The appearance of the concept of function itself marks a major turning point in mathematical thinking methods-from constant mathematics to variable mathematics. The application of functions has fundamentally changed the face of mathematics, from object to theory, method and structure. As far as middle school mathematics is concerned, the importance of function is beyond doubt. It has become a link in middle school mathematics, but it is also one of the most difficult contents for students to understand. Functions are really difficult for students to understand.

First, the analysis of the causes of junior high school students' learning difficulties in function.

The reason of the concept of 1. function itself.

(1) Complexity and dialectics of the concept of "variable".

(2) Diversity of functional concept representation.

(3) The abstraction of functional symbols.

2. Students' thinking development level.

In the study of function concept, students are required to combine numbers with shapes and flexibly switch between symbolic language and graphic language. But in students' cognitive structure, number and shape are basically separated. When students understand the concept of function, they need to construct a scene (analytical, tabular or graphic) in their minds, so that the corresponding laws of function can be vividly and dynamically reflected; Function is the unity of correspondence law, definition domain and value domain. Students should understand their mutual constraints and grasp the three as a whole. However, the development level of students' thinking is still in the immature stage of dialectical thinking. They often look at problems one-sided, static and fragmented. They are not good at linking abstract concepts with concrete examples, nor are they fully qualified for this learning task that can only be understood by dialectical thinking and movement changes.

Second, junior high school students function learning difficulties solutions

(1) Establish a correct view of mathematics and error.

A correct view of mathematics plays an important role in supporting students' learning motivation. Many students have the psychology that "mistakes in math learning mean failure, because learning is to find the right answer". Once students don't get the standard answer or can't treat their mistakes and misunderstandings correctly, they will doubt their learning ability and often encounter such confusion. Students lack confidence in mathematics learning and think that they are not "materials for learning mathematics", which will gradually reduce their motivation to learn mathematics and weaken their achievements in mathematics. Teachers should often give students "frustration" education to help them form the concept of correctly treating mistakes in learning. Teachers should not cover up their own twists and turns or mistakes in solving problems in teaching, so that students have the opportunity to understand the real thinking process and understand that mistakes in learning are normal. They should also guide students to treat mistakes and omissions in their studies with a positive attitude. Although mistakes and omissions can easily make people angry or discouraged, we should also see that this is a good opportunity to improve our cognitive structure and improve our ability.

(2) Cultivate students' ability of learning reflection.

A considerable number of students have not developed a good habit of learning reflection, lack the ability of self-correction, and cannot correctly evaluate their own cognitive process, thus affecting students' further study. Constructivist learning theory holds that students' mistakes cannot be corrected simply by positive demonstration and repeated practice, but must be a "process of self-denial", which is reflection. Therefore, in teaching, we should not only pay attention to the learning of knowledge and skills, but also guide and motivate students to study reflectively in mathematics activities. For example, teachers often organize students to think and discuss questions instead of giving correct answers directly. In the reflection on their mistakes, they adjust their cognitive activities, learn lessons and make progress step by step, which is conducive to making correcting mistakes become students' conscious actions, helping students master good methods of analyzing problems, and then develop good reflection ability.

(3) Attach importance to communication and encourage cooperative learning.

Teachers are busy completing teaching tasks and have little communication with students. On the other hand, students recognize and accept the communication between classmates. Not all the knowledge or understanding of a problem is taught by the teacher. For example, when the teacher explains a problem to the students, the students can't understand it, but it is possible that his classmates can make him understand it. We should advocate and encourage "cooperative learning" and other forms to provide students with opportunities to learn from each other, depend on each other and share learning resources. Especially when mistakes occur, students can solve cognitive conflicts through mutual communication and thinking, so as to achieve the understanding of the nature of errors and knowledge.