It is important to get the kids active in their learning of mathematics. We even mention that mathematical knowledge can be transmitted, only the student can build it for himself. Problem solving becomes a crucial aspect in the learning of mathematics.
Children, by trial and error, develop their reasoning ability and learn to solve problems. They discover that there is often more than one way to solve a problem and more than one answer possible. They also learn to speak clearly when they explain their solutions.
What is a problem?
Four characteristics allow us to determine if we are in the presence of a problem:
There must be a purpose to be achieved;
There must be a certain number of data using which you can make a representation;
The problem has obstacles to overcome;
The person must be an active cognitive search to learn how to solve the problem.
These features allow us to distinguish between the exercise of the problem. When your child needs to apply mechanically, a rule, an operation or a formula, it would be more in the presence of an exercise.
To be in the presence of a problem, there must be a challenging aspect that pushes the child to think and engage intellectually.
It is important to the development of strategies for math problem solver for the student. However, it is recommended to opt for flexible and adaptable approaches rather than for 'recipes' that can overload the memory. They do not allow to adapt to new situations.
We have a process through which the child can move in loops, come and go, etc. This process includes four steps:
1. - understand the problem: this step allows the child to take ownership of the problem. He tries to understand what is required. To do this, we suggest to the child of:
Read the problem a few times;
Represent the problem by a drawing or diagram;
Locate useful information (point, circle, highlight);
Identify useless information, it can block;
Reformulate the problem in his words:
What is it about?
What do we know?
We want to know?
2. - develop a plan: at this stage, the child decides how he's going to do to solve the problem. To do this, the child can opt for different strategies:
Refer to previous experiences;
A plan mentally or drawing (table, chart, list, etc.);
Appeal to material handling as needed;
Simulate the problem;
Proceed by trial and error;
Simplify the problem, for example reducing the value of the figures or breaking up the problem by step.
3. - execute the plans: the child puts into practice what was imagined in the previous step. He therefore applied to the chosen strategy and made the necessary calculations. At this point, it is quite possible that the child needs to reflect on the way or go back to the previous step. It must be systematic and leave traces of his approach to:
Writing what he wants;
Specifying what he did (drawing, equation, etc.);
Writing calculations clearly enough to be able to refer to them later and check out them.
Writing the answer.
Ask your child's teacher to see if this approach is used in class. Thus, you can use the same words as those used in the class. Some teachers associate even professions to better illustrate each step. For example:
(1) understand the problem = Detective
(2) a plan = architect
(3) execute the plan = construction worker
(4) check the results = judge
Problem solving is a crucial aspect in learning of mathematics and allows children to develop their reasoning ability
When your child needs to apply mechanically, a rule, an operation or a formula, it would be more in the presence of an exercise.
It is important to the development of strategies of problem solving flexible and adaptable in the student.