Fact retrieval or compacted procedures in arithmetic – a neurophysiological investigation of two hypotheses

ABSTRACT

There is broad consensus that adults solve single-digit multiplication problems almost exclusively by fact retrieval (i.e., retrieval of the solution from an arithmetic fact network). In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. The fact-retrieval account postulates that these are solved through fact retrieval, just like multiplications, whereas the compacted-procedure account proposes that solving very small additions (i.e., problems with operands between 1 and 4) involves highly automatized and unconscious compacted procedures. In the present electroencephalography (EEG) study, we put these two accounts to the test by comparing neurophysiological correlates of solving very small additions and multiplications. A sample of 40 adults worked on an arithmetic production task involving all (non-tie) single-digit additions and multiplications. Afterwards, participants completed trial-by-trial strategy self-reports. In our EEG analyses, we focused on induced activity (event-related synchronization/desynchronization, ERS/ERD) in three frequency bands (theta, lower alpha, upper alpha). Across all frequency bands, we found higher evidential strength for similar rather than different neurophysiological processes accompanying the solution of very small addition and multiplication problems. This was also true when n + 1 and n × 1 problems were excluded from the analyses. In two additional analyses, we showed that ERS/ERD can differentiate between self-reported problem-solving strategies (retrieval vs. procedure) and even between n + 1 and n + m problems in very small additions, demonstrating its high sensitivity to cognitive processes in arithmetic. The present findings clearly support the fact-retrieval account, suggesting that both very small additions and multiplications are solved through fact retrieval.

HIGHLIGHTS

• Neurophysiological test of fact retrieval and compacted procedures account

• Induced EEG data are sensitive to cognitive processes in arithmetic problem solving

• Both very small additions and multiplications are solved through fact retrieval