E VOLUTION OF THE I NSTRUCTION OF A RITHMETIC T HINKING

A further example of the gradual change from oralization to visualization in late Medieval reading, in both verbal and numeral exercises, has been proposed by G. R. Evans [1975a] in his study of arithmetic textbooks produced during the late XIth _{and early XII}th _{centuries. Most of these are instructional treatises}

on the abacus (a device for calculating, consisting of a frame with rows of wires along which beads are slid), and Evans [id.] traces a new preoccupation amongst the teachers: the novel concern is that pupils should be able to visualize what they describe. Pupils are instructed to commit the figures to mind so that the ‘eye of the mind’ (Occulus mentis)will be able to manipulate them. Accordingly, the novel and (as Evans underlines) conspicuous use of diagrams helps to make abstractions visually accessible. The diagrams form an integral part of the work and are not later additions, as in many treatises for other subjects. But these treatises on the abacus are by no means mere sets of instructions, and the diagrams are

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mostly aimed at making abstractions manageable: it is current in them to use analogies with dialectics, and Evans [id.] posits that it is probable that the pupils who used these texts and began to learn practical arithmetic had some grounding in elementary dialectic. The books have a strong link to Greek works on number theory and the Latin rendering of it, but the medieval writer concentrates on a small piece of a great field and gives practical instruction in its application.

1.3.4. SEPARATED SYLLOGISMS IN NASCENT SYMBOLIC LOGIC

In logic, the clearly separated and syntactically sequenced syllogisms of the late Xth_{-century and XI}th_-

century Aristotelian texts were a nascent form of symbolic logic (i. e., representational and abstractive rather than discursive and argumentative) [Hawkes, 1977; Treitler, 1982]. Again, the novel use of structural spacing in protoscholastic syllogisms and schematic diagrams made them an important transitional stage between the purely rhetorical logic of antiquity and the symbolic logic used by modern mathematicians and philosophers.

An Iconic Memory model of visual information processing, as postulated by Coltheart, Lea, and Thompson [1974], holds that the contents of brief alphanumeric displays are initially held in a high- capacity fast-decay visual-information store (the ‘iconic memory’). Some of these items are subsequently transferred to a more durable form of storage; the remaining non-transferred items are lost. More relevantly, in relation to the use of structural spacing, the model posits that readers (or observers, more generally) can select which items are to be transferred on the basis of physical characteristics of the items such as location, position in a sequence, shape, or other visual cues that differentiate some categories of items from others. Coltheart [1980] refined such a model and argued that iconic memory was not to be confused with visible persistence, which itself depends on mere neural persistence at the photoreceptor level and at various stages in the visual pathways; on the contrary, iconic memory would be a form of

informational persistence, not intimately tied to processes going on in the visual system (as visible persistence is). Iconic memory would thus be post-categorical, occurring subsequent to stimulus identification. Thus, although it is defined as non-episodic (its contents can not be explicitly stated or conjured) it nonetheless carries the physical properties of a stimulus in relation to its representation in semantic or syntactic memory. In sum, it temporarily carries distinctive physical information that is relevant for the signification or the functionality of a stimulus within a system.

More recent experimental studies of visual working memory afford a similar picture of how the various features of an item are bound together into chunks. Combined features (bound together into an information unit) have been shown to produce load effects that are no greater on memory than those for the individual features themselves [Allen, Baddeley, & Hitch, 2006; the effect was particularly strong in simultaneous presentations —as happens when reading a text from a page, specially if its information is

structurally separated]. The binding of elements has moreover been found to depend on underlying organisation: recall for sentences is consistently better than for word lists (even in the presence of disruptive concurrent tasks, be they cognitive or executive) [Baddeley, Hitch, & Allen, 2009]. In a manner reminiscent of the Coltheart model, Baddely, Allen, and Hitch [2010], propose a working-memory model including an episodic buffer, a passive multidimensional store of limited capacity; this episodic buffer acts as a passive (and ephemeral) store, capable of keeping bound features and making them available for processing, but not itself responsible for the act of binding (which will be enhanced if it is emphasised by the visual display).

The novel use from the Xth _{century onwards of structural spacing for the nascent symbolic logic was}

therefore an efficient way of loading the different items in syllogisms and diagrams with physical properties that immediately helped their symbolic value and functionality within the complexities of the deductive arguments that were just then coming into existence.

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