Space of Values: what is available to be adopted by students

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

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. 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. 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. 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. 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. 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 6th to 13th minute of one of 5 50 minute lessons)

8. Mr. Tower Excerpt 1.1

9. Mr. Tower Excerpt 1.2

10. Mr. Tower Excerpt 1.3

11. Mr. Tower Excerpt 1.4

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. 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