What is essential for developing 'automaticity' in numerical fluency?

The development of 'automaticity' in numerical fluency refers to the ability to quickly and accurately recall number facts without having to think through each calculation deliberately. This effortless recall is crucial because it allows a student to focus on more complex problem-solving tasks and concepts rather than getting bogged down by basic calculations.

When students can automatically retrieve number facts, such as multiplication tables or addition combinations, their cognitive load is reduced. This makes it easier for them to engage with higher-level mathematics because they can allocate more of their mental resources to understanding new concepts and solving more complex problems.

In contrast, slow and methodical calculation, while helpful in ensuring accuracy, does not foster that speed and fluency. Relying on calculators extensively can hinder the development of a strong number sense, as it may lead to a lack of familiarity with basic number relationships. Similarly, building complex mathematical models focuses on application and integration of multiple concepts rather than on developing the quick recall of essential number facts. Thus, effortless recall of number facts is indeed vital for achieving automaticity in numerical fluency.