When thought overwhelms the mind, the mind uses the body and the world. Several studies reveal ways that people alone or together use gesture and marks on paper to structure and augment their thought for comprehension, inference, and discovery. The studies show that the mapping of thought to gesture or the page is more direct than the arbitrary mapping to language and suggest that these forms of visual/spatial/action representation are used to “translate” language into mental representations. It is argued that (...) actions in space create patterns in the world that reflect abstractions, that the actions are incorporated into gestures and the patterns into diagrams, a network that integrates gesture, action, the designed world, and abstraction dubbed spraction. (shrink)

Contemporary psychological research that studies how people apply mathematics has largely viewed mathematics as a computational tool for deriving an answer. The tacit assumption has been that people first understand a situation, and then choose which computations to apply. We examine an alternative assumption that mathematics can also serve as a tool that helps one to construct an understanding of a situation in the first place. Three studies were conducted with 6th‐grade children in the context of proportional situations because early (...) proportional reasoning is a premier example of where mathematics may provide new understanding of the world. The children predicted whether two differently‐sized glasses of orange juice would taste the same when they were filled from a single carton of juice made from concentrate and water. To examine the relative contributions and interactions of situational and mathematical knowledge, we manipulated the formal features of the problem display (e.g., diagram vs. photograph) and the numerical complexity (e.g., divisibility) of the containers and the ingredient ratios. When the problem was presented as a diagram with complex numbers, or “realistically” with easy numbers, the children predicted the glasses would taste different because one glass had more juice than the other. But, when the problem was presented realistically with complex numbers, the children predicted the glasses would taste the same on the basis of empirical knowledge (e.g., “Juice can't change by itself”). And finally, when the problem was presented as a diagram with easy numbers, the children predicted the glasses would taste the same on the basis of proportional relations. These complex interactions illuminate how mathematical and empirical knowledge can jointly constrain the construction of a new understanding of the world. We propose that mathematics helped in the case of successful proportional reasoning because it made a complex empirical situation cognitively tractable, and thereby helped the children construct mental models of that situation. We sketch one aspect of the mental models that are constructed in the domain of quantity—a preference for specificity—that helps explain the current findings. (shrink)

Our earliest tools are our bodies. Our hands raise and turn and toss and carry and push and pull, our legs walk and climb and kick allowing us to move and act in the world and to create the multitude of artifacts that improve our lives. The list of actions made by our hands and feet and other parts of our bodies is long. What is more remarkable is we turn those actions in the world into actions on thought through (...) gestures, language, and graphics, thereby creating cognitive tools that expand the mind. The focus here is gesture; gestures transform actions on perceptible objects to actions on imagined thoughts, carrying meaning with them rapidly, precisely, and directly. We review evidence showing that gestures enhance our own thinking and change the thought of others. We illustrate the power of gestures in studies showing that gestures uniquely change conceptions of time, from sequential to simultaneous, from sequential to cyclical, and from a perspective embedded in a timeline to an external perspective looking on a timeline, and by so doing obviate the ambiguities of an embedded perspective. We draw parallels between representations in gesture and in graphics; both use marks or actions arrayed in space to communicate more immediately than symbolic language. (shrink)

The term conceptual simulation refers to a type of everyday reasoning strategy commonly called “what if” reasoning. It has been suggested in a number of contexts that this type of reasoning plays an important role in scientific discovery; however, little direct evidence exists to support this claim. This article proposes that conceptual simulation is likely to be used in situations of informational uncertainty, and may be used to help scientists resolve that uncertainty. We conducted two studies to investigate the relationship (...) between conceptual simulation and informational uncertainty. Study 1 was an in vivo study of expert scientists; the results suggest that scientists do use conceptual simulation in situations of informational uncertainty, and that they use conceptual simulation to make inferences from their data using the analogical reasoning process of alignment by similarity detection. Study 2 experimentally manipulated experts' level of uncertainty and provides further support for the hypothesis that conceptual simulation is more likely to be used in situations of informational uncertainty. Finally, we discuss the relationship between conceptual simulation and other types of reasoning using qualitative mental models. (shrink)

Conceptual integration—“blending”—is a general cognitive operation on a par with analogy, recursion, mental modeling, conceptual categorization, and framing. It serves a variety of cognitive purposes. It is dynamic, supple, and active in the moment of thinking. It yields products that frequently become entrenched in conceptual structure and grammar, and it often performs new work on its previously entrenched products as inputs. Blending is easy to detect in spectacular cases but it is for the most part a routine, workaday process that (...) escapes detection except on technical analysis. It is not reserved for special purposes, and is not costly.In blending, structure from input mental spaces is projected to a separate, “blended” mental space. The projection is selective. Through completion and elaboration, the blend develops structure not provided by the inputs. Inferences, arguments, and ideas developed in the blend can have effect in cognition, leading us to modify the initial inputs and to change our view of the corresponding situations.Blending operates according to a set of uniform structural and dynamic principles. It additionally observes a set of optimality principles. (shrink)

