Elementary Mathematicians from Advanced Standpoints—A Cultural Perspective on Mathematics Education

Abstract

Many challenges face those of us for whom mathematics education research is our life’s work. In some countries where significant attempts are con- tinually being made to reform mathematics teaching, it is often a highly politicised field. While rational arguments and relevant data-gathering are valid parts of a democratic research process, awareness of the broad cultural context is paramount. Despite the challenges that adopting a new cultural perspective brings, episodes and analyses from our sociocultural research field do demonstrate much promise for advancing mathematics educational practices. In particular the relatively new ideas of values and valuing show much research promise. In this paper, referencing Felix Klein’s fundamental ideas, I will analyse the twin pluralised notions of ‘elementary mathematicians’ and ‘advanced standpoints’. In addition research focussed on a third key notion, ‘pedagogical practices’ will be discussed. Finally some of the implica- tions of this three dimensional and culturally oriented research will be presented.