This strategy can be difficult for the students to master. For most of their mathematical lives, they have been taught to start at the beginning of a problem and carry the action through, on a step-by-step basis. The “Working Backwards” strategy, however, takes the opposite turn. The students begin with the end result of the problem, and carry the action backwards to find conditions at the beginning. The mathematical operations are reversed; so, for example, what was subtraction now becomes the inverse operation, namely, addition.
Once the answer has been found, the results can be checked by starting with this answer and carrying the action through from start to finish. This is the one strategy that “advertises” itself by stating the end conditions of the problem and asking to find the starting conditions.
Although, on the surface, the procedure may seem unnatural, it is used in everyday decision making without much fanfare. Take, for example, the task of finding the best route to an unfamiliar place on a map. Typically, we first try to locate the destination point and then gradually work backwards through a network of roads until we get to familiar surroundings. However, when it comes to mathematical applications of this technique, we have to encourage students to include this procedure in their arsenal of problem-solving tools, even where it may not be in an obvious problem-solving technique.
This strategy can be difficult for the students to master. For most of their mathematical lives, they have been taught to start at the beginning of a problem and carry the action through, on a step-by-step basis. The “Working Backwards” strategy, however, takes the opposite turn. The students begin with the end result of the problem, and carry the action backwards to find conditions at the beginning. The mathematical operations are reversed; so, for example, what was subtraction now becomes the inverse operation, namely, addition.Once the answer has been found, the results can be checked by starting with this answer and carrying the action through from start to finish. This is the one strategy that “advertises” itself by stating the end conditions of the problem and asking to find the starting conditions. Although, on the surface, the procedure may seem unnatural, it is used in everyday decision making without much fanfare. Take, for example, the task of finding the best route to an unfamiliar place on a map. Typically, we first try to locate the destination point and then gradually work backwards through a network of roads until we get to familiar surroundings. However, when it comes to mathematical applications of this technique, we have to encourage students to include this procedure in their arsenal of problem-solving tools, even where it may not be in an obvious problem-solving technique.
การแปล กรุณารอสักครู่..