This pathway is for learners who are comfortable with school mathematics but new to open-ended problems. It treats modeling as a sequence of decisions that can be explained, checked, and revised—not as a search for one hidden answer.
Learning goals
By the end of the pathway, a learner should be able to:
- translate a real question into a focused mathematical question;
- define variables with units and identify a useful output;
- separate observations, assumptions, and modelling choices;
- construct a baseline before adding complexity;
- compare a model with a limiting case, estimate, or small dataset;
- explain what a result supports and what remains uncertain.
Six-part course sequence
1. Questions before equations
Learners practise narrowing broad prompts. “How can a city reduce congestion?” becomes a measurable question about one route, time period, intervention, and outcome. A one-page model brief records the decision context before any calculation begins.
2. Quantities, units, and scale
Estimation and dimensional reasoning expose implausible ideas early. Learners build quantity tables, convert units, and use order-of-magnitude checks before selecting a formal model.
3. Assumptions as testable choices
An assumption register records each simplification, why it is needed, and how it may affect the conclusion. Learners distinguish assumptions that simplify notation from assumptions that can reverse a decision.
4. A baseline that can fail clearly
The first model may be a proportional relationship, recurrence, conservation balance, or simple differential equation. Its purpose is to create a reference point. Complexity is added only when a documented failure shows why it is needed.
5. Computation with checkpoints
Spreadsheets or short Python scripts turn the model into an experiment. Every computation includes a hand-checkable case, labelled units, and a saved input-output table.
6. Validation and communication
Learners test sensitivity, compare an alternative assumption, and write a conclusion in three layers: result, interpretation, and limitation. A negative or inconclusive result can earn full credit when the reasoning is sound.
Suggested learning artefacts
- A one-page model brief.
- A variable and unit table.
- An assumption register.
- A baseline calculation with one independent check.
- One reproducible figure or table.
- A short validation memo and revised conclusion.
Public example
From Open Question to Reproducible Model can be used as a compact reading before the first case. The interpolation guide then shows how a familiar mathematical technique still requires choices about nodes, error, and the shape of the data.
Assessment emphasis
Early work is assessed more heavily on question quality, units, assumptions, and checks than on algorithmic sophistication. The pathway is successful when a learner can defend a simple model and identify the evidence required to improve it.