Based on curriculum standards, teaching materials and teaching objects (students), aiming at "students' maximum development" and according to learning tasks, in order to maximize learning benefits, improving the columns of "inquiry" and "thinking" or reconstructing the column of "creativity" in teaching materials can bring students to the "nearest development zone" and encourage students to be independent.

[Keywords:] learning starting point; Mathematical reality; Independent investigation; Independent construction

Mathematics is a compulsory education textbook published by People's Education Publishing House. It is compiled according to the Mathematics Curriculum Standard for Compulsory Education (20 1 1 version). There are a lot of "inquiry" and "thinking" columns in the text, which guide students to observe, analyze, guess and fill in the blanks in the form of questions. Accumulate experience in mathematical activities. Because textbooks are developed for students all over the country, not for a certain region or a certain school, we can't take into account regional differences and students' personality differences. Therefore, we should creatively use textbooks, that is, "teaching with textbooks" (appropriately reconstructing "learning materials"), so that seemingly limited teaching resources can be activated and enlarged, thus expanding students' learning time and space.

Based on the starting point of learning, improve the "learning materials"

The columns of "inquiry" and "thinking" in textbooks are actually learning methods to help students carry out "independent inquiry". Its essence is to introduce scientific inquiry into the classroom, so that students can understand the scientific concept and the essence of scientific inquiry through the inquiry process similar to that of scientists, and cultivate students' scientific inquiry ability (Chai Xiqin). However, in actual teaching, it is often divorced from students' reality, or higher or lower than their learning starting point. Therefore, according to students' reality, a little improvement on "inquiry" and "thinking" in textbooks can not only help students climb the ladder, but also help them really "explore" their learning.

Case 1 intersection line (1) (seventh grade mathematics (Volume II), a compulsory education textbook of People's Education Publishing House (hereinafter referred to as Volume I or Volume II of Grade X).

The textbook requires students to draw two intersecting straight lines at will and observe the positions of the four corners. In practical teaching, it is difficult for students to tell the relationship between the two positions of the four corners. In order to let students fully experience the process of knowledge "occurrence and development" and cultivate and improve the ability of reading pictures and reasoning, "inquiry" can be improved as follows: