ABSTRACT
Generating insights and learning about the insights of others can yield qualitative changes in people's understanding. Writing can also inculcate a more general habit of mind: reflexively considering the potential criticisms of a reasonable person with a different perspective. These habits of mind can generalize to many activities other than writing articles: developing theories, presenting talks, organizing courses, and formulating new research studies, among them. Considered in terms of its relation to education, the research falls into three main projects. The first project focused on providing a sound foundation of understanding of cognitive development from which educational implications could be derived. The second project involved efforts to apply this theoretical foundation to improving education in whole-number mathematics and in science. The third project, which builds on both of the earlier ones, has the goal of accurately describing and improving knowledge of rational numbers.
