The concept of cylinder height has a double meaning. A high line refers to a line segment, and there are countless lines. Height is the measure of high line, and there is only one. The height line and height describe the height of a cylinder from the perspective of "shape" and "quantity" In the teaching of geometric concepts, teachers should downplay the expression of literal forms, fully tap the connotation of concepts, and design multi-level activities to let students know and understand the high essence of columns from multiple angles and dimensions. At the same time, we should pay attention to the accumulation of activity experience and the transfer of knowledge and methods in teaching.

Modern mathematics defines the height of a cylinder as "the distance between two bottom surfaces is the height of the cylinder" [2]. The two bottom surfaces of a cylinder are parallel, and the explanation of "the distance between two parallel planes" in mathematical vocabulary is "the quantity describing the relative position of two parallel planes" [3]. The definition of cylinder height in the textbooks of People's Education Edition and Soviet Education Edition is that the distance between the two bottom surfaces of a cylinder is called the height of the cylinder. As you can see, the height here represents the length. Although the textbook published by Beijing Normal University doesn't define the height of a cylinder, it dynamically presents the process of getting a cylinder by rotating from face to body, and in the teaching of the names of various parts of the cylinder (bottom, side and height), the line segment O'O is defined as the height of the cylinder, and the explanation in related supporting textbooks is that the line segment connecting the centers of the two bottom surfaces of the cylinder is the height of the cylinder. The height here represents the line segment perpendicular to the bottom. Does the height of a cylinder refer to a length or a line segment? Further analysis shows that the "measured value" representing the length should be unique, but the number of columns we often say is unclear. How should these be understood? In the "graphic understanding" of primary schools, it is often necessary to draw the height of some graphics. At this time, "height" refers to a vertical line segment, which is a figure; Height is also used when calculating the area. The "height" at this time refers to the length of a line segment, not a quantity. So "height" has two different meanings: it represents a figure (a line segment meeting certain conditions) or it refers to a quantity (the length of a line segment) [4]. It can be seen that when discussing the height of geometry, there are two different meanings-height line and height. The high line is a line segment, and the height is the measure of the high line [5]. Therefore, we can understand that there are countless heights of a cylinder. In the sense of high line, all line segments perpendicular to the bottom surface and between two bottom surfaces can be regarded as the height of a cylinder; There is only one height of a cylinder. In the sense of height, the length measurement of all high lines of the cylinder is the same. This also shows that height has both the meaning of "shape" and "quantity". In mathematics, some concepts do have multiple meanings. For example, in different backgrounds, "circle" can represent both "circumference" and "round surface"; Plane figures such as triangles, rectangles and parallelograms can refer to the periphery or interior of these figures. The equal sign can represent both the calculation result and the equal relationship between the left and right sides. Fraction has at least five different meanings: the relationship between part and whole, quotient, measure, ratio and operator.