| Researched on High School Mathematical Gifted Students’Understanding Level of Trigonometric formulas, This paper selected one hundred and fifty eight 11 and 12 grade mathematical gifted students from two famous key middle school in Shanghai. The paper conducted Questionnaires based on the Trigonometric Ratios teaching material of Shanghai and proceeded semi-structured interviews. Through literature reviews, the paper choose SOLO to divide understanding level, U-level,M-level,R-leve and E-level respectively, each level corresponding to a identified number.Firstly, the paper determined the level of students’understanding of Trigonometric formulas according to the questionnaires, then chose six typical students to interview and find out the mathematical gifted students’feeling about Trigonometric formulas based on the questionnaires, finally the paper interviewed two very experienced mathematics teachers to find out the overall level and type of high school students’understanding of Trigonometric formulas at present.The paper intend to solve the problem that what level the students on about the undersdanding of Trigonometric formulas and what type they have. The research shows that the mathematical gifted students’have high understanding level of Trigonometric formulas, most students’understanding level is in the R-level and E level. They have high level in conversing between radians measure and degree measure, defining of Trigonometric ratios, inducting formulas and more complex formulas, proving of basic trigonometric formulas and exploring the intrinsic link between the formulas. When faced with complex trigonometric formulas,they do not memorize mechanically, but to take some strategies to remember. Even though the mathematics gifted students have a higher level of understanding of trigonometric formulas, they prefer to understand the Trigonometric formulas by instrumental understanding rather than relational understanding,.The main reason about errors is lacking of deep understanding of the basic definition. The students can not be adapted to the new situation, what is more, subjective topic can also reveals that students are more concerned about the instrumental role of trigonometric formulas instead of the way trigonometric formulas produced and proven. Finally, according to the findings, the paper provides a certain amount of classroom teaching suggestions, focusing on the formation and training concepts. Furthermore, most gifted students should be trained in both intellectual and moral education. |
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