BTM models of algorithmic skills

Abstract

In this chapter I first sketch an overview on the principal contemporary approaches to cognitive arithmetic, showing that these approaches somewhat underestimate the role of online symbolic transformations like those performed in the execution of an algorithm (Rumelhart et al. 1986). Second, I propose to inspect arithmetical skills from an algorithmic stance. Assuming that the Bidimensional Turing machine is a reliable model of the various elements at stake in algorithmic performances, I formulate a set of hypotheses about the development of algorithmic skills and the related algorithmic performances, which may in principle be empirically verified. An eventual confirmation of those hypotheses may also help answering the question about the role of external devices, like paper and pencil, in algorithmic performances. Last, I describe some experiments made on a feed-forward neural network in order to test a developmental hypothesis on the acquisition of a set of basic number facts (in this case, the set of all possible results of single-digit additions).