ABSTRACT
The authors describe their experiences with their father as a teacher, experimentalist, role model, and source of love and inspiration. Based on findings from Bob Siegler's early experimental work, he continued his cognitive development research, eventually moving into the area of children's mathematical strategies. He looked deeply at patterns in the data from his experiments, inquiring of it similarly to how he might pose questions as a child: query, answer, next query. The data indicated that children were likely using many strategies to solve a single problem. Exploring this in greater depth, he found that individual children had attempted multiple strategies. This insight, and subsequent validation of it through experimentation, led to his Overlapping Waves Theory. A child simultaneously possesses and uses multiple strategies to solve problems, with the frequency of use for each becoming more or less frequent based on its success and efficiency over time.
