A spiral curriculum is constructed to help the learner revisit, extend and deepen their knowledge, understanding and skills. Using a spiral model for a mathematics curriculum is often thought to be helpful in helping learners make greater progress in their learning.
A spiral curriculum is based on the principle that efficient and effective learning is a matter of overlaying multiple layers, multiple exposures to the same ideas but getting ever deeper and richer. A spiral curriculum arranges that the same topic, the same idea, the same mathematical theme, is encountered many times, each time slightly differently, or probing more deeply.
The framework See–Experience–Master was formulated to act as a reminder to teachers that learners don’t master ideas on first exposure. They require ongoing experience over time so that they become more and more familiar with the idea and its ramifications. This fits with the framework Manipulating–Getting-a-sense-of–Articulating which can act as a reminder that it is through manipulating confidence-inspiring familiar objects that learners can get a sense of the meaning and import of a conjecture or assertion, and that over a period of time their attempts to refine how they articulate that sense can become more and more succinct and sensible. [see alg-babble].
A spiral curriculum contrasts with a step-by-step mastery curriculum [see mastery learning] in which each step is mastered before proceeding.