core curriculum in advanced education. The teaching of advanced mathematics needs to focus on developing students' innovative thinking and ability in order to meet the needs of talents in the current society. In this paper, we emphasize the importance of the interest-oriented teaching and the teaching of mathematical thought and methodology in the developing the students' creative thinking and innovation ability. Subsequently, we propose three practical teaching approaches for interest-oriented teaching, in order to motivate students' interests in learning. Correspondingly, we present three available approaches for the understanding of mathematical thought and methodology. For each approaches, we specify the working flow in detail through concrete examples, by using which we believe that the students could strengthen their training of thinking, and improve their innovative ability. KEYWORD: Teaching methods of advanced mathematics; Innovative thinking and ability; Interest-oriented teaching; Mathematical philosophy and methodology; Mathematical modeling
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