2. Question: Can you calculate the height of the herringbone beam in the picture? Let's talk about the places to be measured before measurement.
3. Students measure and report the results.
4. Extract the shape of "herringbone beam" and draw a line segment at the part just measured. Point out to the students that this line segment is a height of this triangle.
5. Discussion: What kind of line segment is called the height of a triangle? Describe it in your own words.
6. Reveal the definition of the height of a triangle, from which the corresponding base is obtained.
7. Measure the length and height of the base of some triangles (that is, "try it" in the textbook) and talk about the difference between these heights.
At this point, the students have completed their understanding of the height of the triangle. However, from the situation reflected in the class, although the teacher has revealed the definition of triangle height, the students' understanding of triangle height is far from in place, and the establishment of the concept is still quite vague.
Reflection is obviously taught according to the idea of compiling teaching materials. Why is the effect of students' study not ideal? Through reflection, the author thinks that the problem mainly lies in the following two aspects: First, students' perception of conceptual examples is not sufficient. From the perspective of cognitive psychology, students' understanding of a mathematical concept must be supported by countless physical representations. The richer the physical representation is, the more conducive it is to the establishment of abstract mathematical concepts. The above teaching only abstracts the height of the triangle through an example, which is difficult to help students to truly establish a comprehensive and rich concept representation, so the understanding of the concept is relatively thin and superficial. Second, it ignores the connection between mathematics knowledge and students' existing life experience. In life, students have some specific knowledge about the height of triangular objects. How to upgrade these specific knowledge into abstract mathematical knowledge should be a key point in the teaching of this course. Because of ignoring this connection, the above teaching makes students' understanding of triangle height stay at the level of mechanical memory, lacking a meaningful understanding. Based on this understanding, the author designed the teaching process twice and made a second teaching attempt.
The second teaching clip
1. The teacher shows two herringbone roof truss diagrams (one is a triangular roof truss diagram in the book, and the other is an added one with a slightly changed shape and a slightly shorter height). Ask the students to observe and identify which roof truss is taller. Where did you see it?
Can you reach the height of these two roof trusses? Which piece of wood should be measured? Measure on the homework paper.
3. The physical drawings of the above two roof trusses are abstracted into two triangles, and a line segment is drawn at the part where the height of the roof truss has just been measured. Explain to the students that a line segment like this is called the height of a triangle.
4. Change the shape and placement of the triangle, so that students can continue to identify the height of the triangle and enrich their understanding of the height of the triangle.
5. Let the students describe the height of the triangle in their own words.
6. Reveal the definition of triangle height and draw the corresponding base.
leave out