Case 1: teaching the concept of non-planar straight line
After the definition of non-planar straight line is obtained, the following variant judgments are set: ① Non-intersecting and non-parallel straight lines are called non-planar straight lines; ② Two disjoint straight lines in space are non-planar straight lines; ③ Two straight lines in two different planes are non-planar straight lines; ④ Two straight lines that are not in the same plane are straight lines in different planes.
Students judge whether it is right or wrong through a group of similar concepts, so as to obtain the essential attributes of concepts and correctly distinguish essential and non-essential features in the process of solving problems.
Case 2: Conceptual Teaching of Monotonicity of Functions
Monotonicity of function is a completely formal abstract definition that students come into contact with earlier after entering high school, which has great learning difficulties for senior one students who are still in the stage of concrete image thinking.
Let f(x) be a function defined on r,
① If x 1, x2∈R and X 1
A.①③ B. ②③
C.②④ D. ②
Through the above variations, it is emphasized that the monotonicity of functions x 1 and x2 has three characteristics: first, both x 1 and x2 belong to a monotonous interval; Second, arbitrariness, that is, take x 1, x2 at will, and never discard the word "arbitrary"; Third, there is a size, usually X 1
For an interval [a, b] in the domain, any x 1, x2 ∈ [a, b] has ■ >; 0, the function monotonically increases in the interval [a, b], which provides a basis for learning derivatives in the future.
When teaching new concepts, the concepts put forward under a single background are generally the standard forms of concepts. By changing the background of the problem, we can get the non-standard form of the concept, so as to understand the connotation of the concept, which belongs to the specific level of mastering the concept. The forms of variants are rich and colorful. For geometric concepts, graphic variants can be used to form concepts through intuitive forms. For the concept of declarative semantics, we can use language variants; However, concepts expressed by mathematical symbols can use symbolic variants. Of course, the above-mentioned conceptual variants are not alienated, but are mutually transformed and interrelated.
■ Use variant teaching methods for examples and exercises in textbooks.
There are many math topics in senior high school. Many students have done a topic and will not do it if they change to the same type of topic. Many students take the tactics of asking questions, which is very heavy. Teachers should study the root of the topic, pay less attention to the essence, adopt variant teaching and teach students the essence of mathematics and its thinking methods.
Case 3: Senior High School Mathematics Beijing Normal University Edition Compulsory 2 Page 25 Case 2: As shown in figure 1, in the space quadrilateral ABCD, e, f, g and h are the midpoint of the sides of AB, BC, CD and DA respectively. It is proved that the quadrilateral EFGH is a parallelogram.
Generally, teachers are busy telling the next example after finishing this problem, so that students will not encounter similar problems. If variants are used properly in teaching, it can help students to deeply understand the essence of spatial quadrangle.