Open model exercises is opposite those who have specific requirement and clear conclusion is enclosed exercises, the condition that is eye pointing to a problem imperfectly or conclusion inaccuracy decides a problem. The exercise is the component with mathematical serious teacher and student, proper exercises, can consolidate not only knowledge, form skill, and can inspire thinking, develop ability. In education process, increase except the attention outside becoming type problem, integrated to inscribe, proper design a few open model exercises, can foster the deep sex of student thinking and flexibility, overcome the inflexible sex of student thinking.
One, handle adventitious open problem, the profundity sex that fosters student thinking
Adventitious open problem, place is containing the element with not only solution to the condition, in the process that solves a problem, must use already some knowledge, union concerns a requirement, make comprehensive analysis to the problem from different point of view, judge correctly, conclude, foster the deep sex of student thinking thereby.
Be like: Learn " proper fraction and improper fraction " when, after the meaning that mastered mark of true and false basically already in the student, ask a student: B ／ A is proper fraction, be still improper fraction? Because A, B is not certain number, cannot decide B ／ A is proper fraction or improper fraction so. Reach after the reflection that passes insecurity in the student and intense debate such conclusion: When B ＜ A, b ／ A is proper fraction; When B ≥ A, b ／ A is improper fraction. At this moment the teacher asks further: Can A, B be arbitrary number? Make the student had deeper understanding to the meaning of mark of true and false not only so, and make logistic thinking ability of the student got rising.
Be like again, when learning a mark, the student is right " cent is led " and " with the mark denotive specific amount " often promiscuous not clear, when as a result solves a problem, the mistake appears on this knowledge dot, although the teacher points out their distinction repeatedly, get ideal result hard however. After learning fractional exercise, let a student do a such exercise in school work: "Have two likewise long string, the first bite off 9 ／ 10, the 2nd bite off 9 ／ 10 meters, the part that which cord remains is long? " after this problem is shown, some students say: "Euqally long. " some students say: "Not certain. " I let a student discuss which kinds of view to be opposite, why? The student expresses an opinion in succession, course discussion, unite understanding: "Because the length of two cord did not decide, the length of the first bite off cannot decide, the part that so which cord remains grows to also cannot decide, must know the length with original cord, the share that ability determines to which cord is remained is chief. " let student discussion again at this moment: Do two cord remain partial length to a few kinds of cases there are? Through sufficient discussion, if make conclusions,reach finally: ① is become the length of cord is 1 meter when, the first 9 ／ 10 be equal to 9 ／ 10 meters, the part that so two cord remain is euqally long; ② is more than 1 meter when the length of cord when, the 9 ／ of the first cord 10 be more than 9 ／ 10 meters, what so the 2nd cord remains is long; ③ is less than 1 meter when the length of cord when, the 9 ／ of the first cord 10 be less than 9 ／ 10 meters, because the length of cord is less than 9 ／ 10 meters when, cannot go up from the 2nd cord bite off 9 ／ 10 meters, be less than 1 meter when the length of cord so and be more than 9 ／ 10 meters when, the part that the first cord remains is long.
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