MMP.Preface:3.1 - Form the first account and recover its interpretation

If there is no mathematical question yet, use B.5.FM: identify the participants, propose the relations relevant to the difficulty, work a small consequence and return it to the question. B.5.TU helps when an available theory supplies those relations. Mathematical Thinking provides constructions of objects, operations, representations and arguments when the needed mathematics itself must be developed.

Recover what a request to use a model means in this situation. A structure satisfying stated axioms answers a different question from a representation used to predict an observed process. Both can be useful mathematical work. E.10 clarifies the intended use when the word model conceals it; keep the subject’s established vocabulary when it is already clear.

A drawing, formula, program or learned representation also needs an operation that obtains the requested answer. A person may reason from a diagram; software may solve equations; an experimental arrangement may exhibit a behavior. Make the required interpretation available when another participant must continue the work. A.6.3.RT.OE helps make an expression usable for that operation, and C.29.2 develops a computational formulation when computation is needed. The obtaining procedure can itself become a subject of mathematical investigation.