The fields of mathematics, science, and engineering are replete with diagrams of many varieties. They range in nature from the Venn diagrams of symbolic logic to the Periodic Chart of the Elements; and from the fault trees of risk assessment to the flow charts used to describe laboratory procedures, industrial processes, and computer programs. All can be of great help in clarifying what may be a very complex idea, procedure, or collection of data. There is a diagram with a very simple structure that emerges in virtually every field of scholarship. It is a table with two columns and two rows--plus headings above each column and to the left of each row. This table is referred to in this paper as the two-by-two array or "window", because it has four cells or "panes", as does a simple glass window. And just like a small spreadsheet that only uses columns A and B and rows 1 and 2, each cell or entry has the combined characteristics of the headings above and to the left of it. The two-by-two array is then appropriate for describing the effects of two variables examined at two different levels. Despite their simplicity, these diagrams are extremely helpful in clarifying concepts and relationships, in enumeration of possibilities, as well as in organizing data for problem solving. The author presents six examples of two-by-two arrays that he has found especially helpful in college-level mathematics and science teaching. The purpose of this paper is to illustrate these windows in a variety of academic disciplines and explore the general utility of two-by-two arrays.