On a daily basis, we face some type of problem. Many as routine as, "I am so bored, what can I do today" to more severe or complex problems, such as, "how can I help the homeless". Whatever the problem, we rely on our problem solving skills we learned and acquired in school and life.
It is mathematics, believe it or not, that helps us in solving routine problems, as well as, complex problems. Mathematics enables us to solve problems using various strategies we learn in school from "guess and check" to "looking for patterns". Not only does being a good problem solver help us in our studies but it is required in order to be a successful business manager, scientist, engineer, lawyer, accountant, doctor, etc.
It is mathematics, believe it or not, that helps us in solving routine problems, as well as, complex problems. Mathematics enables us to solve problems using various strategies we learn in school from "guess and check" to "looking for patterns". Not only does being a good problem solver help us in our studies but it is required in order to be a successful business manager, scientist, engineer, lawyer, accountant, doctor, etc.
George Polya, known as the father of modern problem solving, produced a famous four step process for solving problems which is still used today. The four step process presented by Polya are:
(1 ) "understand the problem";
(2) "devise a plan";
(3) "carry out the plan"; and
(4) "look back"
In math and in life, we need to first understand the problem we are facing. We need to determine if we have enough information or too much information.
Once we have an understanding of the problem, we determine how to "carry out the plan". In this step, we can ask questions like:
(1 ) What strategies do we use when solving a particular problem?
(2) Do we draw a picture?
(3) Do we look for patterns?
(4) Do we work backwards?
(5) Do we use a combination of strategies?
When we decide on the strategy, we can then execute or "carry out the plan". It is important to note that we might not always get the correct solution to the problem on our first try. Mistakes might be made and that is OK. We need to learn that making mistakes are part of the problem solving process. We learn from our mistakes and revisit the prior steps to ensure we understand the problem or take another strategy. We keep trying until we find a solution. Once the solution has been found then we reflect on the problem and solution. "Looking back" is an important part of the problem solving process. This will help in detecting any possible errors missed.
(1 ) "understand the problem";
(2) "devise a plan";
(3) "carry out the plan"; and
(4) "look back"
In math and in life, we need to first understand the problem we are facing. We need to determine if we have enough information or too much information.
Once we have an understanding of the problem, we determine how to "carry out the plan". In this step, we can ask questions like:
(1 ) What strategies do we use when solving a particular problem?
(2) Do we draw a picture?
(3) Do we look for patterns?
(4) Do we work backwards?
(5) Do we use a combination of strategies?
When we decide on the strategy, we can then execute or "carry out the plan". It is important to note that we might not always get the correct solution to the problem on our first try. Mistakes might be made and that is OK. We need to learn that making mistakes are part of the problem solving process. We learn from our mistakes and revisit the prior steps to ensure we understand the problem or take another strategy. We keep trying until we find a solution. Once the solution has been found then we reflect on the problem and solution. "Looking back" is an important part of the problem solving process. This will help in detecting any possible errors missed.
Times are changing and creative problem solving is a critical 21st century skill set to have. Therefore, we need to expand and enhance the problem solving strategies we use. The goal is to continue to improve and become better problem solvers over time. Some of the strategies that can be used in solving problems are:
(1 ) guess and check;
(2) draw a picture;
(3) the use of a variable;
(4) looking for patterns;
(5) making lists;
(6) solving a simpler problem;
(7) working backwards;
(8) the use of direct reasoning;
(9) indirect reasoning; and
(10) using a model.
The objective is to have a firm foundation for problem solving to use. The intent is to not only become better problem solvers but to think and work together in solving problems; to present and discuss the findings; and to write up detail solutions for others to follow. These skills will be the basis that will help now and in the future !
(1 ) guess and check;
(2) draw a picture;
(3) the use of a variable;
(4) looking for patterns;
(5) making lists;
(6) solving a simpler problem;
(7) working backwards;
(8) the use of direct reasoning;
(9) indirect reasoning; and
(10) using a model.
The objective is to have a firm foundation for problem solving to use. The intent is to not only become better problem solvers but to think and work together in solving problems; to present and discuss the findings; and to write up detail solutions for others to follow. These skills will be the basis that will help now and in the future !
It starts with a thought . . .
Mr. Gonzalez's Math Class