Amongst philosophers and cognitive scientists, modularity remains a popular choice for an architecture of the human mind, primarily because of the supposed explanatory value of this approach. Modular architectures can vary both with respect to the strength of the notion of modularity and the scope of the modularity of mind. We propose a dilemma for modular architectures, no matter how these architectures vary along these two dimensions. First, if a modular architecture commits to the informational encapsulation of modules, as it (...) is the case for modularity theories of perception, then modules are on this account impenetrable. However, we argue that there are genuine cases of the cognitive penetrability of perception and that these cases challenge any strong, encapsulated modular architecture of perception. Second, many recent massive modularity theories weaken the strength of the notion of module, while broadening the scope of modularity. These theories do not require any robust informational encapsulation, and thus avoid the incompatibility with cognitive penetrability. However, the weakened commitment to informational encapsulation greatly weakens the explanatory force of the theory and, ultimately, is conceptually at odds with the core of modularity. (shrink)

Tetris provides a difficult, dynamic task environment within which some people are novices and others, after years of work and practice, become extreme experts. Here we study two core skills; namely, choosing the goal or objective function that will maximize performance and a feature-based analysis of the current game board to determine where to place the currently falling zoid so as to maximize the goal. In Study 1, we build cross-entropy reinforcement learning models to determine whether different goals result in (...) different feature weights. Two of these optimization strategies quickly rise to performance plateaus, whereas two others continue toward higher but more jagged heights. In Study 2, we compare the zoid placement decisions made by our best CERL models with those made by 67 human players. Across 370,131 human game episodes, two CERL models picked the same zoid placements as our lowest scoring human for 43% of the placements and as our three best scoring experts for 65% of the placements. Our findings suggest that people focus on maximizing points, not number of lines cleared or number of levels reached. They also show that goal choice influences the choice of zoid placements for CERLs and suggest that the same is true of humans. Tetris has a repetitive task structure that makes Tetris more tractable and more like a traditional experimental psychology paradigm than many more complex games or tasks. Hence, although complex, Tetris is not overwhelmingly complex and presents a right-sized challenge to cognitive theories, especially those of integrated cognitive systems. (shrink)

Tetris provides a difficult, dynamic task environment within which some people are novices and others, after years of work and practice, become extreme experts. Here we study two core skills; namely, choosing the goal or objective function that will maximize performance and a feature-based analysis of the current game board to determine where to place the currently falling zoid so as to maximize the goal. In Study 1, we build cross-entropy reinforcement learning models to determine whether different goals result in (...) different feature weights. Two of these optimization strategies quickly rise to performance plateaus, whereas two others continue toward higher but more jagged heights. In Study 2, we compare the zoid placement decisions made by our best CERL models with those made by 67 human players. Across 370,131 human game episodes, two CERL models picked the same zoid placements as our lowest scoring human for 43% of the placements and as our three best scoring experts for 65% of the placements. Our findings suggest that people focus on maximizing points, not number of lines cleared or number of levels reached. They also show that goal choice influences the choice of zoid placements for CERLs and suggest that the same is true of humans. Tetris has a repetitive task structure that makes Tetris more tractable and more like a traditional experimental psychology paradigm than many more complex games or tasks. Hence, although complex, Tetris is not overwhelmingly complex and presents a right-sized challenge to cognitive theories, especially those of integrated cognitive systems. (shrink)

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based learning—particularly how actions generate new internal structures that support problem-solving—are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action-traces recombine during problem-solving. This model (...) is based on a study of two groups of sixth-grade students solving area problems. Before problem-solving, one group manipulated a tangram, the other group answered a descriptive test. Eye-movement trajectories during problem-solving were different between the groups. A second study showed that this difference required the tangram's geometrical structure, just manipulation was not enough. We propose a theoretical model accounting for these results, and discuss its implications. (shrink)

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time (...) are expected near the boundaries between categories. In contrast to previous work that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers. (shrink)

We report on five experiments investigating response choices and response times to simple science questions that evoke student “misconceptions,” and we construct a simple model to explain the patterns of response choices. Physics students were asked to compare a physical quantity represented by the slope, such as speed, on simple physics graphs. We found that response times of incorrect answers, resulting from comparing heights, were faster than response times of correct answers comparing slopes. This result alone might be explained by (...) the fact that height was typically processed faster than slope for this kind of task, which we confirmed in a separate experiment. However, we hypothesize that the difference in response time is an indicator of the cause of the response choice. To support this, we found that imposing a 3-s delay in responding increased the number of students comparing slopes on the task. Additionally a significant proportion of students recognized the correct written rule , but on the graph task they incorrectly compared heights. Finally, training either with repetitive examples or providing a general rule both improved scores, but only repetitive examples had a large effect on response times, thus providing evidence of dual paths or processes to a solution. Considering models of heuristics, information accumulation models, and models relevant to the Stroop effect, we construct a simple relative processing time model that could be viewed as a kind of fluency heuristic. The results suggest that misconception-like patterns of answers to some science questions commonly found on tests may be explained in part by automatic processes that involve the relative processing time of considered dimensions and a priority to answer quickly. (shrink)

