Teacher and pupil subject knowledge and the processes of mathematical instruction in reception classrooms
The overall aim of the Project was to investigate teachers' pedagogical subject knowledge, in particular, through examination of the co-ordination and utilisation of teacher and pupil knowledge in the complex environments of reception classrooms. Phase One and Two (orientation and overview) concerned the design, piloting and revision of criterion-referenced instruments to assess children's informal mathematical knowledge and included preliminary interviews with four reception teachers to consider their pedagogical thinking and decisionmaking.Phase Three and Four (focused exploration) aimed to capture teachers' pedagogical subject knowledge, exemplified in teacher-pupil interactions, as it moved in varied, yet planned and structured ways towards specific goals. Background biographical information obtained from teacher interview and measures of children's mathematical knowledge allowed consideration of the relationship of teachers' subject knowledge and knowledge of their pupils' competence to teaching goals and classroom processes. It was concluded that at the heart of teachers' pedagogical subject knowledge lies subject content knowledge and knowledge of their pupils' conceptions. The observed diversity in practice among the different teachers and their apparent lack of awareness of the rich informal knowledge brought into school - of counting, recognition of numerals, representation of quantity, addition,subtraction and social sharing, appropriate language of measurement and selection of criteria to sort objects - raises some questions with respect to the adequacy of teachers' subject knowledge. The interaction between the processes of assessment of children's prior knowledge and instruction, however, was demonstrated by the way teachers presented tasks and were able to assess the extent to which children could answer questions about content and apply knowledge strategically. This finding poses some challenge to the notion of assessment as a single event or the stable notion of match.Complex views about children's learning were not necessarily translated into practice suggesting that without clear subject content knowledge neither sophisticated theories concerning children's learning nor scaffolded approaches will necessarily lead to effective teaching. Building up a case knowledge concerning teaching processes which this Project has stimulated may be one way to increase our understanding of subject knowledge for teaching and the development of professional practice. Furthermore the interest already generated in the documentation of children's rich informal mathematical knowledge suggests that providing teachers with increased knowledge of children's mathematical thinking may offer another means to enhance their pedagogical subject knowledge.