Edward de Bono devised a simple thinking system called 6 thinking hats which defines how you can approach a problem without descending into argument.
For a long time we have always used argument as a way of discussing ideas and looking for solutions, however argument is very inefficient as its mainly negative and attacking. The argumentative stance can lead to point scoring and antagonism between the persons discussing the idea, leading to a break down in communication.
With the 6 thinking hats approach, people are thinking in the same direction for a short period of time. This same direction thinking, often called parrallel thinking, is highly collaborative and productive. To cover all aspects of the problem, the direction of thinking changes but everyone changes thinking at the same time, maintaining the collaborative nature of the discussion.
This approach helps to open up the topic in discussion and helps avoid any narrow thinking. When considering a problem from these 6 different perspectives you are more likely to establish a robust solution to that problem.
My typical approach is to start with the blue hat to define the objective of the discussion, followed by the white hat to cover all the facts regarding the subject matter.
I perfer to cover the positive thinking before critical thinking, so would follow with the green hat and yellow hats to establish a list of ideas and benefits.
I would then finish off with the red and black hats to help focus on what could practically be achieved and what the team feels is the general approach.
There is an interesting Knowledge Gene on 6 thinking hats for an agile retrospective.