A simple computational alternative to analysis of variance formulas for estimating the k-judge reliability

Formulas requiring the computation of only three standard deviations are presented for computing the interjudge reliability coefficient for any number of judges. These formulas yield coefficients identical to those obtained from a one-way repeated-measures analysis of variance. Even researchers with small handheld calculators can use this simple approach.     

A note on the computation of a table of intercorrelations

Outlined is the method used at present by the Educational Testing Service for computing intercorrelations from basic summations. This procedure is adapted to the use of high speed calculators in performing the calculations, and much of its value lies in the complete system of checks that is a part of the method. Besides the correlations that are the object of the procedure, covariances, means, standard deviations, and the number of cases are also recorded on the completed form to be available for further statistical steps.     

How to build a connectionist idiot (savant)

This paper describes the development of a connectionist model of an idiot savant date calculator using a multi-layer back-propagation network. The model mimics the behaviour of idiot savant date calculators in learning to perform the date calculation task without the need either to develop arithmetical skills or to encode explicit knowledge about regularities in the structure of dates. However, the performance of the model highlights limitations on the use of back-propagation as a general-purpose learning algorithm in complex problem domains. Even with a relatively simple problem like date calculation back-propagation can only succeed when forced to take a highly structured and modular approach to learning.     

Compétences exceptionnelles en mathématiques

Some individuals have exceptional abilities in mathematics. They can either do fast calculations or understand problems, symbols and methods specifically used in mathematics, use them with other symbols and methods to solve other types of problems. Thus, great calculators and children gifted in mathematics are distinguished. This review of the literature presents studies about these abilities to expose the regular characteristics of these individuals, and the educational system that would be the more efficient for gifted children. Thus, this article would present the debates about the cognitive functioning and development of these individuals.     

An audio-tactile display

Several devices have been developed enabling the blind to adapt to digital and visual displays. Most require extensive training and are relatively expensive. The audio-tactile display described in this paper requires very little training and promises to be inexpensive. Prototypes of the display have been developed for a digital stopwatch, a digital clock, and several electronic calculators. Because the device makes use of electrical impulses to communicate with the blind, it also has numerous potential capabilities as a research tool. The device is based on a panel containing columns of braille digits that are made active through a logic circuit interfacing the braille display with a calculator or other device. The subject scans the braille columns and discovers the digits active in each column when a tone is produced simultaneously with the finger contacting the braille digit.     

Memory for everyday objects: where are the digits on numerical keypads?

Memory for the layout of the ten digits 0 to 9 on the keypads of push‐button telephones and calculators was investigated in five experiments. Experiments 1 and 2 revealed that, despite frequent usage of these devices, free recall of the numerical layouts is quite poor; and that the layout on calculators is even harder to recall than the telephone layout. Experiment 4 showed that the same is true for recognition of the layouts. Experiment 3 revealed that part of the recall advantage of the telephone layout can be attributed to its being more plausible and more similar to a schematic or prototypical layout of digits. Experiment 5 indicated that a single case of directing attention to the layouts can enhance recall significantly. The results are integrated into earlier research on memory for everyday objects, and concepts used in laboratory memory research such as interference, inference, and attention are used to explain memory for these everyday objects. Copyright © 1999 John Wiley & Sons, Ltd.     

Graphing calculators and students' conceptions of the derivative

This study compared the effect of using graphing calculators on college students' conceptual understanding of the derivative with the traditional teaching approach in Calculus I course. Students (49 men and 52 women) in four classes at a large public university participated. On a posttest, women who were taught calculus using the graphing calculator had significantly higher scores than those taught by the traditional method.     

The memory of two great mental calculators: Charcot and Binet's neglected 1893 experiments

French neurologist Jean Martin Charcot (1825-1893) and French psychologist Alfred Binet (1857-1911) are almost unknown as investigators who conducted original and fascinating studies in the area of memory. In a series of 1893 experiments, they compared the performance of two expert mental calculators, Jacques Inaudi and Périclès Diamandi, in tasks that consisted of recalling digits. Inspired by Ribot's psychological work (1881), they believed in the existence of not one type of memory but several partial, special, and local memories, each devoted to a particular domain. In all arithmetical prodigies, memory for digits is abnormally developed compared with other memories. Inaudi was considered to be an auditory memory-based mental calculator; when memorizing digits, he did not rely onthe appearance of the items or create visual imagery of any kind. Rather, he remembered digits principally by their sounds. Inaudi's methods of calculation and memorization were original and different from those used by Diamandi, who was a typical visual memory-based mental calculator. The experiments presented in the 1893 article were among the first scientific demonstrations of the importance to psychology of studying different types of memory. The present work gives a translation of this pioneering experimental article on expert calculators by Charcot and Binet, instructive for the comprehension of normal memory.     

