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Space of Values:what is available to be adopted by students
Karen Skilling & John MasonMADIF9
Umeä Sweden2014The Open University
Maths Dept University of OxfordDept of Education
Promoting Mathematical Thinking
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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.
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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’
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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
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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.
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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
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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)
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Mr. Tower Excerpt 1.1
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Mr. Tower Excerpt 1.2
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Mr. Tower Excerpt 1.3
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Mr. Tower Excerpt 1.4
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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
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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
