Effective Reasoning/Why Informal Reasoning?
Informal reasoning is intuitive and not reliant on logical thought or debate within a a formal process developed by philosophers such as Confucius, who promoted debate within families and communities in China, Plato, who evolved logical debate between scholars in Greece or Avicenna, who developed these ideas during the Islamic Golden period, from which developed the study of modes of reasoning which might 'prove' or 'disprove' contentious proposals. However, perhaps because of the word informal in the title, the precise definition of informal logic and reasoning is a matter of some dispute!
Most formal methods are deductive' which means taking an ideas apart and analyzing the integrity of its components.
The alternative is inductive reasoning which means searching for reliable related facts that might support or destroy the proposal.
Reasoning is however much more complicated than a collection of logical proposals. Essentially it is problem solving. Inventing new ways of thinking by both analysis of the problem and synthesis of the solution.
Problem Solving edit
One way to do this is to analyze all the givens and the wanteds to evolve a process. For example, if one is hungry, then one might reasonably search the memory for all edibles and their probable location, or one could search the locality and list everything - eatable or not. Most of us would use a bit of both, by collecting a larder or store and organizing its contents precisely to avoid being hungry in the future.
The Reason WHY? edit
Informal reasoning starts at an early age, 'on Mama's knee' or 'sitting with Nelly'. A wag once said that we humans inherit sanity from our children constantly demanding to know asking "Why?", "Why?", "WHY?". Another suggested we should be careful with wishes in case we got what we wanted.
The Dispute edit
Informal reasoning is disputed because, for some, the term does not exclude formal processes, it simply allows intuition, taste and interpretation that goes beyond the 'clinical' logic and the 'habitual' truth.
For example, it is widely held that it is possible to travel too fast in a vehicle, because of the risk of injury or death.
In fact no-one has yet died from speed. What kills people is the rapid deceleration and sudden stop against an immovable obstacle or the arrival of potential energy that becomes kinetic that kills and maims people.
Informal reasoning says - go slowly, leave space, avoid excessive braking, try to predict what those other idiots are doing.... simply because, in accidents, many different vectors are significant, and we rely on previous experience. As Bismark noticed, we don't have time to make every mistake for ourselves - we learn from others: The famous Nelly, mentioned above, our teachers, our friends, our reading.
Its the economy, stupid! edit
Once you realize that everything is complicated, and getting more so every day, you also realize that these formal thinking tools have their limits. Philosophers, theologians and business gurus do indeed discover bits of useful 'truths', but really, they have as much effect on human reasoning as do meteorologists on the weather. That is to say, they report rather than control the process of thoughtful reasoning.
We all absorb culture form our families and societies: paternalism versus participation at home, control versus guidance at school, religion versus socialism in our society and so on. But we also have male and female traits, and even our brain in two parts. It is not an absolute truth, but in general, men are better at spatial and functional relationships (maybe because they once had to form teams to hunt woolly mammoths). Women, however excel at verbal skills (probably because they had to stop the men from killing each other - who knows?)
Informal reasoning therefore somewhat colored by the gender, religion and profession of the thinker. But its purpose is not simply to solve problems, it is to rethink 'common sense' and 'reason' and to share those new thoughts by what might perhaps be called 'entrepreneurial skills'.
Stuff and Junk edit
As EF Shumaker remarked in his treatise 'Small is beautiful' much of what we do is create 'stuff'. Products, services, beliefs, fears or hopes, all of which are saleable, and most of which are 'junk' - things to throw away, such as the information leaflet in every packet of medicine, or the plastic bags we buy in order to throw away rubbish (which, today, is mostly the pretty packaging).
These unnecessary products and services have always been with us, and are part of our rich human heritage. Without a bored shepherd playing with a reed, maybe we would not have the music of woodwind and brass. It was informal reasoning that made the production of food and shelter a minor concern that ceased to consume all the available 'human resources'.
Thinking is what makes us human. To err is human - maybe to reason is divine? It has been proposed that our intelligence is a survival strategy, our 'unique selling point' in which formal logic has its place alongside education, culture and experience. That language - the medium of thinking - emerged from early tool-making. But the most important tool we ever made is reasoning - thinking things through, however imperfectly me may do that.