Reflections on Skemp’s contributions to mathematical education

Richard Skemp was born in 1919, and died in 1995. This book is not merely a tribute to Skemp’s remarkable careers in mathematics teaching, mathematics education and the psychology of mathematics education, but in many ways is a direct continuation of Skemp’s pioneering research. The book reprints Skemp’s seminal, “mould-breaking” (Tall & Thomas, 2002, p. ii) article on Relational and instrumental understanding (Skemp, 1976), and ends with a late brief article by Skemp, The silent music of mathematics, likening the learning of mathematics to the learning of music — as a lived and shared aural and performance experience, versus a far more passive, isolated pencil-and-paper experience. Skemp comments that some composers can read a printed musical score, or write one by hand, and HEAR the musical sounds that are captured or expressed in the notation. Most lesser mortals need to have the music performed to know what the ball-and-stick ink-on-paper means. It is, as Skemp argues, convincingly as always, similar with mathematics: