Trigonometric Concepts Of Teaching And Research At An Arbitrary Angle APOS Theory

Teaching mathematical concepts is a stepping stone to learn mathematics, students understand and grasp the concept of accuracy will directly affect the students’subsequent learning. Dubinsky (E.Dubinsky) created originated in constructivist learning theory of APOS, and working on the mathematical concept of the learning process, it is pointed out that the individual is an individual to acquire knowledge in a certain order and hierarchy construction process. The new curriculum is based on constructivism as the guiding ideology, in terms of teaching philosophy, teaching materials, teaching methods have undergone a change. How do the teachers to grasp the concept of the new curriculum reform and teaching materials, students’learning situation? In this study,"trigonometric concepts" as the starting point, select a school session of2016high school students and high school, grade three classroom teachers group as the research object, through the issuance of questionnaires and interviews, etc., for "high school any angle trigonometric the concept of "learning to conduct research. The study includes:(1)After the new curriculum, what are students’conceptual understanding of the situation trigonometric?(2) whether the correct understanding of the middle school students to learn trigonometry concepts and high school trigonometry concepts of difference and connection?(3)How do the teachers think in this part of the trigonometric understanding and perception of the new curriculum?(4)Based on the "trigonometric concept or teaching analysis APOS theory and try to give optimum designThe study found:Students are not well distinguish the concept of middle and high school learning trigonometric What is the difference, most of the students think that the content is for junior high school learning content development, main contents trigonometric relationships are still corners of the triangle; Another method of introducing the definition of the unit circle, in radians still vague understanding, thus affecting the trigonometric functions for any angle understanding of the concept; Trigonometric functions are periodic model for understanding enough not even recognize that it is the nature of the function; Most teachers agree that "unit circle" is defined method is superior to "coordinate than the definition of law, but because of teachers’ lack of awareness on the unit circle, failed to play to their strengths in teaching in teaching.Based on this conclusion, the paper APOS theory from any angle perspective on teaching the concept of hierarchical analysis of trigonometric functions, trigonometric functions of any angle and teaching suggestions Teachers should understand the spirit of the new curriculum to help students understand the proper use of the unit circle is the essence of periodic trigonometric functions, combined with the history of trigonometric concepts and theories based on the concept of teaching level APOS gives the order in line with students’ cognitive instructional design.