4. Model with Mathematics.
Modeling may be the mathematical skill most useful in the everyday world. The proficient student, or skilled problem solver needs the ability to utilize the math they already know to solve real world, everyday problems. This ability is a necessity for business leaders, political leaders, military leaders and homemakers. In the classroom the student must have the ability to turn a real world problem into a written equation or inequality, thus describing the situation. Outside the classroom, the same method is used, although the process may vary. Some may solve the problem via mathematics, but many will come to conclusions without realizing they needed math to reach their conclusion.
In order to change a real world situation into an equation or inequality the student needs to be able to use reason for analysis. This will enable him or her to understand and describe how one quantity depends on another. The typical “teeter totter” metaphor used in many classrooms to describe how an equation works is a great example.
Analysis will often include making assumptions or estimating values to determine the validity of a possible solution. When the estimated solution is obviously far from the mark the student must have the ability to revise using a guess and check, half-split or other problem solving process. These methods require a clear understanding of the important elements of the problem. Students must be able to clear the chaff and get to the root prior to finding an answer.
Finally, learning occurs as the student begins to master the necessary techniques. Application of problem solving processes to similar problems requires an ability to reflect on, and recall the steps taken. Only then will the similarities of various real world situations, and their solutions, begin to become clear. This is the reason for the common core requirement to write steps used to find solutions. The act of writing lends itself to reflection, and this reflection completes the learning cycle.
James Wheeler – commoncoremath.net