Preschool children have been proven to possess nonsymbolic approximate arithmetic skills before learning how to manipulate symbolic math and thus before any formal math instruction. It has been assumed that nonsymbolic approximate math tasks necessitate the allocation of Working Memory (WM) resources. WM has been consistently shown to be an important predictor of children's math development and achievement. The aim of our study was to uncover the specific role of WM in nonsymbolic approximate math. For this purpose, we conducted a (...) dual-task study with preschoolers with active phonological, visual, spatial, and central executive interference during the completion of a nonsymbolic approximate addition dot task. With regard to the role of WM, we found a clear performance breakdown in the central executive interference condition. Our findings provide insight into the underlying cognitive processes involved in storing and manipulating nonsymbolic approximate numerosities during early arithmetic. (shrink)

In updating our beliefs on the basis of our background attitudes and evidence we frequently employ objects in our environment to represent pertinent information. For example, we may write our premises and lemmas on a whiteboard to aid in a proof or move the beads of an abacus to assist in a calculation. In both cases, we generate extramental (that is, occurring outside of the mind) representational states, and, at least in the case of the abacus, we operate over these (...) states in light of their contents (e.g., the integers represented by the beads) to generate new representations. In this paper, I argue that our belief updating processes and the grounds of their rational evaluation are partly constituted by extramental representations and operations. In other words, we don’t merely update our attitudes through an internal process of reasoning on the basis of available evidence. If we are to accurately understand and rationally evaluate our belief updating processes and resultant attitudes, we need to examine how we representationally appropriate our extramental environment in the updating process. (shrink)

People frequently report that, at times, their thought has a vocal character. Thinking commonly appears to be accompanied or constituted by silently ‘talking’ to oneself in inner speech. In this paper, we explore the specifically epistemic role of inner speech in conscious reasoning. A plausible position—but one I argue is ultimately wrong—is that inner speech plays asolelyfacilitative role that is exhausted by (i) serving as the vehicle of representation for conscious reasoning, and/or (ii) allowing one to focus on certain types (...) of objects or relations, e.g., causal relations, abstracta, counterfactuals, etc., or to consciously entertain structured propositional contents that it would be hard (or impossible) to focus on or entertain with representations in other (e.g., imagistic) formats. According to this position, inner speech doesn't figure as a justificatory element in our reasoning or as the partial epistemic basis of our conclusions—it merely facilitates reasoning through (i) and/or (ii). In contrast to the view that inner speech is amerefacilitator, I establish that (outside of potentially playing roles (i) and/or (ii)) the language we use itself serves as a crucial source of information in reasoning. In other words, we reason from propositions about the language we use in inner speech as opposed to exclusively reasoning from the semantic contents of the speech. My conclusion follows from how we use language as a cognitive tool to keep track of information, e.g., the contents of premises, lemmas, previous reasoning results, etc., in reasoning. (shrink)

Our conscious thought, at least at times, seems suffused with language. We may experience thinking as if we were “talking in our head”, thus using inner speech to verbalize, e.g., our premises, lemmas, and conclusions. I take inner speech to be part of a larger phenomenon I call inner semiotics, where inner semiotics involves the subjective experience of expressions in a semiotic (or symbol) system absent the overt articulation of the expressions. In this paper, I argue that inner semiotics allows (...) us to bootstrap our way into entertaining thoughts about exact numbers and quantities that we couldn't prior to our competence with a numeric code. I establish that our arithmetic thoughts literally occur as (internal ‘articulations’ of) expressions in a numeric code. However, a problem arises for my view: just as we can slip in overt speech, producing an utterance that deviates from what we mean to say, there is very good evidence that we can slip in inner speech as well. If our arithmetic thought occurs in a numeric code, it's far from clear how we determine when a covert utterance constitutes a slip. In closing, I provide an account of what makes an inner speech utterance a slip. (shrink)

We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the spatial (...) association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension. (shrink)