How are things adding up? Neural differences between arithmetic operations are due to general problem solving strategies.

A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, while retrieval strategies activated parietal cortices. This challenges views that operation types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account.