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2.2.3. Univocal implicative links : the case of some linguistic characteristics.
The complexity of some of the graphs studied above shouldn’t mask the fact that in some
cases they are in fact extremely simple. Their “simplicity” is nonetheless a source of
information that shouldn’t be overlooked. Here we will focus on the study of links between
the items corresponding to the linguistic characteristics of the texts produced by pupils.
These characteristics have to do with the length of text produced, the different modes used
(infinitive, imperative, indicative), subjects (“I”, “we”, “you”). We have also kept the signs
of planning : as a matter of fact the task that is proposed can be interpreted as one of the
writing of a series of actions aiming at putting the figure back together. Some pupils write
in an orderly list of actions. Others note the temporality by using adverbs (now, then etc.).
Others conclude their texts by an indication of the type “here it is, the figure is done” or
simply by using the word “end”. Some disorders can come from planning operations. Thus,
some pupils refer to elements that have not yet been introduced in their text ; others add
constraints that “they had forgotten”.
Lastly, one of last characteristic of the produced writings is that of the inadequate use of definite
articles – “the…” and indefinite – “a, some…” As a matter of fact, the presented elements
can be undetermined by what is preceding them or on the contrary entirely determined. For
instance, if the pupil has said how to build the four points ABCD on two perpendicular lines
which intersection is 0, the circle he is then going to talk about (0 being its centre and going
through the 4 points) is entirely determined. Thus these determinations are not of a linguistic
order : it isn’t because one element has already been quoted in the text that it is thereof
determined, but because the geometrical constraints define it in a unique way. There is no
doubt then, that the tension between the two orders of determination explains the numbers
of disorders in the use of articles.
If there are quite many linguistic characteristics, on the other hand, the graph isn’t really
complex. Three main rules stand out ; the two last ones are univocal.
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(1) “Writing “I” implies “using the indicative mode”(99%).
(2) “Using the infinitive mode” implies “Building a generic subject “we” “(99%)
(3) “Using the imperative mode” implies “building a subject “you””(99%)
The links that come up are expected for the most part since the very use, even partial of the
imperative and infinitive modes are indeed linked to the pronouns which signal what the reader
puts back together : a “peer” for the imperative mode, signalled by the pronoun “tu” (informal
you) and “vous” (formal you), “a generic reader” for the infinitive mode, an “evaluative reader”
signalled by “I” and the indicative mode. However, the presence of univocal relationships
between the chosen pronouns and the modes used, gives an unexpected rigidity since it is
possible, in the indicative mode to use “on (people)” and “tu (informal you)”. Unlike classical
tests suggesting symmetrical links between studied variables, the S.I.A. allows questioning
on these strong constraints, stemming from the written production’s school situation.
This makes it possible to think that the rules pupils use define them as actualisations of
discursive genres. Thus, we suppose that building the reader as a “peer” is characteristic of
a school writing genre in maths class, and therefore can be perceived as legitimate by pupils
for several reasons. It can be that the pedagogical and didactical devices make such positions
possible because help and cooperation are principles put into practice in the language used
in the different subjects taught. It could also be that the ways exercises are written in school
books define such a reader. Building a “generic reader” is also an identifiable characteristic.
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