Marr’s seminal distinction between computational, algorithmic, and implementational levels of analysis has inspired research in cognitive science for more than 30 years. According to a widely-used paradigm, the modelling of cognitive processes should mainly operate on the computational level and be targeted at the idealised competence, rather than the actual performance of cognisers in a specific domain. In this paper, we explore how this paradigm can be adopted and revised to understand mathematical problem solving. The computational-level approach applies methods from (...) computational complexity theory and focuses on optimal strategies for completing cognitive tasks. However, human cognitive capacities in mathematical problem solving are essentially characterised by processes that are computationally sub-optimal, because they initially add to the computational complexity of the solutions. Yet, these solutions can be optimal for human cognisers given the acquisition and enactment of mathematical practices. Here we present diagrams and the spatial manipulation of symbols as two examples of problem solving strategies that can be computationally sub-optimal but humanly optimal. These aspects need to be taken into account when analysing competence in mathematical problem solving. Empirically informed considerations on enculturation can help identify, explore, and model the cognitive processes involved in problem solving tasks. The enculturation account of mathematical problem solving strongly suggests that computational-level analyses need to be complemented by considerations on the algorithmic and implementational levels. The emerging research strategy can help develop algorithms that model what we call enculturated cognitive optimality in an empirically plausible and ecologically valid way. (shrink)

This volume is about the many ways we perceive. Contributors explore the nature of the individual senses, how and what they tell us about the world, and how they interrelate. They consider how the senses extract perceptual content from receptoral information. They consider what kinds of objects we perceive and whether multiple senses ever perceive a single event. They consider how many senses we have, what makes one sense distinct from another, and whether and why distinguishing senses may be useful. (...) They consider the extent to which the senses act in concert, rather than as discrete modalities, and whether this influence is epistemically pernicious, neutral, or beneficial. They explore both the familiar five sense modalities and other candidate sense modalities, including a sense for flavour, inner senses (e.g., a sense for pain), and various senses that may result from using sensory substitution devices. Contributors often represent competing views, and the methods they deploy sometimes differ from one essay to the next—with some drawing upon the sciences and engineering and others relying upon conceptual analysis. All contributors agree, nonetheless, that traditional theorizing about the senses is hampered by a neglect of the senses other than vision, and by the misconception that vision is a passive receptacle for an image thrown by a lens. And many contributors believe that it is unduly restrictive to think of perception as a collation of contents provided by individual sense modalities; they think that to understand perception properly, we need to build into our accounts the idea that the senses work together. The ambition of the volume is to begin to develop better paradigms for understanding the senses, and thereby to move toward a better understanding of perception. (shrink)

New and radically reformative thinking about the enactive and embodied basis of cognition holds out the promise of moving forward age-old debates about whether we learn and how we learn. The radical enactive, embodied view of cognition (REC) poses a direct, and unmitigated, challenge to the trademark assumptions of traditional cognitivist theories of mind—those that characterize cognition as always and everywhere grounded in the manipulation of contentful representations of some kind. REC has had some success in understanding how sports skills (...) and expertise are acquired. But, REC approaches appear to encounter a natural obstacle when it comes to understanding skill acquisition in knowledge-rich, conceptually based domains like the hard sciences and mathematics. This paper offers a proof of concept that REC’s reach can be usefully extended into the domain of science, technology, engineering, and mathematics (STEM) learning, especially when it comes to understanding the deep roots of such learning. In making this case, this paper has five main parts. The section “Ancient Intellectualism and the REC Challenge” briefly introduces REC and situates it with respect to rival views about the cognitive basis of learning. The “Learning REConceived: from Sports to STEM?” section outlines the substantive contribution REC makes to understanding skill acquisition in the domain of sports and identifies reasons for doubting that it will be possible to apply the same approach to knowledge-rich STEM domains. The “Mathematics as Embodied Practice” section gives the general layout for how to understand mathematics as an embodied practice. The section “The Importance of Attentional Anchors” introduces the concept “attentional anchor” and establishes why attentional anchors are important to educational design in STEM domains like mathematics. Finally, drawing on some exciting new empirical studies, the section “Seeing Attentional Anchors” demonstrates how REC can contribute to understanding the roots of STEM learning and inform its learning design, focusing on the case of mathematics. (shrink)

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often (...) conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. (shrink)

How can we explain the intentional nature of an expert’s actions, performed without immediate and conscious control, relying instead on automatic cognitive processes? How can we account for the differences and similarities with a novice’s performance of the same actions? Can a naturalist explanation of intentional expert action be in line with a philosophical concept of intentional action? Answering these and related questions in a positive sense, this dissertation develops a three-step argument. Part I considers different methods of explanations in (...) cognitive neuroscience (Bennett & Hacker’s philosophical, conceptual analysis; Marr’s three levels of explanation; Neural Correlates of Consciousness research; mechanistic explanation), defending ‘mechanistic explanation’ as a method that provides the necessary tools for integrating interdisciplinary insights into human action. Furthermore, a dynamic, explanatory mechanism allows the assessment of the impact of learning and development on expert action in a valuable way that other methods don’t. Part II continues by scrutinizing several cognitive neuroscientific theories of learning and development (neuroconstructivism; dual-processing theories; simulation theory; extended mind/cognition hypothesis), arguing for the complex interactions between different types of processing and different action representations involved in expert action performances. Moreover, according to our discussion of a particular ‘simulation theory’ these interactions can be influenced in several ways with the use of language, allowing an agent to configure a specific action representation for performance at a later stage. The results of Parts I and II are then applied in Part III to a parallel discussion of philosophical analyses of intentional action (discussing i.a. Frankfurt, Bratman, Pacherie and Ricoeur) and cognitive neuroscientific insights in it. Both approaches are found to converge in emphasizing the importance for an expert to develop stable patterns of actions that comply maximally not only with his intentions, but also with his motor expertise and with situational conditions. Consequently, his actions – automatic, or not – rely on this ‘sculpted space of actions’. (shrink)