In his 1979 "Human Development" article reprinted in this anniversary issue, James Wertsch presented an approach to genetic analysis of the shifting regulation of problem-solving behavior in early childhood. In my reflections on Wertsch's seminal contribution, I discuss ways that subsequent inquiry built upon ideas he elaborated in the 1979 article, using my own work as an illustrative case. One strand of my discussion focuses on method. Wertsch's treatment involved lab-based studies, and I discuss how, in my research on early number development, I coordinated laboratory methods similar to Wertsch's with field methods. The second strand broadens the scope of Wertsch's approach to genetic analyses. Wertsch presented a compelling case for the utility of genetic analysis in investigations of the emergence of forms of problem solving. I discuss the importance of extending genetic explanation by incorporating sociogenetic analysis of the reproduction and alteration of collective systems of representation in the social history of communities. As an illustration I present my research on numerical representations used by a remote Papua New Guinea cultural group. I conclude by considering the utility of a genetic analysis of collective forms of representation and the functions these forms serve, in ontogeny as well as in social history.