MP-FRAME - Find the mathematical contribution in an unfamiliar problem

• Situation: Something in the work is unexplained or fails, and you do not yet know whether another observation, a new model, a mathematical construction or a different computation is needed.
• Question: What must become distinguishable or possible for the next answer to be useful?
• First useful result or blocker: A mathematical task with a stated use. For example, a cart’s travel log gives total distance, but that total cannot tell whether the cart returned to its start. Identify the position question first. With straight-line motion and known displacements, a sequence of signed displacements supplies an account that can answer it. MATH.1 constructs the sequences and their composition; MATH.5 derives the accumulated displacement from the elementary displacements. A sensor report must first be interpreted as the movement it measures.
• Start with: FPF B.5.FM. State the working question, identify the participants and relations that may change its answer, and build a small account that yields a consequence. If an unfamiliar theory supplies the account, B.5.TU helps construct its application. B.5.MPC connects the physical, mathematical and computational contributions when the difficulty lies between them. Their bodies are in the FPF publication linked above. If the problem is deciding what an object must let you form or recover, use MATH.16. If it is deciding which distinctions can be forgotten, use MATH.2. If an implication is doubtful, use MATH.6. The question determines the construction; an available formula may settle only part of it. C.29 supplies the interpretation through which a mathematical result answers the original question. C.29.2/.3 develop a needed procedure and its execution.
• Stop or return: After the question changes, test whether the summary still determines the answer. If two runs have the same final position but differ in a requested visit, recover the information that separates them. MATH.2 helps locate the failed identification; B.5.QD develops the next useful question. For a working method changed by the result, ME.7 helps describe the proposed operations and their relations; ME.12 checks the claims in that account and its description. The Preface’s worked use follows these choices in detail.