Resurgent interest in both mechanistic and counterfactual theories of explanation has led to a fair amount of discussion regarding the relative merits of these two approaches. James Woodward is currently the pre-eminent counterfactual theorist, and he criticizes the mechanists on the following grounds: Unless mechanists about explanation invoke counterfactuals, they cannot make sense of claims about causal interactions between mechanism parts or of causal explanations put forward absent knowledge of productive mechanisms. He claims that these shortfalls can be offset if (...) mechanists will just borrow key tenets of his counterfactual theory of causal claims. What mechanists must bear in mind, however, is that by pursuing this course they risk both the assimilation of the mechanistic theories of explanation into Woodward’s own favored counterfactual theory, and they risk the marginalization of mechanistic explanations to a proper subset of all explanations. An outcome more favorable to mechanists might be had by pursuing an actualist-mechanist theory of the contents of causal claims. While it may not seem obvious at first blush that such an approach is workable, even in principle, recent empirical research into causal perception, causal belief, and mechanical reasoning provides some grounds for optimism. (shrink)

In this paper, I present a framework where possible relations between learning and mental models are explored. In particular, I’ll be concerned with non-symbolic gestures accompanying discourse and their role in inducing the construction of models and therefore deep comprehension and learning in the listener. Also, I’ll be concerned with cognitive and socio-cognitive conflicts and their roles in inducing construction of alternative models of a problem and therefore in learning to reason. Human ability to learn is of great importance for (...) individuals interested in change. Indeed, to learn both declarative and procedural knowledge means to change, and in order to be able to intervene on change in a desired way it is necessary to have a theory of the mental representations and processes involved in learning and a theory of the communication and contexts that favour learning. (shrink)

Scientists, either working alone or in groups, require rich cognitive, social, cultural, and material environments to accomplish their epistemic aims. There is research in the cognitive sciences that examines intelligent behavior as a function of the environment (“environmental perspectives”), which can be used to examine how scientists integrate “cognitive-cultural” resources as they create environments for problem-solving. In this paper, I advance the position that an expanded framework of distributed cognition can provide conceptual, analytical, and methodological tools to investigate how scientists (...) enhance natural cognitive capacities by creating specific kinds of environments to address their epistemic goals. In a case study of a pioneering neuroengineering lab seeking to understand learning in living networks of neurons, I examine how the researchers integrated conceptual, methodological, and material resources from engineering, neuroscience, and computational science to create different kinds of distributed problem-solving environments that enhanced their natural cognitive capacities, for instance, for reasoning, visualization, abstraction, imagination, and memory, to attain their epistemic aims. (shrink)

This paper offers an explanation of how collaboration leads to abstract and flexible problem solving. We asked the individual and paired subjects to indicate 3/4 of 2/3 of the area of a square sheet of paper and found that (1) they primarily folded or partitioned the paper rather than algorithmically calculating the answer, (2) they strongly tendened to backtrack and confirm their proto‐plans on externalized traces such as creases on the paper, and (3) only the paired subjects shifted to the (...) mathematical strategy in their second trials. Based on these results, we propose that two factors, individuals' activeness in choosing and confirming the initial strategies and the frequent role exchange between task‐doing and monitoring in collaborative situations, interact in collaboration to generate various solutions differing in the degree of abstraction, which are then reflected upon by the participants to lead them to abstraction. (shrink)

What is the relation between the material, conventional symbol structures that we encounter in the spoken and written word, and human thought? A common assumption, that structures a wide variety of otherwise competing views, is that the way in which these material, conventional symbol-structures do their work is by being translated into some kind of content-matching inner code. One alternative to this view is the tempting but thoroughly elusive idea that we somehow think in some natural language (such as English). (...) In the present treatment I explore a third option, which I shall call the "complementarity" view of language. According to this third view the actual symbol structures of a given language add cognitive value by complementing (without being replicated by) the more basic modes of operation and representation endemic to the biological brain. The "cognitive bonus" that language brings is, on this model, not to be cashed out either via the ultimately mysterious notion of "thinking in a given natural language" or via some process of exhaustive translation into another inner code. Instead, we should try to think in terms of a kind of coordination dynamics in which the forms and structures of a language qua material symbol system play a key and irreducible role. Understanding language as a complementary cognitive resource is, I argue, an important part of the much larger project (sometimes glossed in terms of the "extended mind") of understanding human cognition as essentially and multiply hybrid: as involving a complex interplay between internal biological resources and external non-biological resources. (shrink)

