Learning from experience: manifestations of young children's learning from pedagogic representations

Abstract

This study investigates how influences of teachers’ presentations of mathematical ideas, on children’s mental constructions for number and number operations, are manifested by the language they use to describe their mental calculation procedures, and by the mental visual imagery they report. The methodology is described as postpositivist with a phenomenographic orientation. The research method involved the observation of mathematics lessons of two classes of children aged 7- to 9-years over a two year period and structured interviews with a sample of 26 pupils from these classes at the end of each school term. The language and mental visual imagery described by children in the interviews seemed related to the way the mathematics was presented by their teachers. The use of the ‘metaphoric’ language related to a previous experience may be seen as a manifestation of the influence of that experience on the child’s ‘mental construction’. The interdependence of speech style and classroom activity gave evidence of linguistic relativism. The commonalities in the interview responses suggested that children had acquired the cultural tools of the mathematics classroom. The differences in response suggested they had constructed their own knowledge. The differences were most apparent in the calculation methods employed and the mode of generality of their expression. Linguistic indicators (use of tense, pronouns and causal connectives) also distinguished groups of children at different achievement levels. In non-calculation contexts these differences were not apparent, suggesting that the responses reveal mental constructions not just linguistic traits. The conclusion is drawn: When describing the way they perform mental calculation young children’s mental visual imagery and language use is indicative both of the experiences that have influenced their mental constructions and the qualitatively different mental constructions that have been formed. These manifestations may aid teachers in helping children develop their mental constructions to support further mathematical progression