Teaching And Learning Theory On The Concept Of High School Function

Function, as a main thread, runs through the whole high school courses in high school mathematics curriculum. However, the present situation of the function teaching is not very optimistic due to the high abstraction and complexity of function. In addition, we focus on teaching design, thinking method, information technology and problem-solving skills while doing the research of function instruction. Most people pay more attention to solving problems while ignoring the formation of the concept; focusing on theory but ignoring the practical research. Therefore, this study aims to research the concept of high school function teaching.Based on teaching and learning theory of mathematical concept, combined with the new curriculum standards requirements, this study aims to analyze the advantages and disadvantages of teaching of function concept and the reasons for the present situation; To make improvements on the instructional design of function concept according to the above analysis, and carry out the improved instructional design through classroom to test teaching effects. Specific contents are as follows:Firstly, this study analyzes the teaching theory of guiding function concept through the literature analysis in the two aspects:(1) The analysis of teaching theory of function concept which provides a theoretical basis for the later. (2) The analysis of function content which provides reference and basis for the improvements of instructional design.Secondly, through the analysis of the collected instructional design case, It was found that the teaching of high school function concept has so many advantages which is manifested in the following:thorough understanding of the concept; concept application from easy to difficult, and gradually deepened, which is in accordance with students’ cognitive regularity. But I also found some disadvantages which is manifested in the following three aspects:(1) the ignorance of concept formation process while introducing the concept; (2) explanation of the corresponding relation between function variables by following the three examples in the textbook which are not well understood by the students; (3) concept systematic not being reflected. The main reason for the above teaching situation is that the exam-oriented education is centered on the college entrance examination resulting in teachers automatically shielding test content; new curriculum standards has put forward to return to teaching materials, so everything is given priority to the teaching material content; most teachers mistakenly believe that the concept systematic process is a waste of classroom time.Thirdly, on the theory and the status quo, the author makes some improvements for the instructional design of the function concept from the following aspects:choosing the way of combination of the formation and assimilation while introducing the concept, which neither ignores the formation process of the concept, nor wastes too much classroom time but achieve better learning effects; choosing two simple linear function to guide students to analyze the characteristics of corresponding relations between function variables through list, images and analytic expression, which makes it more easier for the students to understand new content in the original cognitive structure; concept systematic process is essential and it can help students to include the new concepts into the existing cognitive structures.Finally, after carrying out the improved instructional design through classroom and evaluating through classroom observation, teacher observation and evaluation, student interviews, etc., it is find that students are clear on the forming process of the concept, understand more thoroughly and apply more flexibly; The students’ learning enthusiasm is high through the whole class. Students learn to analogy, think, discuss, explore and cultivate their ability of observation, analogy and reasoning.