At the beginning of the 20th century, E. H. Moore, who is is often referred to as the father of American mathematics, accepted a challenge from his University of Chicago colleague, John Dewey, to work out "the real correlation of mathematics with science" and subsequently introduced his famous laboratory method into the teaching of mathematics. While this experiment was eventually abandoned, the underlying ideas that E. H. Moore introduced continue even now to be influential in American mathematics via the work of his students, notably R. L. Moore and Arnold E. Ross, and many others.

The talk will focus on the ongoing work of Focus on Mathematics (FoM), a collaboration of mathematicians with teachers that is the centerpiece of a community of mathematical practice that has been evolving for over two decades in the Boston area. An important goal of the FoM community is to close the gap between school mathematics and mathematics as a scientific discipline, by supporting a culture in which practicing mathematicians and secondary teachers work together to improve both high school and university mathematics education.

That Focus on Mathematics has been deeply (if subliminally) influenced by the ideas of E. H. Moore can be seen in its commitment to the creation of authentic mathematical experiences that support mathematical habits of mind that are typical of seasoned researchers, including experimentation, and the development of keen skills of observation, to reveal sometimes unexpected underlying structures. Language is used not just as a means of communication, but also as a tool for articulating conjectures (scientific hypotheses) that can be further tested and eventually proved (or disproved) through further experimentation and careful mathematical reasoning. In the accompanying breakout session, the audience will be invited to engage personally in the investigation of particular concrete mathematical problems that illustrate these ideas.

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