Here I consider the relative merits of two recent models of explanation, James Woodward's interventionist-counterfactual model and the model model. According to the former, explanations are largely constituted by information about the consequences of counterfactual interventions. Problems arise for this approach because countless relevant interventions are possible in most cases and because it overlooks other kinds of equally relevant information. According the model model, explanations are largely constituted by cognitive models of actual mechanisms. On this approach, explanations tend not to (...) represent any of the aforementioned information explicitly but can instead be used to produce it on demand. The model model thus offers the more plausible account of the information of which we are aware when we have an explanation and of the ratiocinative process through which we derive many kinds of information that are relevant to the evaluation of explanations. (shrink)

Modern integrative systems biology defines itself by the complexity of the problems it takes on through computational modeling and simulation. However in integrative systems biology computers do not solve problems alone. Problem solving depends as ever on human cognitive resources. Current philosophical accounts hint at their importance, but it remains to be understood what roles human cognition plays in computational modeling. In this paper we focus on practices through which modelers in systems biology use computational simulation and other tools to (...) handle the cognitive complexity of their modeling problems so as to be able to make significant contributions to understanding, intervening in, and controlling complex biological systems. We thus show how cognition, especially processes of simulative mental modeling, is implicated centrally in processes of model-building. At the same time we suggest how the representational choices of what to model in systems biology are limited or constrained as a result. Such constraints help us both understand and rationalize the restricted form that problem solving takes in the field and why its results do not always measure up to expectations. (shrink)

We call those gestures “instrumental” that can enhance certain thinking processes of an agent by offering him representational models of his actions in a virtual space of imaginary performative possibilities. We argue that pointing is an instrumental gesture in that it represents geometrical information on one’s own gaze direction, and provides a ritualized template for initiating gaze coordination and joint attention. We counter two possible objections, asserting respectively that the representational content of pointing is not constitutive, but derived from language, (...) and that pointing directly solicits gaze coordination, without representing it. We consider two studies suggesting that attention and spatial perception are actively modified by one’s own pointing activity: the first study shows that pointing gestures help children link sets of objects to their corresponding number words; the second, that adults are faster and more accurate in counting when they point. (shrink)

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are more concrete and familiar, and they are more similar to physical objects and everyday experience. The complementary computational characteristics of grounded and abstract representations lead to trade‐offs in problem‐solving performance. In prior research with (...) high school students solving relatively simple problems, Koedinger and Nathan (2004) demonstrated performance benefits of grounded representations over abstract representations—students were better at solving simple story problems than the analogous equations. This article extends this prior work to examine both simple and more complex problems in two samples of college students. On complex problems with two references to the unknown, a “symbolic advantage” emerged, such that students were better at solving equations than analogous story problems. Furthermore, the previously observed “verbal advantage” on simple problems was replicated. We thus provide empirical support for a trade‐off between grounded, verbal representations, which show advantages on simpler problems, and abstract, symbolic representations, which show advantages on more complex problems. (shrink)

When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well‐studied (...) puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture‐speech mismatches—explanations in which speech conveyed one path and gesture another—at these theoretically defined choice points than they produced at non‐choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem‐solving. (shrink)

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear‐system problems as part of a game. Although none of the participants initially used a mathematical representation, many discovered a parity‐based, mathematical strategy during problem solving. Two accounts of the spontaneous discovery of mathematical strategies were tested. According to the automatic schema abstraction hypothesis, experience (...) with multiple, unique problem exemplars facilitates extraction of the parity relation. According to the comparison‐based abstraction hypothesis, explicitly comparing gear pathways that have different number, but the same parity, should result in extraction of parity. An event history analysis showed that accumulation of experiences with different‐number, same‐parity comparisons predicted discovery of parity; accumulation of unique exemplars did not. Results suggest that comparison‐based abstraction processes can lead to the discovery of a mathematical relation. (shrink)

Determining how we use our body to support cognition represents an important part of understanding the embodied and embedded nature of cognition. In the present investigation, we pursue this question in the context of a common perceptual task. Specifically, we report a series of experiments investigating head tilt (i.e., external normalization) as a strategy in letter naming and reading stimuli that are upright or rotated. We demonstrate that the frequency of this natural behavior is modulated by the cost of stimulus (...) rotation on performance. In addition, we demonstrate that external normalization can benefit performance. All of the results are consistent with the notion that external normalization represents a form of cognitive offloading and that effort is an important factor in the decision to adopt an internal or external strategy. (shrink)

When learners self-explain, they try to make sense of new information. Although research has shown that bodily actions and written notes are an important part of learning, previous analyses of self-explanations rarely take into account written and non-verbal data produced spontaneously. In this paper, the extent to which interpretations of self-explanations are influenced by the systematic consideration of such data is investigated. The video recordings of 33 undergraduate students, who learned with worked-out examples dealing with complex numbers, were categorized successively (...) including three different data bases: verbal data, verbal and written data, and verbal, written and non-verbal data. Results reveal that including written data and non-verbal data leads to a more accurate analysis of self-explanations than an analysis solely based on verbal data. This influence is even stronger for the categorization of self-explanations as adequate or inadequate. (shrink)