Patterns, Rules, & Discoveries in Life and in Science

Inspired by the theme of the Festschrift – "From Child to Scientist" – I have divided this chapter into two relatively distinct parts. In the autobiographical part, I describe a series of important events along my path from Child to Scientist. That part is , necessarily, very personal. I reflect on how early events in my life have influenced the way I think and feel about doing science. The second part is about science, in particular, about how the "child as scientist" discovers regularities in the world, encodes and abstracts them, and uses them to make predictions. The broad domain has to do with quantitative development, which happens to be the topic on which I began my career in cognitive development, so that even the second part of this chapter has an autobiographical flavor to it. I will describe an unsolved question about children's thinking, and speculate about how it might be investigated in the future. The question comes from the area of children's early numerical thinking, an area in which some challenging questions remain unanswered