Knowledge relating to the step-by-step procedure for doing a certain…

Concept: Educational psychology classifies what a learner knows by the form the knowledge takes. Procedural knowledge is "knowing how" — an ordered sequence of actions, rules or algorithms that a learner executes to complete a task. Conceptual knowledge is "knowing why" — the network of relationships among ideas, principles and definitions that gives those actions their meaning.

Application: The stem describes knowledge of the step-by-step procedure used to carry out a mathematical task — for example the ordered steps of the long-division algorithm, or the sequence of operations used to solve a linear equation. Knowledge stored and recalled as an executable sequence of steps is, by definition, procedural knowledge, so "Procedural knowledge" is the correct answer.

Contrast with the neighbouring knowledge types:

• Conceptual knowledge — the interconnected principles and relationships that explain why a procedure works, such as why place value makes regrouping valid. It explains the steps rather than being the steps.

• Abstract knowledge — knowledge expressed in general, symbolic terms detached from any concrete object, such as reasoning about "number" independently of the things being counted. It classifies knowledge by level of generality, not by "how to do".

• Contextual knowledge — knowledge tied to the particular situation, setting or purpose in which it is used, such as recognising which everyday situations call for estimation rather than exact calculation. It classifies knowledge by its situational dependence.

Result: Knowledge of how to carry out a task step by step is procedural knowledge; knowledge of why those steps work is conceptual knowledge. A classroom that drills only the steps builds procedural fluency without the conceptual understanding that supports transfer, which is why mathematics pedagogy insists the two be developed together.