Expediting arithmetic automaticity: Do inefficient computation methods induce spontaneous testing effects?

Before achieving arithmetic automaticity (direct answer recall), learners self-compute answers or use calculators/tables. Mechanisms supporting arithmetic automaticity are of interest because automaticity predicts math achievement and employment outcomes. Future recall is enhanced when, during study, learners attempt to recall the to-be-learned information (“testing effect”). However, learners may not attempt retrieval when another strategy is available (computation, re-reading). We expected learners to more frequently attempt recall when the alternative strategy was inefficient. Participants learned novel arithmetic problems, and could recall answers (if able) or use a computation method, which varied by condition: (i) self-computation; (ii) calculator-computation; and (iii) using a calculator with scrambled keys. Final recall ability was highest after the condition with the most inefficient non-retrieval method (scrambled calculator). We assumed recall attempts preceded computation, but also considered parallel execution. As evidence against parallel retrieval, answer recall rarely interrupted computation (mental/calculator) after it began. Thus, learners should make pre-emptive recall attempts.     

Aspects of programmable calculator stimulus control and data acquisition in a psychophysiology laboratory

Advantages and disadvantages of programmable calculator control of research laboratories are discussed. Comparisons are drawn with microcomputers such as the Imsai 8080. While microcomputers have greater flexibility in sampling multiple measures at multiple rates and combining timing tasks with data acquisition, calculators are easier to program for applications combining data acquisition with mathematical processing. Calculators also offer advantages to laboratories that do not have access to programming or maintenance services.     

The role of number words: the phonological length effect in multidigit addition

We explored the role of phonological representations of number words in exact calculation. The reaction times and accuracy of responses in multidigit addition problems were compared across three groups of participants (young healthy, older healthy, and 3 patients with severe aphasia) and two types of addition problems: phonologically long in English (containing the bisyllabic number word ??seven??) and short in English (monosyllabic number words??e.g., ??six??). Older healthy participants were significantly faster and more accurate in calculation than younger healthy participants. The older participants showed no evidence of a phonological length effect. However this effect was apparent in the younger adults, with longer reaction times on phonologically long problems. Furthermore, there was an association between the presence of a phonological length effect and the overall speed of response, suggesting that less proficient calculators were more reliant on phonological mediation of performance. The aphasic participants retained the ability to complete multidigit additions and were as accurate as the younger healthy group, although the response times of two of the 3 patients were slow. The aphasic participants varied with regard to the presence of a phonological length effect. Two participants showed no evidence of phonological mediation, while 1 displayed a phonological length effect. The results suggest that language resources are not mandatory for exact addition, although they may be used to scaffold math performance in less competent calculators. Evidence of phonological mediation of performance in aphasic participants may provide insight into the integrity or otherwise of inner speech in severe aphasia.     

Safety equipment use and crash involvement among cyclists – Behavioral adaptation,precaution or learning?

The present study has investigated relationships between cyclists’ safety equipment use, crash involvement, and other safety relevant behavior. The main focus is on relationships that indicate either behavioral adaptation (safety equipment use leads to riskier behavior) or precautionary behavior (safety equipment is used for cycling in risky situations). Three consecutive surveys were conducted in 2015, 2016, and 2017 years among 650 Norwegian cyclists. Most items were dichotomized and analyzed with logistic regression models. In contrast to the behavioral adaptation hypothesis, regular use of safety equipment (bicycle lights, high-visibility clothing, and helmets) was found to be negatively related to some types of high-risk behavior (listening to music and taking chances while cycling). Regular use of bicycle lights and high-visibility clothing is also negatively related to collision involvement. Safety equipment use was found to be positively related to regular winter cycling and cycling in mixed traffic (not on sidewalks), and it is most likely used as a precautionary measure in such situations. Some cyclists learn from crash involvement by starting to use safety equipment after a crash, but the results do not indicate that crash involvement deters from cycling. The main conclusion from the study is that recommending, promoting or even mandating safety equipment for cyclists can be expected to improve safety and that behavioral adaptation is not likely to occur, at least not to an extent that will outweigh the positive safety effects. The results do not support reservations against the use of “sporty” (well-equipped) models in campaigns for promoting cycling.     

