Children's understanding of the relationship between addition and subtraction

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 − 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.     

Epicureanism About Death and Immortality

In this paper I discuss some of Martha Nussbaum’s defenses of Epicurean views about death and immortality. Here I seek to defend the commonsense view that death can be a bad thing for an individual against the Epicurean; I also defend the claim that immortality might conceivably be a good thing. In the development of my analysis, I make certain connections between the literatures on free will and death. The intersection of these two literatures can be illuminated by reference to my notion of a Dialectical Stalemate.     

Examining Mediators of the Link Between Generativity and Well-being

Generativity involves raising and guiding the next generation, contributing to society, and creating new products and ideas. It has clearly been related to personal well-being, yet little is known about why this relationship exists. According to McAdams and de St. Aubin (J Pers Soc Psychol, 62:1003–1015, 1992), generativity is motivated by a desire for symbolic immortality, a need to be needed, and society’s expectation that one should be a contributing member. It was therefore hypothesized that the satisfaction of these variables would fully mediate the relationship between generativity and well-being. Structural equation modeling showed that symbolic immortality alone fully mediated the relationship.     

How Does It Feel to Be a Star?

Over the past three decades, research on the social dimensions of emotions has grown exponentially, particularly in the area of “emotion management.” In this project, we will attempt to add to this body of research by studying the social aspects of labeling or “instantiating” feelings. The data for the project come from televised red-carpet interviews conducted with celebrities immediately prior to awards ceremonies. By focusing on the generic aspects of the emotional claims-making put forth by interviewers and interviewees, we demonstrate how the labeling of emotions is an interpretive, interactive task.

Human embryonic stem cell research and the discarded embryo argument

Many who believe that human embryos have moral status are convinced that their use in human embryonic stem cell (hESC) research can be morally justified as long as they are discarded embryos left over from fertility treatments. This is one reason why this view about discarded embryos has played such a prominent role in the debate over publicly funding hESC research in the United States and other countries. Many believe that this view offers the best chance of a compromise between the different sides in this debate. This paper focuses on what seems to be the most plausible argument for this view about discarded embryos. It shows that this argument is unsound regardless of how one understands the claim that embryos have moral status. It also discusses the implications of this conclusion for attempts to use this argument as a basis for public policy.

BREAKING A TABOO: FRANK TIPLER'S THE PHYSICS OF IMMORTALITY

Abstract. In his book The Physics of Immortality. Frank Tipler has broken a longstanding intellectual taboo by dealing as a physicist with the theological themes of God and immortality, as well by arguing that theology can provide material for concept formation in the field of physics. His work on the anthropic principle convinced Tipler that, since the emergence of intelligent life is of the essence of the universe as a whole, the future of life is of fundamental significance. His Omega Point theory takes theological theories of the future's significance seriously from a scientific point of view. Theories of computers play a central role in Tipler's theory of immortality, and even though many critics have misunderstood his thrust in these theories, they are worthy of further exploration. Perhaps Tipler's most important contribution is his insistence that the world as described by physics is more open to interaction with biblical and theological perspectives than is often believed.     

The spread of fear: Symbolic generalization mediates graded threat-avoidance in specific phobia

Overgeneralization of fear and threat-avoidance represents a formidable barrier to successful clinical treatment of anxiety disorders. While stimulus generalization along quantifiable physical dimensions has been studied extensively, less consideration has been given to symbolic generalization, in which stimuli are indirectly and arbitrarily related. The present study examined whether the magnitude and extent of symbolic generalization of threat-avoidance and threat-beliefs differed between spider-phobic and nonphobic individuals. Initially, participants learned two sets of stimulus equivalence relations (A1?=?B1?=?C1; A2?=?B2?=?C2). Next, one cue (B1) was established as a conditioned stimulus (CS?+?; threat) that signalled onset of spider images and prompted avoidance, and another cue (B2) was established as a CS– (safety cue) that signalled the absence of such images. Subsequent testing showed that phobics compared to nonphobics exhibited greater symbolic generalization of threat-avoidance to threat cues A1 and C1 (indirect CS+ threat cues related via symmetry and equivalence, respectively), while all individuals showed nonavoidance to indirect safety cues A2 and C2. The enhanced symbolic generalization of threat-beliefs and avoidance behaviour observed in spider phobics warrants further investigation.     

Working memory and number line representations in single-digit addition: Approximate versus exact,nonsymbolic versus symbolic

How do kindergarteners solve different single-digit addition problem formats? We administered problems that differed solely on the basis of two dimensions: response type (approximate or exact), and stimulus type (nonsymbolic, i.e., dots, or symbolic, i.e., Arabic numbers). We examined how performance differs across these dimensions, and which cognitive mechanism (mental model, transcoding, or phonological storage) underlies performance in each problem format with respect to working memory (WM) resources and mental number line representations. As expected, nonsymbolic problem formats were easier than symbolic ones. The visuospatial sketchpad was the primary predictor of nonsymbolic addition. Symbolic problem formats were harder because they either required the storage and manipulation of quantitative symbols phonologically or taxed more WM resources than their nonsymbolic counterparts. In symbolic addition, WM and mental number line results showed that when an approximate response was needed, children transcoded the information to the nonsymbolic code. When an exact response was needed, however, they phonologically stored numerical information in the symbolic code. Lastly, we found that more accurate symbolic mental number line representations were related to better performance in exact addition problem formats, not the approximate ones. This study extends our understanding of the cognitive processes underlying children's simple addition skills.     

Reduction of false recognition through haptic presentation of objects

False recognition of an item that is not presented (the lure) can occur when participants study and are tested on their recognition of items related to the lure. False recognition is reduced when the study and test modalities are congruent (e.g., both visual) rather than different (e.g., visual study and auditory test). The present study examined whether such a congruency effect occurs for haptic and auditory modalities. After studying items presented haptically or auditorily, participants took a haptic or auditory recognition test. False recognition was reduced when both the study and test were haptic, but not when the study was auditory and the test was haptic. These results indicate that cues encoded through the haptic modality can reduce false recognition.     

Modeling parallelization and flexibility improvements in skill acquisition: from dual tasks to complex dynamic skills

Emerging parallel processing and increased flexibility during the acquisition of cognitive skills form a combination that is hard to reconcile with rule-based models that often produce brittle behavior. Rule-based models can exhibit these properties by adhering to 2 principles: that the model gradually learns task-specific rules from instructions and experience, and that bottom-up processing is used whenever possible. In a model of learning perfect time-sharing in dual tasks (Schumacher et al., 2001), speedup learning and bottom-up activation of instructions can explain parallel behavior. In a model of a complex dynamic task (Carnegie Mellon University Aegis Simulation Program [CMU-ASP], Anderson et al., 2004), parallel behavior is explained by the transition from serially organized instructions to rules that are activated by both top-down (goal-driven) and bottom-up (perceptually driven) factors. Parallelism lets the model opportunistically reorder instructions, leading to the gradual emergence of new task strategies.