Higher and Better Mathematics Thinking Methods in Senior High School is a book published by Cai in September 2009 by Zhejiang University Press. Most of the contents of this book are developed and improved on the basis of the classroom practice of the original Zhejiang Science Innovation Experimental Class.

A few highlights:

1, strategically important-pay attention to the infiltration of mathematical ideas

In mathematics learning, it is difficult to achieve the ideal effect simply by practicing the tactics of asking questions. We must put ourselves in a higher realm of solving problems. The higher level of mathematics learning in senior high school mainly refers to arming yourself with mathematical ideas and effectively guiding problem solving. If mathematical knowledge is mathematical content, which can be recorded and described by words and symbols, then mathematical thought is mathematical consciousness.

2. Find another way-organically combine mathematics competition knowledge with college entrance examination mathematics.

The mathematics proposition of college entrance examination follows the examination syllabus and teaching syllabus, which embodies the proposition principle of "comprehensively examining the basic knowledge, focusing on the main content, repeatedly examining the hot knowledge and occasionally examining the cold knowledge". In the strategy of solving problems, the college entrance examination generally downplays the special skills of solving problems, and pays more attention to careful design in the general methods of solving problems.

3. Grasp all-collect and refer to all the original questions of the college entrance examination in the past five years.

This paper systematically sorts out the final questions in the national key middle school entrance examination papers and the last mock exam in recent five years, selects the most typical questions, and makes a detailed analysis from the aspects of background, methods and expansion.

4. Source exercise-All materials have been carefully tested by excellent students.

It is worth mentioning that the author used the contents of this book as special materials for reviewing the college entrance examination and distributed it to the students of key classes in Hangzhou No.2 Middle School in 2006, and achieved good results. At that time, the average score of mathematics in the college entrance examination of this class was 1.43, and 50% of the students in the class were admitted to Tsinghua and Peking University, among which Lu Yi was the first in science in the college entrance examination of Zhejiang Province.