Subject: 5 most critical mathematical concepts

Posted by Louis Macovsky on 12/3/2010
In Reply To:5 most critical mathematical concepts Posted by Tim Joy on 12/2/2010

Message:

I offer a rephrasing of Tim’s question for your amusement:

Rather than a list of 5 or 10 mathematical concepts…how about a list of 10 (more or less) curves explained by mathematical relationships.

If we are talking behavior over time (BOT) then…

Any mathematical equation or numerical relationships that can create ANY curve depicted graphically by ONE stock and ONE inflow and/or ONE outflow except in the case of oscillatory behavior where two stocks each with one inflow and one outflow with circular feedback. Rational numbers encouraged. No built-in trig functions allowed. Pulse, step, and delay functions permitted after exhausting all other possibilities without built-in functions.

Therefore we are only discussing basic algebra “emerging” as continuously integrated ODEs.

If a student can look at a BOT graph and at a minimum verbalize the basic relationship (<, >,=) between input and output, I would think that the student has validated the success of the instructor.

That student is now prepared to begin a life of interpreting news reports, financial reports, scientific journal articles, etc. especially if there is a BOT graph illustrating the information within. Better yet a student that can read an article and then sketch the graph and then based on that graph describe the probable underlying basic mathematical relationships.

He or she will no longer need a talking head to do his or her critical thinking. The student will ask what is the cause(s) of increase and/or what is the cause(s) of decrease of …. the state variable or the critical subject of the question/problem. And perhaps then ask what are the algebraic relationships between those causes…and maybe ask where are the leverage points.

Will you graduate a Ross Perot (graphs based on real world data) or a Sarah Palin (catchy sound bites with little meaning in reality)? (Sorry but I could not resist).

Louis Macovsky
Wilsonville, Oregon

Follow Ups:

5 most critical mathematical concepts - Louis Macovsky 12/4/2010