Possible number systems

Number systems—such as the natural numbers, integers, rationals, reals, or complex numbers—play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people’s concept of a number system by asking them whether “number lines” of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms’ ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).     

A Multimodal Study of Childhood Trauma and Distress Tolerance in Young Adulthood

Individuals with a history of childhood trauma experience deficits in emotion regulation. However, few studies have investigated childhood trauma and both perceived (i.e., self-report) and behavioral measures of distress tolerance. The current study evaluated associations between childhood trauma (i.e., physical abuse, sexual abuse, and witnessing family violence) and measures of perceived (Distress Tolerance Scale) and behavioral distress tolerance (i.e., Paced Auditory Serial Addition Test, breath-holding). Participants were 320 undergraduate students with a history of interpersonal trauma (e.g., sexual/physical assault). Structural equation modeling was used to evaluate associations between frequency of childhood trauma type and distress tolerance. Greater childhood physical abuse was associated with higher perceived distress tolerance. Greater levels of witnessing family violence were associated with lower behavioral distress tolerance on the breath-holding task. No significant effects were found for Paced Auditory Serial Addition Test performance. Associations between childhood trauma and emotion regulation likely are complex and warrant further study.     

Single Parenthood and Adolescent Sexual Outcomes

Research suggests that children of single parents are at heightened risk of precocious sexual behavior, STDs, and other risky sexual outcomes. However, few such studies have addressed the type of single-parent family (single mother or single father), or differences across other-sex parent–child dyads. While gender essentialist models assume differences among youth living only with mothers or with fathers, constructivist models propose more flexible modes of parenting that lead to more similar outcomes. Using data from the National Longitudinal Study of Adolescent to Adult Health (n?=?2570) on youth between the ages of 15 and 19, we compared sexually-related outcomes among adolescents, both boys and girls, who lived with a single mother or a single father. These outcomes include sexual intercourse and knowledge, use of contraception, attitudes toward intimacy and pregnancy, and diagnosis of sexually-transmitted diseases. The results from linear and logistic regression models indicated few differences between single-mother and single-father families, or between same-sex and opposite-sex parent–child matches, using p values of .05 or smaller. Our results called into question essentialist models that posit higher risks for adolescents living with a particular parent or with an opposite-sex parent.     

‘Give Me a Reason to Live!’ Examining Reasons for Living Across Levels of Suicidality

Scholarly research focusing on social psychological factors (e.g. mental health) and social environmental factors (e.g. childhood trauma) has found these measures to be correlated with suicidality. However, such literature has tended to overlook what may impact one’s reasons for living. Using a sample of over 1,200 students from a Canadian university, the goal of the current study is to empirically test, by employing multivariate nested regression models (by levels of suicidal behaviour), known and relative unknown correlates with reasons for living, with a particular focus on strength of religious faith, which is a well-known predictor for suicidality, but less studied as a reason for living. Results show that, among students with serious suicidal ideation and/or a previous suicide attempt, the strongest predictor for student’s reasons for living was strength of religious faith. Strength of religious faith has seldom been acknowledged or identified as an important measure in assessing one’s reasons to live. These findings have implications for the role of religiosity among suicidality research, especially studies that focus on reasons for living.     

The concept of risk and responsible conduct of research

Assessment of risk is one of the key issues in the field of responsible conduct of research which covers discourses of research ethics and research integrity. The principle of minimizing risks and balancing of risks and benefits is one of the main requirements of research ethics. In addition, the content of informed consent that is another fundamental principle of research ethics derives from the assessment of risks and benefits related to a particular research project. Risk assessment also plays a crucial role in methodological design of the research project. This is an important point where research ethics and research integrity discourses overlap. Firstly, because the choice of a control group (e.g., placebo control) is a key ethical issue related to the protection of the research subjects' interests. Secondly, because the quality of the research data, that is one of the key elements of research integrity, is closely connected to the choice of research methodology as well. The problem of biased interpretation or manipulation of risk related features of biomedical research should also be taken into account. Despite the importance of the concept of risk to the field of biomedical research, its relevance has not yet attracted a sufficient attention in the responsible conduct of research debate.     

Teaching ethics: More than an honor code

An honor code is certainly a good place to start teaching engineering students about ethics, but teaching students to live honorably requires far more effort than memorizing a code of ethics statement or applying it just to academic performance. In the School of Engineering at Grand Valley State University, we have followed the model provided by the United States Military Academy at West Point. For our students this involves an introduction to the Honor Code as part of a larger Honor Concept at the very beginning of their studies and then making it an integral part of their preparation as engineers. The challenge is significant because the culture at large does not support living with an Honor Concept. This paper will begin with a discussion of the cultural context in which we must teach, because that context has changed significantly in the years since many faculty members were students themselves. The rest of the paper will detail the approach that we have taken to teach ethics as an engineer’s way of life. “The shortest and surest way to live with honor in the world is to be in reality what we would appear to be. All human virtues increase and strengthen themselves by the practice and experience of them.” Plato An earlier version of this paper was presented at the 2005 conference, Ethics and Social Responsibility in Engineering and Technology, Linking Workplace Ethics and Education, co-hosted by Gonzaga University and Loyola Marymount University, Los Angeles, CA, USA, 9–10 June 2005.     

The intensity-difference limen for 6.5 kHz: an even more severe departure from Weber's law

Intensity-difference limens (DLs) were obtained for tones of 6.5 kHz over levels of 30-90 dB SPL. The tones had Gaussian-shaped envelopes whose duration was expressed as equivalent rectangular duration D, that of a rectangle enclosing the same area as the envelope. D ranged from 0.314 to 30 msec. DL behaviors such as the "severe departure from Weber's law," the "midlevel hump," or the "midduration hump"--that is, a rise in the DL over a range of short durations--were identified using trend analysis. The DL versus level followed a "severe departure" that increased as duration dropped to D approximately 1-2 msec. That midlevel hump then fell with further shortening of the tone pip, producing a mid-duration hump. Materials for this article may be accessed through the Psychonomic Society's Norms, Stimuli, and Data archive, at www.psychonomic.org/archive.     

Prospective memory: The relative effects of encoding,retrieval, and the match between encoding and retrieval

Previous prospective memory studies have revealed some important features of encoding, retrieval, and the match between the encoding and the retrieval that contribute to prospective memory performance. However, these studies have not provided evidence concerning the relative importance of these three factors because no study has investigated all three in a single design. We developed a laboratory-based paradigm that allowed us to manipulate different characteristics of encoding, retrieval, and the match between encoding and retrieval simultaneously in a single experiment. The results of eight experiments showed that all three factors have an influence on prospective memory performance, but that the match between encoding and retrieval has a significantly larger influence than either encoding or retrieval factors.