Arithmetic Complexity in Multi-Digit Calculation: Paradigms, Attitudes, and Neural Correlates

Abstract

Arithmetic skills are important in daily life, education, and career development. Yet laboratory research on arithmetic often employs decision paradigms and single-digit tasks, which raises the question of generalizability to production paradigms. Moreover, findings drawn from low math anxious samples may underestimate the difficulties experienced by high math anxious individuals, particularly in complex arithmetic tasks involving multi-digit numbers. To deal with these issues, this dissertation focuses on carry/borrow effects in multi-digit addition and subtraction across paradigms, math attitudes, and neural processes in four preregistered studies. Studies 1 and 2 compared decision and production paradigms in two-digit arithmetic regarding cognition and emotion. It was found that the choice of paradigm affected the observed arithmetic effects, particularly accuracy, and that production paradigms elicited higher state math anxiety than decision paradigms, particularly in individuals with higher trait anxiety. Study 3 examined math attitudes across the lifespan, showing that math anxiety increases and math self-concept decreases with age, with a lower math self-concept being associated with higher arithmetic complexity effects. Study 4 used functional near-infrared spectroscopy (fNIRS) to explore how domain-general and domain-specific brain resources contribute to complexity in three-digit arithmetic. Results showed that fronto-parietal activation increased with arithmetic complexity and this increase was moderated by working memory capacity. In sum, this dissertation shows that arithmetic with carry/borrow operations is not always equally difficult but also affected by task context (paradigm) as well as individual attitudes and working memory resources. This has implications for how arithmetic skills should be assessed and supported in educational and applied settings.