Computing and comparing correlation and regression coefficients using a pocket calculator

Programs suitable for pocket calculators using reverse Polish notation are described. Program 1 computes regression coefficients, correlation coefficient, and standard error of estimate for paired data. Program 2 performs at test to compare the slopes of two regression lines. Program 3 computes F ratios to test the departure of a regression slope from zero and to test linearity of the regression. Programs 4 and 5 test the significance of (differences between independent and correlated correlation coefficients, respectively.     

Neural correlates of arithmetic calculation strategies

Recent research into math cognition has identified areas of the brain that are involved in number processing (Dehaene, Piazza, Pinel, & Cohen, 2003) and complex problem solving (Anderson, 2007). Much of this research assumes that participants use a single strategy; yet, behavioral research finds that people use a variety of strategies (LeFevre et al., 1996; Siegler, 1987; Siegler & Lemaire, 1997). In the present study, we examined cortical activation as a function of two different calculation strategies for mentally solving multidigit multiplication problems. The school strategy, equivalent to long multiplication, involves working from right to left. The expert strategy, used by “lightning” mental calculators (Staszewski, 1988), proceeds from left to right. The two strategies require essentially the same calculations, but have different working memory demands (the school strategy incurs greater demands). The school strategy produced significantly greater early activity in areas involved in attentional aspects of number processing (posterior superior parietal lobule, PSPL) and mental representation (posterior parietal cortex, PPC), but not in a numerical magnitude area (horizontal intraparietal sulcus, HIPS) or a semantic memory retrieval area (lateral inferior prefrontal cortex, LIPFC). An ACT-R model of the task successfully predicted BOLD responses in PPC and LIPFC, as well as in PSPL and HIPS.     

HIV‐Related Behaviors Among Prison Inmates: A Theory of Planned Behavior Analysis1

Prison inmates have high prevalence rates for both HIV and AIDS, creating a great need for HIV prevention efforts. We tested the theory of planned behavior (TPB) in 3 domains: intention to engage in condom use when released, intention to not share tattoo equipment in prison, and intention to not share needles or tattoo equipment when released. A total of 478 inmates (87% male) completed TPB and sexual and needle‐use risk behavior measures. TPB constructs accounted for a significant variance in intention to use condoms among African American, Hispanic, and Caucasian inmates, though the strength of the relationships differed by ethnicity. The TPB was less successful for intention to share tattooing equipment and not to share needles or tattoo equipment after release.     

Identification of Differential Item Functioning in Multiple-Group Settings: A Multivariate Outlier Detection Approach

We focus on the identification of differential item functioning (DIF) when more than two groups of examinees are considered. We propose to consider items as elements of a multivariate space, where DIF items are outlying elements. Following this approach, the situation of multiple groups is a quite natural case. A robust statistics technique is proposed to identify DIF items as outliers in the multivariate space. For low dimensionalities, up to 2–3 groups, a simple graphical tool is derived. We illustrate our approach with a reanalysis of data from Kim, Cohen, and Park (1995) on using calculators for a mathematics test.     

COMPUTERS

Abstract: I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind.     

The influence of parent-child relationship on young adolescents' use of safety equipment. The Norwegian Longitudinal Health Behavior Study

The purpose of this longitudinal study was to examine the extent to which the parent-child relationship, as perceived by young adolescents at age 13, may account for the use of various types of safety equipment at age 13 and 14 in terms of seat belts, bicycle helmets, motorcycle helmets when passenger, reflectors on the clothing when outside in the dark, and lifejackets when on board small boats. Parental influence was assessed in terms of three scales: Parental support, parental monitoring of the youngsters, and opposition towards the parents, with satisfactory internal consistencies (alphas >0.78). The results showed that each of the three constructs significantly accounted for an independent portion of the variance in the use of safety equipment measures. In sum they accounted for 20% of the variance in the use of safety equipment at age 13, and about 10% at age 14. The findings are discussed with regard to the implications for accident prevention measures aimed at young people.     

Collateral social development accompanying reinforcement of outdoor play in a preschool child

A 3-yr-old preschool girl with deficits in both motor and social repertoires was socially reinforced by teachers for use of outdoor play equipment, as a contribution to her motor skills and as a tactic to produce increased social contact with other children. Her use of outdoor play equipment, and various examples of her social interaction with both teachers and children were scored in the course of experimental development and analysis of her rate of equipment use. Equipment use increased greatly under the social reinforcement contingency; certain desirable examples of social interaction with other children showed a collateral development; other examples of adult-oriented development remained constant; and one class of undesirable baby-like behavior decreased markedly. Thus, the study provided a picture of what other behavior changes may take place in the course of behavior modification aimed at a single response class.