(一)过去“因式分解”这一章教材的安排与教学方法。原教材是按照因式分解的方法编排的。即提取公因式法、分组分解法、公式分解法。在讲乘法公式分解时,是将公式一个个分割开来进行的。这样来安排教材,不仅不符合学生的认识过程,而且打乱了知识的系统性,显得繁琐、重复。例如学生学习了提取公因式以后,就学分组分解法,而分组后仅限于用提取公因式法分解,不能运用公式,一直到学会用公式分解以后,再分组时,才允许用公式进行。又如,在用公式分解的这一节里,是把七个乘法分成四段,分别讲解,在一教时里,只教一种公式这样,学生也只会一个一个地学与用,遇到综合性的习题,就发生了困难。过去的教学方法是“填鸭式”的。每一节课,教师总是把教材嚼得烂熟,一点点地塞给学生。对学生的接受能力和他们的积极性,估计不足。因此学生的潜力,也就无法发挥,只能做做教师的“瓶子”或“鸭子”。因为教材的繁琐、重复和安排的松弛,因而学生的接受能力与 (a) The arrangement and teaching methods of the chapter “The Factoring” in the past. The original textbook is arranged according to the factorization method. That is, the public factor method, the group decomposition method, and the formula decomposition method are extracted. When formulating the decomposition of the multiplication formula, the formulas are separated one by one. Arranging teaching materials in this way not only fails to meet the student’s understanding process, but also disrupts the systematicness of knowledge, making it seem tedious and repetitive. For example, after students learned to extract the common factor, they studied the group decomposition method. After grouping, they were limited to using the extracted common factor method, and they could not use the formula. They could not use the formula until they learned to use the formula to decompose them. For example, in this section of formula decomposition, seven multiplications are divided into four sections and explained separately. In a teaching time, only one formula is taught. Students will only learn and use one by one. Comprehensive problems have arisen. The teaching method of the past was “cramming.” In each class, the teachers always chewed the materials thoroughly and stuffed them little by little. There is an underestimate of students’ ability to accept and their enthusiasm. Therefore, the potential of students cannot be fulfilled. They can only be teachers’ “bottles” or “duck.” Because of the cumbersomeness, repetition, and arrangement of teaching materials, students’ ability to accept