1970: Week 2 -- Learning is not a counting noun… so what should we count?

D Cormier's comments
We had super fun first week. Contributions were emotional, exploratory, smart and surprising… what else could you want from a week? One of the major themes that I heard during the week and, interestingly, at the conference where I talked about it, was measurement. We live in a world obsessed with measurement. We’ve had many beautiful examples of ways to visualize what is happening in Rhizo15. I’ve seen a number of conversations around ‘success indicators’ and ‘ways in which i feel good about what I’m doing.’ When we forward the learning subjective, what does it make possible?

Get out there and count! What can we measure that isn’t learning? Think about all the other facets of the human experience… can we do better? What about all the fancy tools we’ve seen… can they help? Should we throw it out all together? Can we help people measure themselves? Is there a better way of looking at it? Be theoretical. Be practical… but GRADE ME

Opponents of rhizomes stress counting eg outcomes.  What of interactions? What can be measured? Come up with something collective and cool – for administrators and students. What is worthwhile? Map the rhizome?

This is such a familiar topic that I think people found it hard to add much to the normal sorts of discussion The appeals to visual depictions and other 'fancy tools' will be discussed later. The applicability of measurement to areas like the emotional, or self-measurement might help better clarify the issues, and the reference to grading raises an important practical context. But thinking of that context makes the ethical emphasis --should we count etc -- pretty well irrelevant to practice. In practice we do count, measure and grade,and a better focus might have been to discuss what is gained and lost by this ubiquitous practice. Given that most of the active participants were in education, I was hoping to see some discussion about how student assessment was actually accomplished by most of them. In particular, as I suggested in a rather terse post, is it possible to really persist with student-centred, non-judgmental stances in pedagogy when it comes to summative assessment? If there is conventional summative assessment, there is hierarchy, whatever the friendly and impersonal relations we might pursue in classrooms.

Most practitioners know it is a very dubious business, I would have thought. Despite all the paraphernalia of criteria and moderation, for example,  a great deal of subjectivity remains. Participants might have been asked to think about this subjectivity -- is it 'good' subjectivity, or just bias?. Bourdieu's work springs to mind for me, showing how 'objective' assessment really reproduces habitual judgements about 'style', bodily hexis, accent and other forms of social class and gender judgements. That would be the way to challenge 'objectivity', in my view,  not by referring to some humanist subjectivity that is being trammeled by measurement. I cannot think of a more deadly criticism to make of modern universities than that they do not assess students objectively.

What might be less well-known is that assessment policy often assumes a level of quantification that is not really applicable to assessment data. Once things have numbers attached, those numbers can be added, multiplied or divided regardless of whether this makes sense in the real world. Thus I can average all the street numbers in my street, or, if I code male gender as 1 and female as 2, I can get an average gender. In student assessment, it might be possible in the real world to think consistently of 4 or 5 categories of student answer -- outstanding, very good, good, poor and fail, say -- but using a percentage scale to grade student work assumes there are 100 categories. Percentages then lend a spurious numerical quality to those grades and it is common to produce weighted averages, sums, ordinary averages and so on as if everyone knew what they were percentages of, so to speak.

Of course, there is an assessment device where the use of percentage scales does make sense -- the 100 question test, say with 100 multi-choice or yes/no questions. Those that got the right answers in all 100 would get 100% , if you only got half right you would get 50% and so on. Such a system would be anathema to most UK academics though and would attract all the usual complaints about trivializing learning and so on. So instead, they keep the marking systems based on that sort of test,  preferring to trivialize when they mark but not when they set the questions!

Using software like EXCEL to do the sums involves further assumptions, so that if we use it to create standard deviations of our distributions, choosing the first option, SDP (routinely done in my institution), the software produces a result based on the assumption that the data comes from at least 100 cases and is a representative sample of the population for which the SD is being calculated. This was not usually the case in my experience. Nevertheless the SD value was solemnly discussed at Exam Boards, SDs of different course were compared -- and so on. It became a sign of virtue to deliver a 'low' SD for some reason. Those who had been wised up simply removed the zero scores from the raw data and achieved what was wanted.

Deleuze and Guattari might be of assistance in explaining how this sort of objective practice persists, and what underpins it, if anyone wanted to pursue the issue through them (I think there are some perfectly good and rather less convoluted critiques of positivism which would be just as good). I think there are two possible lines: (a) the argument that intensive differences with ordinal numbers produce extensive empirical systems which are then 'metricated';
similarly (b) numbers are handy to differentiate and distribute resources organize people, say among nomads, but they tend to be captured by the State, and this is crucial for the development of capitalism.

