You'll note that the thesis/proof diagram uses cross-hatching to represent the introduction's thesis area, the opening sections of the body paragraphs, and the first part of the concluding paragraph.
These areas represent areas of control. They are the natural orientation points that readers look to for guidance. If you are clear and unambiguous here and you take pains to make sure that these areas interrelate with each other, you will guarantee that your paper has unity.
In order to maintain control over these areas effectively, however, you must yourself have a clear idea of where your logic is going. You should also have asked yourself what the most effective order is for the points you're going to develop. If you have four points, one per paragraph, it should be clear to the reader (either explicitly or implicitly) why the first one comes first and the third one third (etc.). Sometimes, as when you're moving chronologically, you have no choice. When you do have a choice, remember that the first and last positions are the most emphatic.
What about outlining ahead of time? You may have had a bad experience with outlining in grade school or you may just not like the Roman numeral system. What's less important than the form is your developing what Mortimer Adler calls an "intellectual schematic" before you write. How can you provide the reader with a good map of your thought if you're not operating with one yourself? You don't have to work this out on paper--you can do it in your head. Remember, however: no matter how effervescently creative your thesis/proof paper, it needs to have a plan (proof + proof + proof = thesis). Why not make this plan explicit, especially if you're going to be effervescently creative.
An alternative (or supplement) to the outline is the abstract. The abstract is a short summary of what you're going to present in your paper. Some professional journals print these in the table of contents or at the head of the articles themselves. This way readers can see quickly what the article is about and what its logic is. Each sentence can be viewed as representing--in strict sequence--a section of the article as it is unfolds. Here, for example, is an abstract from an article entitled "Sex Differences in Mathematical Achievement: Adding Data to the Debate":
We can see at a glance what this article is going to address and in what order of points. The logic is tight and presumably the article will be as well if it follows this scheme closely (it does).
Education literature reports male superiority in mathematics starting at about high-school age and increasing thereafter. Studies of course grades, on the other hand, show that females outperform males at all school levels in all academic fields. One explanation of better course performance in college mathematics by females that maintains the idea of male superiority in this discipline is a selection argument--only very able females take college mathematics, while a more heterogeneous group of males takes mathematics course. This study compared the performances of about seven hundred women and men in two college algebra courses at the University of Colorado at Boulder. The analysis of students' grades and examination scores indicate that females did better than males in these courses. The study also investigated whether the higher achievement might be attributed to a more mathematically able group of females electing college algebra. The findings reject this argument as an explanation for women's superior performance.
Another name for an abstract is a precis, and here is a closer-to-home example written for David Barnhill (Religious Studies) by Matthew Hedrick. Matthew is writing on Akira Kurosawa's film masterpiece, "Rashomon." David characterizes the precis as excellent. Once again, note how we can see the entire logical structure of a paper compactly presented.
Kurosawa's Rashomon has been said to mean many different things. Ian Jarvie doesn't agree with past opinions of the film being about relative truth and the ways different people perceive the same event. Jarvie considers this idea of relativism a "cheap philosophy." Instead he sees Rashomon as a narrative on human morals and how our ideals of honor and self-pride affect our judgment. Each character tells a different version of a common experience, and different aspects of their respective stories are presented in a different light. Bravery becomes cowardice, and murder turns into an act of passion as we look through the different witnesses' eyes. According to Jarvie, all of the stories cannot be true because there appears no evidence to determine so. So all the viewer sees is a series of varied stories that all contradict each other. Another aspect has to do with the freedom Kurosawa takes with the "eyewitness principle." It is unclear who is doing the narration at times, and some of the narrators are explaining events they themselves did not observe. This freedom of narration is not something Kurosawa pioneered, but he does use as a tool to provide a new outlook on screen action. To complete his idea of Rashomon being a film about a "moral quest," Kurosawa adds the element of the crying baby that is found by the three men in the gate. The woodcutter feels guilt for his previous actions and adopts the baby as a sort of penance for his behavior. This behavior validates his final confession while also reaffirming the priest's beliefs concerning the good in man.