From "Learning by the Design of Teaching" to "Teaching by the Design of Learning"——a Review and Improvement of Teaching Design and Planning for "Monotonicity of Function"

A good many contradictions of math education assembles at the first lesson of monotonicity of function,which constitutes challenged to the design and planning and process for every math teacher.Teaching design and planning based on the concept of by the design of paid more attentions to the of teachers than to learning of learners,emphasize on the transferring process of knowledge and the student’s obedience to the power of teachers,thus neglect the independent reflection and purport conformation.However,teaching design and planning based on the concept of teaching by the design of learning,with an attentive view to the learning process of students,emphasized on the evolution process of monotonicity of function from intuitive graphic character to natural language description and then to math denotation depiction,and also emphasized on the genetic evolution process of math knowledge,help to master the cognitive strategy by experiencing the symbolic construction of monotonicity of function.