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有这样一道思考题:修一条公路需经过一块一民方形耕地(如图),已知AD二巧米、CF=6米、AF l/EC。求这条公收占用耕几的面积。(要求用最优方法解答)┌─┐│沪│└─┘二二二二二二二二二二二二二二二二石二名二气二认1二仁二1二盆二二二二飞侣七气二用此题抽测某班20名中上等学生,结果只有7名学生能写出“6x15二90(平方米)”这一答案。经调查发现,不知解题的学生的原因有三:①AECF不象平行四边形,②知道AECF是平行四边形,但不知它的底和高是多少;③知道6米是平行四边形底边的长,但不知底边上的高是多少。这三种情况都说明学生受感知因素的消极影响,对平行四询衫的本质属性缺乏正确认识。为避免上述现象的发生,我认为教师在教学生认识平行四边形的基本特征时,既要出示如图1这样的教具,又要出示如图2、图8、图4、图6这样的变式模型,在讲平行四边形的高时,教师既要训练学生会作图6的高,也要训练学生会作图7、图8、图9的高。这样,学生通过观察、比较,就能抓住“两组对口一助一令刀叭{闰l图忿,砚4图6边都平行的四边形”这一平行四边形的本质特征,就能认识到,平行四边形中,任意一边上的点到对边所引的垂线就是它的高,而这条对边就是它的底。
There is such a question of thinking: repair a road to go through a piece of a square of arable land (pictured), known AD two clever meters, CF = 6 meters, AF l / EC. Seeking this section occupy a few acres of land area. (Requires the best way to answer) ┌ ─ ┐ │ Shanghai │ └ ─ ┘ two two two two two two two two two two two two two two two stone two gas two recognize one two two two one two two two two Fever seven Qi two pumping test 20 students in this class, only 7 students can write “6x15 two 90 (square meters)” this answer. The survey found that students do not know the problem for three reasons: ① AECF is not like a parallelogram, ② know AECF is a parallelogram, but I do not know how much the bottom and height; ③ know 6 meters parallel to the bottom edge of the parallel, but I do not know What is the height of the bottom edge? All three cases show that students are negatively affected by perceived factors and lack of a proper understanding of the essential attributes of the parallelogram. In order to avoid the above phenomenon, I think that when teaching students understand the basic characteristics of the parallelogram, it is necessary to produce teaching tools as shown in Figure 1, but also to produce such as Figure 2, Figure 8, Figure 4, Figure 6 such a variant Model, speaking parallelogram high, the teacher should not only train students to be high in drawing 6, but also to train students to make plans 7, 8, 9 high. In this way, by observing and comparing, students can grasp the essential features of the parallelogram that “the two groups of counterparts help each other make a parallel”, that is, In a parallelogram, the perpendicular from the point on either side to the opposite side is its height, and the opposite side is its bottom.