A case of ‘task-switching acalculia’

Abstract

In this study we describe a patient (FR) with left frontal lesions due to a cerebrovascular disorder of embolic origin. Beyond a general slowness, FR showed deficits in simple multiplication only when problems were presented in a mixed operations list (multiplication, addition, and subtraction), while no such deficits were observed for the same multiplication problems in blocked presentation. Deficits were restricted to trials directly affected by a switch (increased switch costs), but not to subsequent trials (no increased mixing costs). Thus, we provide the first detailed description of a condition which could be termed ‘task-switching acalculia’ in a stroke patient. This case highlights the need for mixed operation lists in the diagnosis of acalculia.

Keywords:

• Multiplication
• Fact retrieval
• Frontal lobe
• Executive functions
• Task set

Acknowledgments

This study was supported by the START program of the Faculty of Medicine at the RWTH Aachen University (AZ 145/07).

Notes

¹The concepts and terms ‘cerebral attitude’ and ‘determinative perseveration’ were adapted from von Kries (1895) and Ach (1926).

² Probability of a multiplication problem was at zero after the first addition or subtraction problem and increased after every further addition/subtraction problem to reach 1 after the fourth non-multiplication problem. On the other hand, the probability for a further multiplication problem decreased from the first to the second problem to reach zero after the third problem.

³Although arithmetic fact retrieval performance has been shown to depend on the level of education (Delazer et al., 2003), there may be relevant exceptions. In particular, performance may strongly depend on the frequency of usage. To give an example: A waitress will possibly retrieve simple arithmetic facts with great ease, although she may have completed only a relatively small number of years of formal education. Whereas FR had completed an average number of years of formal education, his job in a sales and marketing department implicated a frequent use of calculation. Unfortunately, however, it is very difficult to quantify this frequency to match it with control participants. Crucially, however, the patient showed pathologically increased switch costs in comparison to every single control subject – irrespective of age and level of education (see section 4).

⁴For technical reasons, only the first digit of the result was registered for addition problems. Nevertheless, if, for instance, ‘1’ was entered as first digit of a two-digit result in response to the problem 5 + 2, it seems plausible to assume that FR wanted to enter the ‘correct’ multiplication result rather than the actual addition result. In no case, this result could have been interpreted as ‘correct’ subtraction result.