Promoting Instructional Design For High School Students To Understand Mathematical Concepts

The understanding of the concept is abbreviated "Concept Understanding". In this paper the "Concept Understanding" is referring to the understanding of mathematical concept. Through the survey to students and mathematical teachers, they all make the recognition that "learning mathematical concepts, understanding is important", so how to promote the students to understand mathematical concepts will become very important. And the way to promote the students to understand the concept is more, but they must be reflected to teaching, and the teaching need to design. This paper is based on instructional design; we hope that effective teaching design can promote the understanding of concept.Chapter 1 is about how to understand the concept of mathematical concept, and what is the meaning of it. So we first discussed the meaning of mathematical concept and the content of mathematical understanding, on this basis, we elaborate on the "Concept Understanding". Chapter 2 overview the design of the mathematical concept from the General Teaching design and Mathematics Teaching design, targeted to address the conceptual design. On the basis of the first two chapters, Chapter 3 focuses on how to promote students to understand the concept through teaching design, in a few principles, were analyzed the main ingredients theoretically .Chapter 4 Revealed that effective designing can promote the understanding of the concept with surveys and the case. Finally (Chapter 5) we make a reflection to this study, and promoted the further research directions.The main conclusions are:Understanding of mathematical concepts, is to establish appropriate psychological characterization from a psychological point of view, it is simply a good grasp of the nature of mathematical concepts from a practical teaching and operable, namely, the connotation and extension of it.Mathematics teaching design has been a certain amount of research, achieved certain results, but also to further improve: strengthen theoretical study, pay attention to practical application, ho(?) forefront of concern, and strengthen teacher training.From the point of view of teaching design, to promote the high school students understanding of the concept of math, we should first pay attention to three changes: change of mathematical concept, the change of students, the changes of teachers; based on three principles: in accordance with the "Teaching" teaching system design pattern design; according to the Center for classroom instructional design model of the design process; follow instructional design based on the understanding of the basic framework. Specific design process can be launched from five aspects: understanding of the concept of Mathematics, analysis of learners, established understanding of the objectives, the design of teaching strategies, the evaluation of understanding concept.Survey showed that high school students attach great importance to the understanding of mathematical concepts; understanding of the concept can be understood from three dimensions, that is, the personality of students, teachers teaching and understanding of the evaluation. from the three levels of analysis test, we can see there are significant differences where the different gender and different grades are in the first level, which, boys have more recognition of the importance of "personalization" to "Concept Understanding", a high-grade student agree on the important role of personality in "Concept Understanding" more than sophomore. In the Correlation, "student's personality" and "Teachers" are not significantly related, and they are all significant with "assessment of understandable".The problems reflected from the survey about teachers' "concept teaching" are: the background of the concept are not paid sufficient attention, could be further enhanced about multimedia teaching, the evaluation of understanding the concept should be more diverse, and often.Case shows that the teaching design based on "Concept Understanding" can promote high school students in the understanding of mathematical concepts.