Structure of Attention
Inviting learners to say ‘what is the same and what is
different’ about several entries in a Structural Variation Grid,
or simply to ‘say what you see’ initiates a movement of
their attention. They may gaze at the whole (and be aware that
there appear to be missing or hidden entries in a grid) or at the whole
of a particular element such as a cell entry; they may discern details
such as particular entries, or details within an entry (such as two
rows to each cell, or the presence of various mathematical signs); they
may recognise relationships within a cell (such as an equation) and
between cells (such as all having two factors or the upper part being a
calculation and the lower part an answer or vice versa); they may
perhaps perceive some relationships as properties which apply across
all visible cells and so might apply to all cells; they may even be
able to reason on the basis of those properties in order to justify
their prediction of what will appear in different cells, or where a
particular entry is to be found.
As a teacher with a class, the problem is that different learners may
be attending in different ways. If as teacher you are attending
in one way, say talking about properties of cells, when learners are
busy discerning details or recognising relationships between particular
entries, there may be a mismatch and consequent breakdown in
communication. By being aware of what you are attending to, and
how, you can either direct learner attention appropriately, or put your
own focus of attention to one side and try to enter the experience of
some of the learners.
What is Attention?
For William James, philosopher and psychologist, attention is what
makes it possible to perceive, conceive, distinguish and
remember. It is the basis of all our psychological functioning
(James 1890 p 424). As might be expected, he deals with a number of
important issues concerning attention in general. For example, he
argues on the basis of experiments that attention is not simply what
the eyes are looking at, or indeed any other particular source of sense
im¬pressions (p 438). He links attention to anticipative
imagination (p 439-411) as a prerequi¬site for discerning anything
at all. James develops this theme of discernment, or discrimination, to
make use of what he calls Helmholtz’s law, that
we leave all impressions unnoticed which are
valueless to us as signs by which to discriminate things (p 456).
.
In other words, we notice what we are attuned to discern (this theme
has been articulated by psychologists, dramatists, novelists and
artists since the end of the 19th century at the very leat). James goes
on to discuss pedagogic implications such as that it is useful for
teachers to work with learners to strengthen and attract their
attention in order to improve motivation, since people engage with what
catches their attention (James 1890, p 446). To do this re¬quires
being aware of what in learners’ previous experience can be used
as a basis of previ¬ous attention-experience, what John Dewey
referred to as ‘psychologising the subject mat¬ter’
(Dewey 1902, p 12).
James sees attention as a form of ‘free energy’, since when
you make an effort to attend to something you can sustain it for only
very short periods before attention wanders (p 420) requiring a further
expenditure of effort, but when attention is engaged it requires no
energy expendi¬ture at all for it to remain focused for long
periods of time.
I agree with James that ‘my experience is what I agree to attend
to’ (his emphasis), although his wording might be taken to imply
voluntary agreement, which is certainly not always the case. At each
moment, as my attention shifts, I am the totality of that attention;
the totality of my experience is my attention. Attention is not just as
what puts me in touch with the world of my experience, but what creates
and maintains that world. This is meant to include things of which I am
subliminally or covertly aware, sometimes through body awareness,
sometimes through social awareness, sometimes through emotional
resonance, and sometimes through cognitive awareness. None of
these need be conscious. This makes attention difficult to study
directly, because it is no good asking people ‘what are you
attending to?’ since the very question alters the focus and locus
of that attention.
Where I differ with James is in his metaphor of attention or
consciousness as a flowing stream, for it seems to me that his own
descriptions (e.g. James 1890 p456 quoting Müller), as well as my
observations, lead to the conclusion that attention is briefly sharp
and alert, and then slowly declines into absence of awareness until
some fresh stimulus wakes it up again. The sense that we have of
experience flowing by is actually much more episodic and fragmentary
(Mason 1988), as attempts to reconstruct recent and distant experiences
demonstrates all too clearly.
You can attend to things physically present and also to things not
physically present (locus); you can ‘gaze’ while pondering,
and you can concentrate very specifically on some small detail (focus).
You can be aware of one single detail, and you can be multiply aware
cognitively, multiply aware enactively, and multiply aware affectively
(multiplicity). Once focused, attention can be diverted by rapid
movement within your field of vision, especially if it is peripheral,
and changes in other sense impressions can also attract your overt
attention.
There are deep physiological questions about whether you actually
attend to several things at once, or whether you rapidly cycle through
a variety of foci, the way computers now do. There is also an
issue about whether consciousness directs behaviour or is subject to a
‘user illusion’ of being in charge, as Tor Norretranders
(1998) proposes. Whatever may be the case, personal experience is
sufficient to highlight important aspects of attention which can be
used to improve both teaching and learning.
Whether attention is the subjective experience of physiological
functioning, as Théodule Ribot (1890) would have it, or the
engine for physiological response to environment, as William James
(1890) proposes, there seem to be quite distinctive if subtly different
forms of attention:
Holding Wholes (gazing)
Discerning Details (features & attributes)
Recognising Relationships (part-part, part-whole)
Perceiving Properties (leading to generalisation)
Deducing from Definitions (reasoning on the basis of
explicitly stated properties stated independently of particular objects)
Shifts between these are rapid, often subtle, but vital in order to
engage in mathematical thinking. While gazing, some sudden movement,
perhaps even apparent motion produced from circadian eye movement can
suddenly switch attention to awareness of details amongst a mass of
other, undiscerned detail. As details are detected and
discriminated, the mind automatically looks for relationships:
differences and samenesses. To do this requires something being
relatively invariant as a background against which to detect
change. Recognising relationships tends to focus on particulars,
whereas perceiving properties is a move to the more general, to the
particular as exemplary or paradigmatic. Formalising in mathematics is
the overt action which accompanies a shift from perceiving properties
to taking certain properties as definitive and so as the basis for
further reasoning. Discerning these subtle shifts in the structure of
attention develops Marton’s notion of learning as discerning
variation, because it provides a more detailed structure of what might
attended to, and how.
Vor references see main SVGrids page.