Option (a) can be found argued extensively in the more abstract philosophical works like Deleuze 2004. We are asked to consider arguments that are very difficult to summarize  but apparently what we need to consider is ‘the original, intensive depth which is the matrix of the entire space’ (62).  Every couple and polarity [as in binary distinctions] ‘presupposes bundles and networks, organized oppositions presuppose radiations in all directions ’. We need to think of a conception of time unconstrained by any human figures, like circular structures, time unfolding itself, and ceasing 'to be cardinal and becom[ing] ordinal' (111) -- that is non-metric, intensive time. The individual subject is understood, wrongly , as possessing species characteristics as such, but should be seen instead as result of individuation consisting of ‘fields of fluid intensive factors’, producing all the individuated forms , acting as 'pure ground' (190).  Chapter 5 argues that it is intensive processes that produce extensity, the ordinary metric, measurable world.  Intensive processes can only be assigned any dimensions ordinally, [ordinal but not interval measurement] and in particular are indivisible.  There is an intensive version of depth and distance—the latter is more easily grasped as proximity.  Together, they constitute an intensive spatium, a field of potentials that produce the real world. Embryology is now understood as involving a series of intensive differences between the fluids which the embryo or egg sac contains, while thermodynamic systems can also be grasped intensively, as 'differences of level, temperature, pressure, tension, potential' (280). Qualities are best seen as signs of the equalization of intensive differences in extensity -- and so on.

If modern physics and biology work with intensive differences indicated by ordinal numbers, it seem ludicrous that educationists should insist on fully metric interval scales in the name of greater scientificity.

Option (b) should be more accessible to fans of ATP, and the same sort of philosophical argument about ordinal numbers is apparent in Chapter 12 on the nomads. Thus we find that nomads used numbers first, as a principle of organization:
numbers are always connected to war machines , as a matter of 'organization or composition'(428); number acts 'as an inscription written on the earth'. This is contrasted with the development of 'metric power', the political use of arithmetic as in imperial bureaucracies operating taxation and election systems, and, later, political economy and the organization of work.  Numbers in capitalism are used 'to gain mastery over matter, to control its variations and movements' (428). Metrication becomes a central component of the all-conquering capitalist axiomatic.

In nomad societies,
there is autonomous arithmetical organization described as 'The Numbering Number' (429) , and it relates to conditions of possibility and effectuating the war machine.  State armies require the treatment of large quantities, for example, but war machines operate with smaller quantities with autonomous arithmetic, describing the distribution of something in space, rather than dividing space itself.  'The number becomes a subject', it is independent of space: this happens only with smooth space, however.  Numbers move through this smooth space.  The geometry of smooth space is 'minor, operative' (430), 'a geometry of the trait'. Nomadic numbers are movable.  They do not just measure.  In nomad culture, the number 'is the ambulant [camp] fire'.  Numbers suggest directions [as in the flow between two intensities?].  Numbers are not used to organize armies on the march [rendered by our heroes as 'The numbering number is rhythmic not harmonic'] but are important in fighting [think of the old Maoist slogan 'March divided, fight united'].  Sometimes random numbers are important [with a quote from Dune on how to walk without attracting the attention of the Great Worms!].  Numbers becomes ciphers [that is nominals, with all their other characteristics made irrelevant -the ability to subdivide them, for example].  Ciphering belongs to or possibly leads to an esprit de corps and leads to characteristic strategies such as ambush and diplomacy.  When it takes the form of a war machine, this numerical organization looks impersonal, but 'it is no crueller than the lineal or state organization' (431).  Numbers are used to select leaders from lineages and to direct action against the state apparatus: in this sense, they are themselves a deterritorializing activity which cuts across lineal territory.  We always encounter complex and articulated numbers, rather than some large homogenized quantity.

That is probably enough. D&G might be used as a sledgehammer to crack the nut within which lies the argument that it is not numbering itself which is oppressive, that numbering does not have to be abandoned to the ludicrous claim that human subjectivity cannot be measured. Clearly it can be -- the issue is how and with what numbers? Even qualitative researchers cannot operate without any numbers whatsoever: they tend to use 'soft quantification' in statements like 'most of the group', 'the most frequently raised issue', 'many people felt' and so on.  Most people use the same sort of device when they describe their feelings -- they feel 'better', 'more deeply in love', 'acutely depressed', 'very unhappy' and so on. Is it really oppressive to ask them to specify in a bit more detail what they mean -- rate their feelings on a 1--10 scale, say, just like doctors ask us to rate the pain we feel after injury?

If you want to see some real controversy, try some of the work in sports psychology --devising a scale for 'motivational climate' say (notes here). Or, of course, learning styles (notes here).
All sorts of conditions, including anxiety and all aspects of performance, are metricated in the form of scales. Are these particular scales valid? Should they be opposed to a subjectivism that claims that motivation, anxiety and so on are entirely subjective (and welcome, creative?) states. Is there a defence in that such scales might 'work' nonetheless?
A late post to the group indicated the real issues. A participant wanted to devise measures of the participation rates in his online course...

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