1. 1 Space of Values: what is available to be adopted by students Karen Skilling & John Mason MADIF9 Umeä Sweden 2014 The Open University Maths Dept University of Oxford Dept of Education Promoting Mathematical Thinking

2. 2 Domain  We consider the space of values to which students are exposed through teacher utterances –relation to the tasks provided –and the nature of the interactions between with students.  We restrict attention to values associated with care for mathematics and care for students because –there are endemic tensions both in and between these –Mathematics is a caring profession in which these need to be balanced  Interested in how specific values are made available, transacted and even promoted through student- teacher and student-student interactions.

3. 3 Theoretical Frame  Mathematics teaching as a caring profession  It is vital for the effectiveness of their actions that practitioners display both –care for the people they serve –care in the exercise of their profession.  Extremes are all too familiar: –Wanting students to ‘have fun’; simplifying tasks to make them ‘doable’ and so removing all challenge –Ignoring student state and presenting mathematics ‘clearly’

4. 4 Values  ‘Values’ is used variously to refer to ethical, moral, political, philosophical and spiritual dimensions, as well as to social, cognitive and psychological experiences.  We restrict our attention to the domain of mathematics: –encountering and experiencing mathematical thinking in classrooms.  Distinguish between –values espoused in private, –espoused with students, –and available to be experienced by students,  Focus principally on the latter, though using the former two as a guide

5. 5 Values in Mathematics  How mathematics is approached and engaged in, as being experienced by the full psyche: –behaviour-enaction, –emotions-affect, –intellect-cognition, –and attention-will  Via the construction or adaptation of one or more ‘mathematical selves’ which channel energies in characteristic ways.  We aim to probe beneath the surface of socio- mathematical norms (Yackel & Cobb 1996) which concentrate on practices, to consider what values are manifested.

6. 6 We look for  sense-of-coherence,  appropriate challenge (Jaworski 1994),  respect and trust so that significant mathematical and personal choices are possible,  the kind of support provided during periods of frustration and not-knowing,  recognition of the frustrations when coming-to-know.  There are obvious connections with self-efficacy, agency and many other socio-psychological constructs too numerous to mention much less integrate into this paper

7. 7 Evidence  Use of transcripts from recent study (Skilling 2013) of classrooms where a high degree of student engagement had been detected.  Previous study had collected –Teacher survey –Pre- and post-lesson interviews with the teachers –Lesson observations –Video-taped lessons –> transcripts –Teachers’ self-reported beliefs were compared to their observed practices  Report here on one of these teachers –Part of one observed lesson (lasting from the 6 th to 13 th minute of one of 5 50 minute lessons)

8. 8 Mr. Tower Excerpt 1.1

9. 9 Mr. Tower Excerpt 1.2

10. 10 Mr. Tower Excerpt 1.3

11. 11 Mr. Tower Excerpt 1.4

12. 12 Comments  Many of the values identified might only emerge AS values with –Experienced repetition –Experienced and noted repetition –Scaffolding & Fading –Being pecifically explicitly remarked upon

13. 13 Tentative Conclusions  The same teacher act could be interpreted positively, negatively or neutrally by students  Complexity and range of values displayed and thus interpretable  Any space of values can be –Nullified by inconsistency –Neutralised through becoming un-reflected upon practice –Amplified through explicit marking  Classroom ethos likely to be significant factor  Trying to assign specific values to specific acts less fruitful than maintaining the complexity of human interactions  Space of Values could be useful as prompt to reflect on alignment between espoused, enacted and interpreted values