The Teaching Of Function Monotonicity In High School Subject Teaching (Mathematics)

Functional monotonicity is a core property of the function,a key part of high school mathematicsis,and a widely-acknowledged teaching difficult point.The learning of functional monotonicity throughout the whole high school time.Therefore,the teaching of Functional monotonicity has great academic value.The teaching of the definition of functional monotonicity is analyzed and reviewed from the perspective of "teaching" and "learning".The relevant literature on the comprehensive application of the definition of Functional monotonicity is also analyzed.This research investigates students from three senior one classes in the cognitive situation of the definition of Functional monotonicity.The results show that for the definition of functional monotonicity,most of the students involved in the test,they score higher on tests that are related to "memory" while score lower on tests that are related to "understanding" "application","analysis","comprehensive"etc;The achievements of students from three senior one classes exist significant differences;The scores of different gender students do not exist significant differences.The researcher interviews several senior three mathematic teachers.The results shows that the situation the students use the functional monotonicity to solve the problems of inequality,equations,parameter range,zero point,extreme value,and maximum value,is difficult.In this paper,the theory of constructivism,"zone of proximal development",mathematical concept learning,working memory capacity,are employed to analyze students' difficulties in learning the definition of functional monotonicity.The difficulty of comprehensive use of function monotonicity are analyzed by using two integrated use cases of functions.Finally,an "eight segment" instructional design on the definition of functional monotonicity is introduced by the researcher.Two teaching cases in terms of the comprehensive application of functional monotonicity are also designed by the researcher.