MATHEMATICS KNOWLEDGE WAREHOUSE · READER MAP
Mathematics Dependency Graph | Typed Prerequisite and Capability Routes
Mathematics is connected. Later ideas often reuse earlier relationships, but not every connection is the same kind. Some ideas are genuine prerequisites; others are helpful foundations, alternate representations, transformations or ways to check a result.
Six useful kinds of connection
| Connection | Reader meaning |
|---|---|
| Requires | An earlier idea must be secure enough for the later work to function reliably. |
| Represents as | The same relationship can appear in words, diagrams, tables, graphs or symbols. |
| Transforms to | A valid mathematical operation changes one form into another. |
| Generalises to | An earlier pattern becomes a broader mathematical rule or object. |
| Enables | An earlier skill may not be absolutely required, but it makes later work much easier or more flexible. |
| Verifies | One method or representation can be used to check whether another answer is sensible. |
Important learning corridors
- Arithmetic → Algebra
- Fractions & Ratio → Functions
- Algebra → Functions → Calculus
- Geometry → Trigonometry → Vectors
- Probability → Statistics
- Representation & Verification
Why this matters for a struggling student
If a student struggles with algebra, the answer is not automatically “go back to Primary Mathematics.” A tutor should look for the particular connection that is failing. If distributive structure is insecure, repair that relationship and reconnect it to the current algebra. If the earlier relationship is already secure, keep the work at the current level.
A map is not a diagnosis
The graph helps readers see why Mathematics is connected. Actual student work is still needed to decide whether a particular earlier idea is relevant to a present difficulty.