1. 'Maths Talk': Interaction, Concepts and Teachers' 'Subject Knowledge ' Viv Ellis

2. Three interesting problems 1. Boris’s (and Mr Gove’s) emphasis on teachers’ ‘subject knowledge’ and its relationship with highly effective teaching 2. Young children’s conceptual development and its relationship to spoken language 3. How to link the above two to make a different to kids!

3. The first problem O Studies of impact of teachers’ subject matter knowledge and pupil attainment (c.f. Floden & Meniketti 2005; Hattie 2011): O Only for secondary Mathematics teaching is there any evidence that ‘more’ subject matter study has a positive effect on pupils’ attainment O Hawkins et al (1998) found a positive effect on fourth graders attainment of teachers majoring in ‘mathematics education’ or ‘education’; children taught by teachers who had majored in ‘mathematics’ did less well O Rowan et al’s 2002 study showed that elementary school teachers with advanced degrees in mathematics were associated with lower growth in mathematic achievement by their pupils

4. So what? None of the studies address questions about what professionally valuable knowledge teachers gained through their subject matter preparation

5. The second problem O Language and learning O Exploratory talk, dialogue, ‘inter-thinking’ O Challenging the IRF or IRE sequence O Thought and language O Vygotsky, Britton, Bullock, Barnes, Alexander, Nystrand, Mercer, etc etc

6. For example: Dialogic teaching O the different contexts of talk – whole class, collective (teacher-led) group, collaborative (pupil-led) group, individual; O the purpose of questions (e.g. elicitation, recall, instruction, management, routine, probing) and their structure (e.g. closed, open, directive, leading, narrow, discursive); O the form of answers (e.g. factual, analytical, speculative, hypothesising, evaluative) and their length; O the feedback which answers receive (e.g. evaluative, motivational, diagnostic, neutral); O the way answers are built upon in order to take thinking forward; O the length of exchanges; O roles and procedures for pupil-pupil discussion; O classroom climate and relationships; O classroom organisation and layout; O lesson planning and structure; O the teacher subject knowledge needed for extended exchanges; O ground rules governing the effective conduct of dialogic talk in classroom settings (attending, O listening, speaking loudly and clearly, respecting alternative viewpoints etc). (Alexander 2003)

7. Scientific and Spontaneous Concepts Spontaneous Concepts Scientific Concepts Impose on child logically defined concepts Scientific concepts move ‘downwards’ towards greater concreteness Evolve in highly structured and specialized activity of classroom instruction Concepts emerge from the child’s own reflections of everyday experience Spontaneous concepts move upwards towards greater abstractness Develops in child’s everyday learning environment Mature concepts Object Concept In the ZPD

8. Young children’s concept development O May not be conceptual (whether from a Piagetian or Vygotskian perspective) O May not be about moving from concrete to abstract but between two sets of discursive practices based on ‘problems of practical and material necessity rather than problems of symbolic control’ (Walkerdine 1985, 1989) O But also when the context is familiar, young children may certainly be capable of drawing inferences that are conceptual (Donaldson 1978)

9. Pleasurable symbolic play O The imaginative situation, the defining characteristic of symbolic play, makes ‘play a means of developing abstract thought’ and therefore ‘a leading factor in development’ (Vygotsky 1978) O Language and thinking are ‘generated by the power and pleasure children have in mastering the art of story’ (Fox 1989)

10. `Right then I’ll make a sale poster and I’ll get my pen and write “for sale” So they write FOR SALE and Joshua writed ‘a hundred and fifty hundred pounds for that thingy’ - Joshua story 61 (5:9)

11. ‘There’s ten witches all around our country There’s ten witches in our country Oh God there’s another three in our country so we’ll have to kill thirteen now’ - Joshua story 55 (5:9)

12. O Story as a means of understanding physical, spatial and temporal concepts O As mathematical learning develops, the expectation is that the metaphorical cloak is stripped away to focus on the underlying concepts and this is what children find difficulty with (Walkerdine 1982) O How can affectivity, narrative, imagination and symbolic play be harnessed to enhance mathematical learning?

13. ‘Whereas adults differentiate their thought with specialised kinds of discourse such as narrative, generalisation and theory, children must, for a long time, make narrative do for all’ (Moffett 1968)

14. The third problem: how to make a difference? O And would the same approach be beneficial for teachers? O What approaches to CPD with specific attention to Mathematics will lead to better outcomes for kids?

15. Thank you! viv.ellis@brunel.ac.uk