Let us consider the following question commonly raised by students taking mathematics courses at any level, but primarily I have heard this from high school students:

“How is this going to be used [helpful] in ** my** life”?

Sadly, there is no really good answer to this question. At least one of the reasons why this is the case is because, for a vast majority of them, they will * NOT *be using most/any of the math that is being taught in classes i.e. geometry, calculus, complex analysis, complex algebra on trigonometric, logarithmic, etc. functions, etc. With that fact in mind, what teachers need to emphasize {and this is really hard both to verbalize and for students to really grasp} is the critical thinking skills/problem solving ability combined with the logical formulation of mathematics that all students should get from taking mathematics.

What I mean is that it is true that 90% of students will not be taking partial derivatives of trigonometric and other ridiculous things in mathematics for the purposes of their day-to-day occupation/existence; however, the rules behind how/why mathematicians are able to do those things i.e. the proof and use of logic to define systems/branches of mathematics will be used by them.

First, they must use logic aka common sense aka rational thought in their everyday lives to get and maintain their job and present/conduct themselves in a professional manner that, usually, impresses their superiors.

Secondly, by understanding how mathematical proofs operate i.e start with an assumption and proceed using definitions and other proven results, they can apply that to everyday arguments, discussions, and general decision making for themselves and within their jobs.

This raises a new question for teachers that they can and must answer

“how can I [the teacher] make them [the students] understand this”?

My best answer is to focus less on lecturing and spend more time on both applications of mathematics {patently obvious is physics, but economics works for some as well} and showing examples of logic problems that occur on a daily basis in “the real world”. From there, teachers can begin to make the case for mathematical proof and how that is helpful to make students better overall writers, and by emphasizing how the logical underpinings of proofs can be extrapolated to legal and nonlegal arguments/contexts. This should peak lots of student interest because they can start thinking about clever and logical ways to make and win arguments with both their peers, and {unfortunately} their parents. * CLEARLY *we, the instructors, are NOT encouraging arguments/conflicts between our students and their parents; however, this will be a direct result of emphasizing logic and its applications in day-to-day life when we use arguments and proof as two huge examples.

Furthermore, instructors can try and shift from a traditional style to a self-discovery style and see how well students enjoy actually learning, by/on themselves, the mathematical content and its potential applications. There are lots of risks to using self-discovery, and a huge one is the dual required presence of a text that is designed to encourage self-discovery and a teacher who has the skills to translate what they read to “its ‘real” meaning. Plus, this does not even mention the practical limitations imposed by CCSS, budgets, and manpower conflicts present in most districts.

All that being said, I truly believe that making students recognize the true benefits of mathematics as it applies to their daily lives yields so many benefits; unfortunately, there are just as many hurdles that can prevent teachers from achieving this wondrous ideal. One final area that teachers can direct student attention to for application is technology/programming that is used in computers/internet/etc.

Overall, I want everyone to recognize that while these options are available and that they appear to go a long ways to closing the gap between “abstract” mathematics and “the real world”, it must be recognized that none of these are a “silver bullet” solution; however, it is obvious that continuing to teach mathematics the same way as it was 100+ years ago is a certain path to failure. Hence all the time constraints, logistical, and other issues must be recognized as existing, they must be dealt with to allow these needed changes to take place in math ed.

Anyways, that about wraps it up. In short, students have serious complaints about the usability of mathematics in “real life”, and it is on the teacher to provide an answer to their complaint. The answer can be found by looking @ the logic underlying all of mathematics and the applications of mathematics in physics and technology and economics {money rules!!!!!}.