Before students use charting for mathematical problem solving, they can attempt flowcharting problems like the one below. These will help the children “back- up” and think about what they have to do before actually solving the problem.
, the computer or the flowchart will only perform the tasks you instruct it to perform so each programmer must know what they will do before actually solving the problem.
the process of
FEEDING WILD BEARS.
(figure available in print form)
The preceding chart lists a possible sequence of steps used to feed a wild bear. Students , when diagramming a non-mathematical problem such as this one will learn that the
in which a task is completed is very important for a successful finished product. Students will realize that many steps they would normally take for granted, for example “getting the bear food”, is important for the successful completion of the task (one would not want to accidentally awaken the bear without the insurance of bear food’). When programming computers, it is the “obvious” steps that we tend to forget about and so do not receive the desired results. Students, when charting similar familiar tasks, will learn to be very explicit in their directions. This explicit recitation of steps will help the student develop the directional thinking patterns that are so necessary in problem solving.
Students may be asked to design flowcharts of activities they enjoy such as buying a can of soda from a machine, making a peanut butter and jelly sandwich, performing a simple dance step, etc.. The lesson for the students to learn is that end results do not simply appear out of thin air. A sequential process must be followed for a task to be completed. Students will also discover by observing their classmates’ charts that some tasks may be approached and solved in many different ways and yet each will obtain the desired results. Too often students view mathematics and any field associated with it, as inflexible and learnable only through memorization. This is a grave injustice to the children and to the field of mathematics. In effect, working of computers and flowcharting will help students assimilate their previously learned skills in computation with an enjoyable, highly motivating lesson about problem solving
The student should be encouraged to draw flowcharts that their classmates may also follow. This will emphasize the need for clear, concise instructions in a sequential order. I find that most children are impressed that their flowcharts) or the order in which they decide to solve a problem, are never necessarily wrong, but usually fixable. It is important for students to realize that an intelligent attempt at finding the answer to a problem is just as important as obtaining the correct answers. We, as educators, can unconsciously place entirely too much emphasis on right and wrong rather that on the thinking process involved. Students will benefit from this “ungraded” thinking process and in the long run, will develop a new thinking pattern for solving problems.