Subtraction and Negative Numbers: Examining the Problem Size Effect in Mixed Formats. Technical Report 2006-02

Every simple subtraction problem can formally be stated that for any integers a and b, a – b = a + (-b). Therefore a simple subtraction problem can be stated equivalently by “adding the opposite.” Although, the problems are theoretically the same, the addition of negative numbers is assumed to be difficult to conceptualize. In the following experiment the authors have compared response times and error rates for corresponding additive and subtractive forms of single-digit arithmetic problems. The authors found that participants solved problems of the form a – b significantly faster than problems of the form a + (-b). Furthermore, there was no evident problem size effect and thus an interference theory was suggested