The approximate number system (ANS) is a hypothesized mechanism responsible for the representation and processing of numerical information in an imprecise fashion. According to the predominant theory, the ANS is essential in solving simple numerical tasks such as comparing which of two quantities is numerically larger, and some research has indicated that individual differences in its acuity influence higher-level mathematical performance. Because of this farreaching role of the ANS, it is essential to assess its acuity with measures that are reliable, and valid. The present work reviews and synthesizes many of the methodological problems that are relevant for measuring ANS acuity in young children. We discuss issues related to task comprehension, the role of non-numerical perceptual properties of the stimuli, the role of inhibition, and the appropriateness and reliability of the ANS acuity indices. Recommendations and open questions are summarized.

Meta-analytic evidence indicates that the quality of the attachment relationship that infants establish with their primary caregiver has enduring significance for socioemotional and cognitive outcomes. However, the mechanisms by which early attachment experiences contribute to subsequent development remain underspecified. According to attachment theory, early attachment experiences become embodied in the form of cognitive-affective representations, referred to as internal working models (IWMs), that guide future behavior. Little is known, however, about the cognitive architecture of IWMs in infancy. In this article, we discuss significant advances made in the field of infant cognitive development and propose that leveraging insights from this research has the potential to fundamentally shape our understanding of the cognitive architecture of attachment representations in infancy. We also propose that the integration of attachment research into cognitive research can shed light on the role of early experiences, individual differences, and stability and change in infant cognition, as well as open new routes of investigation in cognitive studies, which will further our understanding of human knowledge. We provide recommendations for future research throughout the article and conclude by using our collaborative research as an example.