Testimony and Children’s Acquisition of Number Concepts

An enduring puzzle in philosophy and developmental psychology is how young children acquire number concepts, in particular the concept of natural number. Most solutions to this problem conceptualize young learners as lone mathematicians who individually reconstruct the successor function and other sophisticated mathematical ideas. In this chapter, I argue for a crucial role of testimony in children’s acquisition of number concepts, both in the transfer of propositional knowledge (e.g., the cardinality concept), and in knowledge-how (e.g., the counting routine)

Does Doing an Apprenticeship Pay Off? Evidence from Ghana

In Ghana there is a highly developed apprenticeship system where young men and women undertake sector-specific private training, which yields skills used primarily in the informal sector. In this paper we use a 2006 urban based household survey with detailed questions on the background, training and earnings of workers in both wage and self-employment to ask whether apprenticeship pays off. We show that apprenticeship is by far the most important institution providing training and is undertaken primarily by those with junior high school or lower levels of education. The summary statistics indicate that those who have done an apprenticeship earn much less than those who have not. This suggests that endogenous selection into the apprenticeship system is important, and we take several measures to address this issue. We find a significant amount of heterogeneity in the returns to apprenticeship across education. Our most conservative estimates imply that for currently employed people, who did apprenticeships but have no formal education, the training increases their earnings by 50%. However this declines as education levels rise. We argue that our results are consistent with those who enter apprenticeship with no education having higher ability than those who enter with more education.Apprenticeship; Africa; Training; Treatment; Control function