NOT.7:1 - Problem frame

Use this when a notation can express the required content, yet reading or changing that content is unnecessarily difficult. A reader repeatedly loses a dependency, has to reconstruct a grouping, or must change the same assumption in several places. Another symbol or a shorter inscription may leave the difficult operation unchanged.

Begin with one such operation on an actual expression. Find what the reader has to locate, infer, remember or alter. Change the notation or its editing arrangement at that point, then compare the operation and another operation that the change could burden.

The result is a repaired notation with a reason to prefer it for the intended work, or a decision to retain the existing form. A useful diagnosis may instead identify missing subject knowledge, an unavailable operation or inaccessible content that a notation change cannot supply.

The reader needs the subject criterion for a correct result and enough knowledge of the existing notation to inspect its interpretation. NOT.1 supplies a missing use requirement; NOT.2–.3 supply formation and interpretation. A sketch and a worked comparison can be enough for a local repair.

Keep a sufficient familiar form when no consequential reading or change difficulty is present. If the underlying account is wrong, repair that account. Use EXD.1–.3 when the needed work is to construct an explanation; use the instructional method appropriate to the missing capability when the reader cannot yet perform the required subject operation.