Math and the Future.

  The other night, I ran across an online article from the American Scientist in which the author gave 5 reasons for mathematical modeling being taught in school.

Her reasons are sound.  She did not make any new points, only those who want to change how math is taught have made before. 

It is good seeing this topic addressed in a place outside of mathematics because the word needs to get out.

In addition, she eloquently discusses how mathematical modeling is often used to create a good enough answer for a mess real world problem.  I like that she talks about a "good enough" answer, rather than a perfect one.

The first reason the author gave for teaching mathematical modeling is that modeling offers the students a chance to make genuine choices rather than performing the math by rote.  Unfortunately, standardized tests are set up to have nice, easily graded problems rather than messy real life problems.  Students must make choices in regard to the parameters used, the math needed, and determine if the solution is reasonable before communicating their findings.

Second, most real modeling problems have multiple solutions rather than just one so everyone stands a good chance of being "right".  Solutions to mathematical modeled problems must use valid mathematical arguments and make contextual sense.  Many times solutions are approximations rather than precise answers depending on the complexity of the problem.

Third, many of the "real world" problems presented in textbooks are not very interesting and certainly not practiced that way in business, economics, or other fields.  Mathematical modeling problems are practical and answer a question someone needs in order to make a decision.  One example is when companies are testing new drugs, they need to know the point at which it can be released safely to the public.

Fourth, there is an idea in school that you must learn a certain amount of material within a specific time period.  In reality, mathematical modeling problems may take a longer period of time to find the answer.  They also allow students to use the tools they want while practicing skills they need reinforced.  There is not an easy solution because the process of modelling requires a person to try, adjust, and try again until a solution is found.

Last, modeling shows students that mathematics can be a team sport rather than having to work in solitude.  In real life, teams are used to solve problems when modelling.  Collaboration allows communication and a solution to be found faster than working alone.

The thing about modelling problems is you can find them all around you. One example might be rating the food in the cafeteria using a list of criteria so the student knows what the most and least important characteristics in order to determine the best food.

These are all valid points.  Tomorrow, I'm going to provide several websites with modeling problems.  Some of the problems will be not bad while others will require quite a bit of work.

Let me know what you think.  Have a great day.