Towards a New Epistemology of Mathematics

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

---

Predictors of maternal language to infants during a picture book task in the home: Family SES, child characteristics and the parenting environment

This study investigated the contribution of child characteristics and parenting environment to the relationship between family SES/demographic characteristics and maternal language to infants. 1157 children were drawn from a representative sample of 1292 infants born to mothers in rural Appalachian counties and rural counties in southern minority U.S. communities. Mothers and their 6–8 month old babies were videotaped at home while talking about a wordless picture book. Mothers' language output and complexity were analyzed. Child temperament, age, and parenting environment (knowledge of child development and observed mother–child engagement) were predictors of maternal language. Furthermore, their inclusion reduced the magnitude of the association between demographic characteristics and maternal language. Tests of mediation suggested that the parenting environment partially mediates the relationship between SES/demographic characteristics and maternal language. Findings are discussed with respect to identifying proximal processes that explain how SES may exert its influence on the language of young children.     

Understanding and using principles of arithmetic: operations involving negative numbers

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers ( Dixon, Deets, & Bangert, 2001 ). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation. Participants ( N = 44) completed two tasks. In the Evaluation task, participants rated how well sets of equations were solved. Some sets violated principles of arithmetic and others did not. Participants rated non-violation sets higher than violation sets for two different principles for subtraction with a negative number. In the Word Problem task, participants read word problems and set up equations that could be used to solve them. Participants who displayed greater knowledge of principles of arithmetic with a negative number were more likely to set up equations that involved negative numbers. Thus, participants' knowledge of arithmetic principles was related to their problem representations.     

Interdependence of parenting of mothers and fathers of infants

This study examined the relations among parenting behaviors of 97 coresident mothers and fathers of infants during a dyadic free-play setting. The authors examined the extent to which observed sensitive and intrusive parenting behaviors in mother-child and father-child dyads were related and how perceived marital quality may be associated with the similarity between maternal and paternal parenting behaviors. The authors found support for interdependence of parenting by mothers and fathers. High perceived marital quality was associated with interdependence of sensitive parenting behaviors in mother-infant and father-infant interactions. Negative parenting behaviors by mothers and fathers were interrelated regardless of marital quality. The findings highlight the importance of studying parenting by mothers and fathers as embedded within particular family systems.     

Parental expressed emotion toward children: prediction from early family functioning

Expressed emotion (EE), an index of family member criticism and emotional overinvolvement, predicts outcome among adults and children with mental disorders. However, limited research exists on factors contributing to EE. Aims of the current study were to (a) examine EE in mothers of young children; (b) assess relationships between demographic factors and EE in a diverse sample; and (c) investigate whether family stress and functioning, including quality of marital relationship, life events, maternal stress, and family environment, predict EE. In the current study, 276 mothers completed questionnaires when their children were between 1 and 3 years of age and a measure of EE when their children were in kindergarten. Results indicated that family expressiveness was the most consistent predictor of EE. Further research seems warranted to better delineate associations between family functioning and EE.     

Do captive mandrills invent new gestures?

Studies of intraspecific behavioral variability have documented cases where behaviors are present in some populations or groups but are absent in others. In some cases these differences cannot be explained by recourse to environmental or genetic variation, and may instead represent “traditions”. Despite many examples of animal traditions in acoustic communication, relatively few examples exist of gestural traditions. Here I report on a study of communication across eight captive groups of mandrills (Mandrillus sphinx) in which a prominent gesture (Hand extension) was unique to two groups. Habitat variability, genetic differences, and sampling bias were not sufficient to account for the gesture’s limited distribution across the study groups. Within the two groups where the gesture did occur only the juveniles in the group performed it, consistently directing it toward adults. Quantitative analysis of the contexts and responses associated with the gesture suggested that juveniles utilized it to provoke adults. Moreover, the gesture appeared to minimize the risk juveniles incurred while inciting adults, suggesting that repeated social interactions shaped the gesture’s form. Interestingly, both the groups where the gesture emerged contained few juveniles. With limited play partners, these juveniles may have resorted to harassing adults as an alternative social play outlet. The creation of this novel gesture may thus be due to the combined influence of a shortage of play partners and of the increased free time for playful social exploration afforded by captivity. Although juveniles frequently “eavesdropped” on dyadic interactions involving the gesture and would subsequently initiate an interaction with the recipient of the gesture, there was no definitive evidence for social transmission; the gesture could instead have been independently invented by each juvenile. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Spiritual needs: Gender differences among professional spiritual care providers

The current study explored gender differences regarding spirituality by comparing the relative frequency with which male (n = 85) and female (n = 103) professional chaplains experience various facets of the spiritual experience. The women in the sample reported experiencing five of the seven spiritual constructs examined significantly more often than men, including the need for (1) belonging, (2) meaning, (3) hope, (4) beauty, and (5) acceptance of death. No significant gender differences were found for spiritual needs related to morality concerns or religious practices.     

Using a virtual reality system to study balance and walking in a virtual outdoor environment: a pilot study.

Falls and fall-related injuries are a major problem for elderly persons. Most falls occur during walking and turning, and the risk of falling increases when attention is diverted to something besides walking. It is often difficult to standardize methods for testing balance and fall tendency in a clinically relevant setting. We describe the development of a system using a virtual environment (VE) to assess how attention demanding and unexpected events influence a person's capacity to control balance and movement. The hardware in the system consists of a head-mounted display (HMD), a magnetic tracker system, and two SGI computers. The software consists of the image generation of the VE and the management and visualization of motion tracking data. In a preliminary pilot study eight subjects (age 23-80) participated. Each subject walked on a normal floor and was visually presented a familiar outdoor environment in the HMD. They were exposed to different unexpected events, such as a virtual snowfall and tilting of the VE. Disturbances of balance and walking patterns such as changes in speed, stride length and balance reactions like slipping were observed. Two subjects experienced symptoms of cyber sickness with a SSQ score above 25 points. Walking with sensors only did not affect walking time, but in VE the subjects generally walked more slowly. Virtual tilting of the environment had an impact on balance performance during walking. This effect was not observed while the test subjects were walking in a virtual snowfall. The model needs further development but may hold a potential for clinical use.     

Testing for the presence of 1/f noise in continuation tapping data.

A number of recent papers have suggested that the series of time intervals produced in continuation tapping may have fractal properties. This proposition, nevertheless, was only based on the visual appraisal of graphical results, and was not statistically supported. In the present study, we applied the ARMA/ARFIMA modeling procedures proposed by Wagenmakers, Farrell, and Ratcliff (2005) to test for the presence of long-range dependencies in continuation tapping data. Our results demonstrate the presence of long-range dependencies in most series and offer strong support for the hypothesis that fluctuations in tapping series are fractal in nature.