A novel problem or task may seem difficult at first, but with enough practice, it can become easy and routine. Practice and the process of learning is often accompanied by some mild cognitive uneas...

Research into mathematics often focuses on basic numerical and spatial intuitions, and one key property of numbers: their magnitude. The fact that mathematics is a system of complex relationships that invokes reasoning usually receives less attention. The purpose of this special issue is to highlight the intricate connections between reasoning and mathematics, and to use insights from the reasoning literature to obtain a more complete understanding of the processes that underlie mathematical cognition. The topics that are discussed range from the (...) basic heuristics and biases to the various ways in which complex, effortful reasoning contributes to mathematical cognition, while also considering the role of individual differences in mathematics performance. These investigations are not only important at a theoretical level, but they also have broad and important practical implications, including the possibility to improve classroom practices and educational outcomes, to facilitate people's decision-making, as well as the clear and accessible communication of numerical information. (shrink)

Prior research found correlations between reflection test performance and philosophical tendencies among laypeople. In two large studies (total N = 1299)—one pre-registered—many of these correlations were replicated in a sample that included both laypeople and philosophers. For example, reflection test performance predicted preferring atheism over theism and instrumental harm over harm avoidance on the trolley problem. However, most reflection-philosophy correlations were undetected when controlling for other factors such as numeracy, preferences for open-minded thinking, personality, philosophical training, age, and gender. Nonetheless, (...) some correlations between reflection and philosophical views survived this multivariate analysis and were only partially confounded with either education or self-reported reasoning preferences. Unreflective thinking still predicted believing in God whereas reflective thinking still predicted believing that (a) proper names like ‘Santa’ do not necessarily refer to entities that actually exist and (b) science does reveal the fundamental nature of the world. So some robust relationships between reflection and philosophical tendencies were detected even among philosophers, and yet there was clearly more to the link between reflection and philosophy. To this end, demographic and metaphilosophical hypotheses are considered. (shrink)

This commentary addresses omissions in De Neys's model of fast-and-slow thinking from a metacognitive perspective. We review well-established meta-reasoning monitoring (e.g., confidence) and control processes (e.g., rethinking) that explain mental effort regulation. Moreover, we point to individual, developmental, and task design considerations that affect this regulation. These core issues are completely ignored or mentioned in passing in the target article.