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Student Research Studio

A supervised pathway from reproducing one result to formulating, testing, and communicating an independent mathematical-modeling question.

The studio is designed for learners ready to move beyond a closed assignment. Independence is introduced in stages: first by reproducing evidence, then by changing one modelling choice, and finally by defending a question and evaluation plan of their own.

Entry evidence

A learner is ready to begin when they can:

  • explain a baseline model in their own words;
  • read a labelled result table or figure critically;
  • modify and rerun a small computational experiment;
  • identify at least one assumption that affects interpretation;
  • keep a dated record of decisions and results.

Advanced mathematics is helpful for some projects, but disciplined documentation is a more important entry condition.

Five research gates

Gate 1 — Reproduce

The learner regenerates one approved figure or table and explains the calculation behind it. The goal is not to copy code but to establish that the evidence chain is understood.

Gate 2 — Perturb

One parameter, input, boundary condition, or modelling assumption is changed. The learner predicts the direction of the effect before running the experiment and records whether the prediction was supported.

Gate 3 — Validate

The learner designs a check that could expose a weakness: a limiting case, alternative baseline, held-out scenario, numerical refinement, or sensitivity analysis.

Gate 4 — Formulate

Only after the first three gates does the learner propose an independent question. A short protocol defines the primary metric, comparison, evidence threshold, and scope before additional computation begins.

Gate 5 — Communicate

The final output contains a research question, model boundary, methods, claim-evidence map, limitations, and reproduction record. Public prose is written manually from reviewed results; private notebooks and raw experiment notes remain private.

Mentoring structure

Meetings are organised around decisions rather than progress percentages. A compact agenda asks:

  1. What changed since the last review?
  2. Which saved result supports the current claim?
  3. What is the strongest competing explanation?
  4. What is the next decision, and what evidence is needed for it?

The learner maintains ownership of the model while the mentor challenges scope, validation, and communication.

Research record

Each project keeps:

  • a question and scope note;
  • an assumption and data-provenance register;
  • dated experiment entries;
  • configuration files or notebook parameters;
  • machine-readable result tables;
  • a claim-evidence map;
  • approved figures separated from temporary plots;
  • a limitations and next-evidence note.

Suitable starting cases

Student-suitable entries can be explored through the project index. Public research notes such as When the Timetable Lies to the Ventilation System offer a bounded question, explicit counterevidence, and figures that can be critiqued without exposing the private computational workspace.

Completion standard

Completion does not require a positive result. It requires a transparent question, a coherent model, an appropriate comparison, inspectable evidence, and a conclusion that stops where the evidence stops.

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