1. IDENTIFYING DEEP SUBJECT KNOWLEDGE An evaluative study of the nature of primary teachers’ deep subject knowledge when teaching mathematics Paul Broadbent MA DISSERTATION 2012 How does the Maths Specialist Teachers (MaST) programme develop deep subject knowledge in the participants? How does deep subject knowledge differ from the basic mathematical knowledge that teachers bring to the classroom? How does deep subject knowledge impact on pedagogy? What is deep subject knowledge? Lack of subject knowledge is an issue. The Williams Report (2008) based key recommendations around this and the Cambridge Primary Review (2010) acknowledged that primary teachers’ subject knowledge is their greatest vulnerability. Methodology Layered evaluation, structured as three case studies. This research analysed the nature of deep mathematical knowledge and critically evaluated the impact of the Maths Specialist Teachers (MaST) programme on the participants’ subject knowledge, through interviews and classroom observations from a sample of three participants from Lincolnshire in the first year of the programme. Pedagogical Content Knowledge (PCK) Curricular Knowledge (CK) Subject Matter Knowledge (SMK) Shulman’s categories of subject knowledge (1987) Transformation Foundation ConnectionContingency The Knowledge Quartet (Rowland et al 2003) Basic Mathematical Knowledge (BMK) Knowledge of Teaching Mathematics (KTM) Knowledge of Learning Mathematics (KLM)  Qualifications  Beliefs  Confidence  Connections  Progression  Representation  Concepts  Interaction  Response Deep Subject Knowledge (DSK) Experience and Professional Development Deep Subject Knowledge model (Broadbent 2011) From the literature review I developed an analytical framework for observations and interviews. Findings… Making connections is a key aspect of deep knowledge and is developed through teacher research of mathematics topics and the curriculum Representation makes the knowledge relevant to pupils – developed through CPD and planning Interaction and response developed through confidence in the subject and CPD Higher maths qualifications are not a key attribute of effective teaching in primary schools – CPD is Beliefs and attitudes are largely from a teachers own experience as a pupil – ITT important role Basic Mathematical Knowledge Qualifications: at school and university (DfE 2010) Beliefs: attitudes, enthusiasm, discovery, transmission or connectionist approach (Williams 2008, Askew et al. 1997) Confidence: mental skill and general ‘feel’ for mathematics - relational rather than instrumental understanding (Skemp 1976) Knowledge of Teaching Mathematics Connections: in maths and curricular links (Shulman 1987, Ball 1990, Askew et al 1997, Rowlands et al. 2003) Progression: knowledge of curriculum (Shulman 1987, Rowlands et al. 2003) Representation: language, images, action on objects and symbols (Alexander 2010, Haylock and Cockburn 1997, Barmby et al. 2009, Shulman 1987, Rowlands et al. 2003) Knowledge of Learning Mathematics Concepts: dealing with misconceptions (Williams 2008, Ofsted 2008) Interaction: the quality of discussion, pupil talk, reasoning and language (Alexander 2010, Williams 2008) Response: dealing with questions as they arise, flexibility, decision-making and the ability to ‘think on your feet’ or ‘grab the moment’ (Williams 2008, Alexander 2010, Ofsted 2009) Future research questions… Can the Deep Subject Knowledge Model be used for other curriculum areas and at KS3/4?? What form of CPD is the most suitable to develop deep subject knowledge? Are specialist subject teachers rather than generalist teachers needed in primary schools?