Design learning new sequence
I first heard about learning sequence in Yu Zhiqiang's lecture. Teacher Yu thinks that classroom teaching is a problem of selecting materials and establishing sequences, while Research on New Thinking of Primary School Mathematics talks about designing new learning sequences in a wider scope by means of "restructuring structure, updating content and rolling development".
This book believes that by integrating the contents of different fields, new learning sequences can be designed. For example, taking "multiplication and division" as the core, the perimeter and area of the rectangle, multiplication and division, and the content of multiplying two digits by two digits are integrated under the theme of "Mathematical problems on the basketball court" to form a teaching unit. Starting with step measurement and visual inspection, we accumulate experience for the study of rectangular perimeter, get the multiplication distribution law from two different calculation methods of rectangular perimeter, explain the algorithm of multiplying two digits by two digits with the multiplication distribution law, and solve the complex calculation problem of rectangular area. This integration makes the learning of various knowledge points interlocking, forming a network knowledge structure.
The book mentions that "there is pregnancy before, there is breakthrough in the middle, and there is development after", and it adopts rolling development. Pre-pregnancy: combine the accessible knowledge points, make the necessary foundation for learning an important knowledge point in the early stage, and reduce the difficulty of learning new knowledge for the first time. Breakthrough: Let students take the initiative to use the original knowledge, break through the difficulties in the exploration of new knowledge, make empirical materials mathematical and mathematical materials logical. Lateness: refers to the transfer of mathematical knowledge and methods obtained in the exploration of "breakthrough in learning", and expands the depth, breadth and flexibility of knowledge application.
In fact, no matter whether they study textbooks or a class, their ideas are all the same. I once designed a teaching case with the concept of pre-pregnancy, mid-breakthrough and post-development, and even won the first prize of Wenzhou case evaluation, which was really unexpected.
Practice and Theory of Three Links in Teaching
Classroom teaching should follow the law of students' thinking in acquiring mathematical knowledge, that is, the law of problems, the law of situations and the law of mathematical thinking development, and the corresponding teaching process should be organized according to three links: introduction, development and consolidation.
According to mathematical thinking, the problem law is introduced to trigger students' thinking activities. Grasp the connection point between old and new knowledge, and arouse students' thinking in the conflict between old and new knowledge. According to the situational law of thinking, through analysis and comparison, the principles and conclusions are abstractly summarized by means of operation, diagram and simulation. Consolidate according to the development law of thinking. There are not only basic training to imitate examples, but also variant training to increase non-essential interference factors and flexible training to solve multiple problems.
Inheritance and development of application problem teaching.
The book explains the ins and outs of application problems and problem-solving teaching for us, which is a puzzling thing for front-line teachers since the new curriculum. Once upon a time, application problem teaching disappeared and became a topic that no one wanted to mention. It seems that anyone who mentions it can't keep up with the development of the times and will stick to the rules. In fact, our lack of education is just a sign of books. In this book, Mr. Zhang Lao specially discusses the relevant contents of application problem teaching, giving people a feeling of being suddenly enlightened.
Application problem is to express the relationship between known quantity and unknown quantity by language, characters, figures and tables, and solve the problem of unknown quantity. Although the curriculum standard does not appear the name of the application problem, the textbook does not list the application problem as a separate teaching unit. However, application consciousness should be a teaching goal, and it should be a teaching consciousness and teaching method, which should run through the whole process of mathematics learning.
The book holds that attention should be paid to helping students distinguish between conditions and problems, establishing a contact system of "problems", "conditions" and "algorithms", and making good use of line training, supplementary training, topic training, selective training and variant training, so that the five kinds of training can become a powerful starting point for teaching.
At the same time, in the process of solving problems, we should implement the following ideas:
(1) The idea of comparison: comparison is a common method in thinking activities. It has two basic forms, one is vertical comparison, that is, the comparison of the development and change of quantitative relations at different levels; The other is horizontal comparison, which compares different analysis methods and different solutions at the same level of the development and change of quantitative relations. The teaching of comparative method enables students' thinking activities to expand rapidly from the old and new connection points, and makes full use of the existing problem-solving experience based on "known", so it is beneficial to form the logical connection of problem-solving methods.
(2) Corresponding thinking: Finding the corresponding relationship between quantitative relations is an important thinking method to solve application problems, which should be used as basic training in the teaching of integer and decimal compound application problems, fractional application problems and proportional application problems.
(3) Hypothetical thinking: first assume one condition in the problem as another similar condition, so that the solution of the problem tends to be simple and clear.
(4) the idea of replacement: replace one quantity with another, so that the quantitative relationship tends to be clear.
(5) the idea of transformation: the standard of transformation comparison; From the non-corresponding relationship between quantity and quantity to the corresponding relationship.
In short, through reading and studying this book, we can understand the ideas and characteristics of textbook compilation, make better use of textbooks, carry out effective teaching, and let teaching promote students' development, more accurately, promote students' thinking development.