There are many people who use math in daily life problem solving and others who don't know how to do it. They don't know how the individual math chapters interact together with a larger whole. If they knew how it interacted with a larger whole they wouldn't ask "When will I ever use math?".

Here's what Russel Ackoff professor of systems sciences had to say about it

http://www.youtube.com/watch?v=UdBiXbuD1h4 (3 parts)

Analytical thinking allows you to analyze the system at hand in a way that let you describe its behavior, its structure; it allows you to answer the “how?” question. Yet, it never helps you answering the “why?” question.

So, we [Ackoff and his colleagues] had to develop a new way of thinking; the “systemic thinking” [,or sometimes it’s called “synthesis”]

Synthesis, or systems thinking, allows you to truly understand the system and answer the “why?” question. Actually, it also has 3 steps (the same numbers of step for the traditional analysis), and each single step is interestingly quite the “opposite” to the corresponding step in analysis!

Traditional Analysis

1. You take the thing you want to understand apart.

2. You explain the behavior of each part taken separately.

3. You explain the behavior of the containing whole. So if we’re trying to explain a university, we have to first explain the education system of which the university is a part.

Synthesis (or Systems Thinking)

1. You take the thing you want to understand as a part of a larger whole.

2. You aggregate your explanation of the parts into an understanding of the whole.

3. You dis-aggregate the understanding of the whole into an understanding of the parts, so that we explain by identifying their role or function of a system in the larger system which it’s a part. And the explanation of a behavior of a system lies in its role or function in the larger system of which it’s a part.

Example - You go to a business school and you look at the course structure. You study marketing as a separate subject, finance as a seprate subject, production as a seperate subject. The net result is at the end of the business school you have no understanding of what a business is and not even the understanding of its parts. You can't study production independently without understanding how it interacts with marketing, finance, personnel, product and so on