I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or

Principles of Neural Science

Prior to the twentieth century, theories of knowledge were inherently perceptual. Since then, developments in logic, statis- tics, and programming languages have inspired amodal theories that rest on principles fundamentally different from those underlying perception. In addition, perceptual approaches have become widely viewed as untenable because they are assumed to implement record- ing systems, not conceptual systems. A perceptual theory of knowledge is developed here in the context of current cognitive science and neuroscience. During perceptual experience, association areas in the brain capture bottom-up patterns of activation in sensory-motor areas. Later, in a top-down manner, association areas partially reactivate sensory-motor areas to implement perceptual symbols. The stor- age and reactivation of perceptual symbols operates at the level of perceptual components - not at the level of holistic perceptual expe- riences. Through the use of selective attention, schematic representations of perceptual components are extracted from experience and stored in memory (e.g., individual memories of green, purr, hot). As memories of the same component become organized around a com- mon frame, they implement a simulator that produces limitless simulations of the component (e.g., simulations of purr). Not only do such simulators develop for aspects of sensory experience, they also develop for aspects of proprioception (e.g., lift, run) and introspec- tion (e.g., compare, memory, happy, hungry). Once established, these simulators implement a basic conceptual system that represents types, supports categorization, and produces categorical inferences. These simulators further support productivity, propositions, and ab- stract concepts, thereby implementing a fully functional conceptual system. Productivity results from integrating simulators combinato- rially and recursively to produce complex simulations. Propositions result from binding simulators to perceived individuals to represent type-token relations. Abstract concepts are grounded in complex simulations of combined physical and introspective events. Thus, a per- ceptual theory of knowledge can implement a fully functional conceptual system while avoiding problems associated with amodal sym- bol systems. Implications for cognition, neuroscience, evolution, development, and artificial intelligence are explored.

/pdf/perceptual-symbol-systems-4spsk97r61.pdf

Perceptual symbol systems.

(1998). Human cognitive abilities: A survey of factor analytic studies. Gifted and Talented International: Vol. 13, No. 2, pp. 97-98.

Human cognitive abilities: A survey of factor analytic studies

http://semantics.uchicago.edu/kennedy/classes/s09/experimentalsemantics/feigenson-etal04.pdf

Core systems of number

Let's start from scratch in thinking about what memory is for, and consequently, how it works. Suppose that memory and conceptualization work in the service of perception and action. In this case, conceptualization is the encoding of patterns of possible physical interaction with a three-dimensional world. These patterns are constrained by the structure of the environment, the structure of our bodies, and memory. Thus, how we perceive and conceive of the environment is determined by the types of bodies we have. Such a memory would not have associations. Instead, how concepts become related (and what it means to be related) is determined by how separate patterns of actions can be combined given the constraints of our bodies. I call this combination "mesh." To avoid hallucination, conceptualization would normally be driven by the environment, and patterns of action from memory would play a supporting, but automatic, role. A significant human skill is learning to suppress the overriding contribution of the environment to conceptualization, thereby allowing memory to guide conceptualization. The effort used in suppressing input from the environment pays off by allowing prediction, recollective memory, and language comprehension. I review theoretical work in cognitive science and empirical work in memory and language comprehension that suggest that it may be possible to investigate connections between topics as disparate as infantile amnesia and mental-model theory.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0140525X97000010

What memory is for.

This study examined infants' use of contour length in num- ber discrimination tasks. We systematically varied number and con- tour length in a visual habituation experiment in order to separate these two variables. Sixteen 6- to 8-month-old infants were habituated to displays of either two or three black squares on a page. They were then tested with alternating displays of either a familiar number of squares with a novel contour length or a novel number of squares with a familiar contour length. Infants dishabituated to the display that changed in contour length, but not to the display that changed in num- ber. We conclude that infants base their discriminations on contour length or some other continuous variable that correlates with it, rather than on number.

https://whitman.edu/documents/academics/psychology/clearfield_mix1999.pdf

Number Versus Contour Length in Infants' Discrimination of Small Visual Sets

We tested whether mental rotation training improved math performance in 6- to 8-year-olds. Children were pretested on a range of number and math skills. Then one group received a single session of mental rotation training using an object completion task that had previously improved spatial ability in children this age (Ehrlich, Levine, & Goldin-Meadow, 2006). The remaining children completed crossword puzzles instead. Children's posttest scores revealed that those in the spatial training group improved significantly on calculation problems. In contrast, children in the control group did not improve on any math tasks. Further analyses revealed that the spatial training group's improvement was largely due to better performance on missing term problems (e.g., 4 + ____ = 11).

Spatial Training Improves Children's Mathematics Ability

A review and synthesis of the literature on quantification in infancy and early childhood is provided. In most current conceptualizations, early quantification is assumed to be number based. However, the extant literature provides no clear-cut evidence that infants use number to perform quantitative tasks. Instead, new research suggests that quantification is initially based on nonnumerical cues, such as area and contour length, whether or not a task involves discrete items. The authors discuss the implications of these findings with respect to early quantification and its relation to later numerical development.

Multiple cues for quantification in infancy: is number one of them?

There is a well-known relation between spatial ability and mathematics dating back to the work of early twentieth century factor analysts. This connection is a ripe opportunity for educators, who might use spatial training to improve math learning. However, a closer look at the literature reveals gaps that impede direct application. The primary problem is that although this relation is well established in older children and adults, its emergence in early development and subsequent developmental interactions are not well documented. Moreover, there is a need for more mechanistic explanations that might be leveraged to improve math education. In this chapter, we attempt to address these issues by reviewing the existing literature to identify instances where answers are available and others where further research is needed.

The relation between space and math: developmental and educational implications.

1. Historical Trends and Current Issues 2. Quantification in Infancy 3. Quantification in Early Childhood 4. Quantification of Discrete Sets: A Synthesis 5. Continuous Amount 6. Relative Quantity 7. Nonverbal Representation of Quantity 8. Acquiring Conventional Skills 9. The Whole Child

Kelly S. Mix

Papers

Number Versus Contour Length in Infants' Discrimination of Small Visual Sets

Spatial Training Improves Children's Mathematics Ability

Multiple cues for quantification in infancy: is number one of them?

The relation between space and math: developmental and educational implications.

Quantitative Development in Infancy and Early Childhood