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Children rely on their approximate number system (ANS) to guess quantities from a young age. Studies have shown that older children displayed better ANS performance. However, previous research did not provide an explanation for this ANS improvement. We show that children’s development in ANS is primarily driven by improved attentional control and awareness of peripheral information. Children guess the number of dots on a computer screen while being eye-tracked in our experiment. The behavioral and eye-tracking results provide supporting evidence for our account. Our analysis shows that children estimate better under the longer display-time condition and more visual foveation, with the effect of visual foveation mediating that of time. It also shows that older children make fewer underestimations because they are better at directing their attention and gaze toward areas of interest, and they are also more aware of dots in their peripheral vision. Our finding suggests that the development of children’s ANS is significantly impacted by the development of children’s nonnumerical cognitive abilities. 

Real-time in situ mass spectrometry analysis of airborne particles is important in a number of applications, including exposure studies in ambient air, industrial settings, and assessing impacts on visibility and climate. However, obtaining molecular and 3D structural information is more challenging, especially for heterogeneous solid or semi-solid particles. We report a study of extractive electrospray ionization mass spectrometry (EESI-MS) for the analysis of solid particles with an organic coating. The goal is to elucidate how much of the overall particle content is sampled, and the sensitivity of this technique to the surface layers. It is shown that for NaNO3 particles coated with glutaric acid (GA), very little of the solid NaNO3 core is sampled compared to the GA coating, while for GA particles coated with malonic acid (MA), significant signals from both the MA coating and the GA core are observed. However, conventional ESI-MS of the same samples collected on a Teflon filter and extracted detects much more core material compared to EESI-MS in both cases. These results show that for the experimental conditions used here, EESI-MS does not sample the entire particle, but instead is more sensitive to surface layers. Separate experiments on single component particles of NaNO3, glutaric acid or citric acid show that there must be a kinetics limitation to dissolution that is important in determining EESI-MS sensitivity. We propose a new mechanism of EESI solvent droplet interaction with solid particles that is consistent with the experimental observations. In conjunction with previous EESI-MS studies of organic particles, these results suggest EESI does not necessarily sample the entire particle when solid, and that not only solubility but also surface energies and the kinetics of dissolution play an important role.