Teachers who have taught first-grade mathematics are familiar with this part of the content, and they must also know the basic arithmetic of "subtraction within 20"-"breaking the ten method". In the old textbooks, "breaking the ten method" is placed in a very obvious position, and students are guided to master it step by step through the demonstration of the solution of examples. The "subtraction within 20" in the experimental textbook of curriculum standard begins with "subtracting a few from more than ten" in 1 class, and the formulas and examples in "subtracting a few from more than ten" are sufficient to reduce and do not involve abdication. The second lesson "1 1 subtract a few" involves abdication and subtraction, and this lesson has the "ten-break method". There is a scene in the textbook "Congcong buys a ball". Take three balls from 1 1 to guide students to find math problems in life situations and find solutions. The specific operation method is to use the learning tool "pendulum calculation" to show the methods of "red" and "smart" in the book. Red is directly counted from 1 1, leaving 8; Cong Cong divided 1 1 into 10 and 1 by "ten-break method". First, take three from 10, and the remaining seven, plus 1, equals eight. This design in the new textbook conforms to the concept of "new curriculum standard" and embodies the ideas of "proceeding from the reality of life", "letting students learn valuable mathematics" and "designing students to actively observe, experiment, guess, verify, reason and communicate".
However, the author found such a problem in the teaching process: when we let children practice and encourage them to "use their own methods to calculate", the important "breaking the ten methods" in textbooks was ignored, and almost no students chose this way of thinking to solve problems. Most children choose the red method-count three directly from 1 1 and get the remaining eight. Under the emotional struggle, the teacher had to personally demonstrate Cong Cong's "ingenious algorithm" under the projection, the key content in the textbook-breaking the ten methods. However, the problem has not been solved. When the teacher once again respected the students' feelings and asked the children to evaluate the advantages and disadvantages of the two algorithms, a new problem appeared again: all the children thought the "red method" was better, and no one was willing to take the initiative to accept the "ten-breaking method" in the textbook.
The author thinks that this phenomenon in the classroom is quite representative, which reflects a very important problem in the experiment of curriculum reform-the neglect of students' existing experience by textbook writers and teaching implementers. Still taking the teaching content of "Breaking Ten Laws" as an example, we made the following two mistakes in textbook compilation and teaching design:
First, the grasp of students' psychological characteristics is inaccurate. First-year students mainly think in images, but their logical thinking ability is low. For them, the best way to subtract 3 from 1 1 is to subtract 3 from 1 1. And it turns out that their method can be completed in only one step, which is indeed simpler than calculating 10 minus 3 and then calculating 3 plus 1. Between these two algorithms, children will naturally choose the former.
Second, the design of teaching materials does not conform to students' cognitive laws. 1 1 is the "nearest neighbor" of 10. Taking 1 1 as the beginning of abdication subtraction can reduce the difficulty of the textbook and make it easier for students to understand. 3 is a smaller number within 10, calculated first.
1 1 minus 3 is also to reduce the difficulty of the textbook. And we blindly consider reducing the difficulty, which just deprives students of interest and stimulation in trying other methods. Imagine if 1 1 minus 5 appears in the textbook first, and 5 is in 10.
Less than 1 1 is not a decimal, so students need a process of thinking. In the process of thinking, they may try and find new methods. There is also 1 1 minus 5 in the experimental textbook, but it is 1 1.
After subtracting 3, this design can't further open students' minds, and students will be influenced by the original experience and preconceived effect, and the key point in the textbook-breaking ten methods will not be broken.
The author believes that it is not enough to have some avant-garde ideas and theories in the "curriculum reform experiment", whether it is the writer of teaching materials or the executor of teaching. Good teaching must be targeted, students-oriented and all students-oriented. To respect students, we must respect their understanding and experience, their thinking and discovery, and their psychological characteristics and cognitive laws. Only by truly understanding students can we truly realize "let every child learn valuable mathematics in life situations".