Teaching Mathematics Then and Now: Still Hazy after All These Years? A Reaction Paper to Algebra in the Elementary Schools

In his song “Still Crazy after All These Years,” Paul Simon (1974) writes, “I seem to lean on old familiar ways.” Shipley's article “Algebra in the Elementary Schools,” written in 1912, offers the opportunity for us to reflect on what we have accomplished, what we have learned, and what remains hazy even 100 years later with respect to teaching and learning mathematics. Do we still lean on old familiar ways of teaching algebra? This article has many messages that are relevant to us today in thinking about algebra and about teaching and learning mathematics in general. In addition, it raises the following questions: How does Shipley's conception of algebra compare with our conception of it today? What broader issues does he address that are still prevalent today? How far have we come in our implementation of his ideas? What aspects of teaching and learning mathematics in elementary school remain hazy after all these years?