Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body‐based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action‐cognition transduction to investigate the cognitive relevance of directed actions to students’ mathematical reasoning in the area of geometry. The hypotheses we test include (1) that cognitively relevant directed actions have a direct (...) effect on performance (direct cognitive relevance hypothesis), (2) that cognitively relevant directed actions lead to more frequent production of gestures during explanations, which leads to improved performance (mediated cognitive relevance hypothesis), and (3) that performance effects of directed actions are influenced by the presence or absence of gesture production during mathematical explanations (moderated cognitive relevance hypothesis). We explore these hypotheses in an experiment where high school students (N = 85) evaluated the truth of geometry conjectures after performing cognitively relevant or cognitively irrelevant directed actions while playing a movement‐based video game. Contrary to the direct and mediated cognitive relevance hypotheses, we found no overall differences in performance or gesture production between relevant and irrelevant conditions. Consistent with the moderated cognitive relevance hypothesis, cognitive relevance influenced mathematical performance, as measured by the accuracy of students’ intuitions, insights, and the validity of their proofs, provided that students produced certain kinds of gestures during mathematical explanations (i.e., with explanatory gestures as the moderator). Implications for theories of grounded and embodied cognition and the design of embodied forms of educational interventions are discussed. (shrink)

Many experiments with infants suggest that they possess quantitative abilities, and many experimentalists believe that these abilities set the stage for later mathematics: natural numbers and arithmetic. However, the connection between these early and later skills is far from obvious. We evaluate two possible routes to mathematics and argue that neither is sufficient: (1) We first sketch what we think is the most likely model for infant abilities in this domain, and we examine proposals for extrapolating the natural number concept (...) from these beginnings. Proposals for arriving at natural number by (empirical) induction presuppose the mathematical concepts they seek to explain. Moreover, standard experimental tests for children's understanding of number terms do not necessarily tap these concepts. (2) True concepts of number do appear, however, when children are able to understand generalizations over all numbers; for example, the principle of additive commutativity (a+b=b+a). Theories of how children learn such principles usually rely on a process of mapping from physical object groupings. But both experimental results and theoretical considerations imply that direct mapping is insufficient for acquiring these principles. We suggest instead that children may arrive at natural numbers and arithmetic in a more top-down way, by constructing mathematical schemas. (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)

Recently, a cottage industry has formed with the expressed intent of analyzing the nature of personal-level reasoning and inference. The dominant position in the extant philosophical literature is that reasoning consists in rule-governed operations over propositional attitudes. In addition, it is widely assumed that our attitude updating procedures are purely cognitive. Any non-cognitive activity performed in service of updating our attitudes is external to the updating process—at least in terms of rational evaluation. In this paper, I argue that whether one (...) has rationally updated one’s attitudes and whether the resultant attitudes are rational can (at least partially) depend on one’s interactions with one’s environment and body to scaffold one’s ability to arrive at attitudes that are rationally appropriate given one’s evidence. (shrink)

We see no grounds for insisting that, because the concept natural number is abstract, its foundations must be innate. It is possible to specify domain general learning processes that feed into more abstract concepts of numerical infinity. By neglecting the messiness of children's slow acquisition of arithmetical concepts, Rips et al. present an idealized, unnecessarily insular, view of number development.

The study has two objectives: to introduce grip force recording as a new technique for studying embodied numerical processing; and to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line, A Theory of Magnitude and Embodied Cognition account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip (...) force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research. (shrink)

With his massive redeployment hypothesis (MRH), Anderson claims that novel cognitive functions are likely to rely on pre-existing circuits already possessing suitable resources. Here, we put forward recent findings from studies in numerical cognition in order to show that the role of sensorimotor experience in the ontogenetical development of a new function has been largely underestimated in Anderson's proposal.

Rips et al. claim that the principles underlying the structure of natural numbers cannot be inferred from interactions with the physical world. However, in their target article they failed to consider an important source of interaction: finger counting. Here, we show that finger counting satisfies all the conditions required for allowing the concept of numbers to emerge from sensorimotor experience through a bottom-up process.