Easy retrieval of memorized math facts is a predictor of success in more advanced mathematics. Recognizing the research in this area, the Common Core State Standards explicitly include math fluency as part of the mathematics standard.
Automaticity is the ability to respond to a specific math fact prompt quickly and correctly with minimal effort. When a fact becomes automatic, it can be retrieved from memory without thought.
When a child is still using strategies, rather than direct retrieval, to recall a fact, the time to answer a specific fact is typically over three seconds. During the phase of practicing toward automaticity, speeds are typically three to four seconds per fact. Automaticity arises when the speed of recall is two or three seconds or less.
Fluency is a measure of automaticity over a class of facts.
In its level selection screen, Mathtopia+ and Mathtopia allow you to see at a glance if a child is using strategies (no or one star), practicing towards fluency (two stars), or fluent at a level (three stars).
Automaticity arises from overlearning, the process of practicing a fact past mastery to solidify its fixed status in memory. The addictive nature of Mathtopia encourages overlearning.
Children begin to develop fluent speed with math facts in second and third grade. By fourth grade, many children exhibit direct retrieval of math facts. However, older children an even adults can improve overall math performance by strengthening areas of weakness in math fact fluency.
Happy math facting!