A componential model for mental addition

A componential model capable of representing simple and complex forms of mental addition was proposed and then tested by using chronometric techniques. A sample of 23 undergraduate students responded to 800 addition problems in a true-false reaction time paradigm. The 800 problems comprised 200 problems of each of four types: two single-digit addends, one single- and one double-digit addend, two double-digit addends, and three single-digit addends. The results revealed that the columnwise product of addends, a structural variable consistent with a memory network retrieval process, was the best predictor of mental addition for each of the four types of problem. Importantly, the componential model allowed estimation of effects of several other structural variables, e.g., carrying to the next column and speed of encoding of digits. High levels of explained variance verified the power of the model to represent the reaction time data, and the stability of estimates across types of problem implied consistent component use by subjects. Implications for research on mental addition are discussed.