Function is one of the important basic concepts in mathematics. It reveals the interdependence and changing nature of quantitative relationships in the real world, and is an important model for describing and studying the changing laws of the real world. In the high school entrance examination questions in various places over the years, the examination of functions and their graphs has always been an important test point in the high school entrance examination, mainly testing the understanding and application ability of the graphs of functions and their properties. As an important knowledge point for testing basic knowledge and basic skills, a large number of questions of various types and difficulty levels appear. Therefore, the teaching of functions is undoubtedly the focus of junior middle school mathematics teaching, but it is also a difficult point. So, how can we enable students to truly understand functions and be able to use the knowledge they have learned to solve any problems related to functions? There is no doubt that introductory teaching of functions should be placed at the top of function teaching. Therefore, how to grasp the introductory teaching of functions and truly lead students into the door of functions has become the key to whether students can truly understand function knowledge. Now I will describe in detail some of my insights in the introductory teaching of functions as follows:
1. Enrich the methods to stimulate students’ interest in learning functions
For students, functions are a brand new something. Therefore, stimulating students' interest in learning functions is the first important task of introductory function teaching, and adopting rich methods is a crucial step to successfully stimulate students' interest. It must be noted that all means taken should be based on "new", use "new" to inspire students, create a new and unknown knowledge field for students, and let students' hearts be full of mystery and yearning for functions. With enthusiasm and desire to understand functions, know functions, and learn functions. For example, it is to make students feel as if they have returned to the time when they first picked up their schoolbags and walked into campus a few years ago, with a desire to read and knowledge in their hearts.
2. Use appropriate examples to guide students to actively participate in the exploration of new knowledge
Appropriate examples are a golden key for students to explore and discover new knowledge. Function is a very abstract thing for students. Therefore, how to set up appropriate examples is crucial for students to initially perceive the characteristics of functions. In teaching, I set up the following example and related questions:
Example: Calculation:
(1) (2)
Question: 1 , During the calculation process of question (1), what happened to the calculation result? Why did this happen?
2. Who remains the same throughout?
3 . If we use Who caused the changes?
5. Can students imitate question (1) to explain the phenomenon in question (2)?
6. Can students Can you use some appropriate expression to express the relationship you discovered in (1) (2)?
3. Strike while the iron is hot and cultivate students’ ability to explore and learn independently
Through the research and study of the previous examples, students are guided to independently explore the four questions listed in the textbook and understand and master the basic knowledge of functions. And set the following questions:
1. Are there any similarities between these four questions and (1) (2) we studied earlier? What are the similarities? (Guide students to name variables, The meaning of independent variables, dependent variables, constants and functions)
2. Can the relationship between these four questions be expressed by some appropriate formula like (1) (2)? ?(Guide students to understand the three expression methods of functional relationships and appreciate their respective characteristics and strengths)
4. Strengthen application, learn new things and review old ones
1. Strengthen communication with students’ existing knowledge Knowledge connections. The idea of ??change has been infiltrated into the learning and exploration of algebraic expressions, equations, inequalities, etc., guiding students to further understand the concepts of variables and functions based on these previously learned knowledge.
2. Pay attention to students’ understanding and accurate application of necessary mathematical language and symbols.
While reviewing and exploring the connection between functions and existing knowledge, students are guided to gradually learn and master standardized mathematical terms, describe and communicate some phenomena, and enhance their sense of symbols, such as "When x=a, the corresponding function value is b" etc.
5. Learn and then think, let students experience the sense of happiness and accomplishment
Guide students to review the entire process of exploration and learning, and feel the joy of acquiring new knowledge through their own labor with a sense of accomplishment and stimulate interest in learning further functions.
Of course, in actual teaching, the methods and means of introductory function teaching are ever-changing, but no matter what method or means are adopted, the ultimate goal is the same, that is, through these methods and means, we can I like to learn functions and understand functions, and ultimately enable students to have the ability to apply functions to solve practical problems. Therefore, the teaching of functions focuses on introductory teaching, and the success or failure of introductory teaching depends on the appropriateness of teaching methods and means.