Los significados de la aleatoriedad de los profesores de matemática y de biología en formación

En este trabajo se analizan los significados de la aleatoriedad de 583 profesores de matemática y 325 profesores de biología en formación, de la provincia de Mendoza, Argentina. Se aplicó un cuestionario con doce ítems relativos a sucesos de los contextos de juego, cotidiano y físico natural. En cada uno de ellos el estudiante debe reconocer si el suceso es aleatorio o no, y luego argumentar su decisión en base al sistema de categorías propuesto por Cardeñoso (2001). Los resultados evidencian algunas diferencias significativas, los estudiantes de Biología logran un mayor reconocimiento de la aleatoriedad y sus argumentaciones desde la incertidumbre y la causalidad son significativamente mayores; mientras que los argumentos de la multiplicidad son significativamente mayores entre los estudiantes de matemática

Classical, quantum and biological randomness as relative unpredictability

International audienceWe propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness — its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity. Abstract We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness—its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity

Comprensión de la aleatoriedad por futuros profesores de educación primaria

Las nuevas directrices curriculares para la probabilidad en la educación primaria requieren una formación específica de los futuros profesores, que ha de estar basada en la evaluación previa de sus necesidades formativas. Con objeto de contribuir a dicha formación, en este trabajo se analizan las respuestas abiertas a un problema utilizado en las investigaciones sobre percepción subjetiva de la aleatoriedad. Los resultados muestran una mezcla de concepciones correctas e incorrectas, algunas de las cuáles son paralelas a las que el concepto de aleatoriedad ha recibido a lo largo de su historia. El formador de profesores podría partir de estas concepciones y hacerlas progresar para que los futuros profesores adquieran un significado completo del concepto, que les capacite para su futura labor docente

Cryptographic Analysis of Random Sequences

Cryptographically strong random sequences are essential in cryptography, digital signatures, challenge-response systems, and in Monte Carlo simulation. This thesis examines techniques for cryptographic hardening of random sequences that are not cryptographically strong. Specific random sequences that are considered include d-sequences, that is sequences that are reciprocals of primes, and a new sequence obtained by the use of a specific two-dimensional mesh array. It is shown that the use of many-to-one mapping on blocks of the raw sequence improves the quality of autocorrelation function. Various types of many-to-one mappings are used and their effect on the autocorrelation function is compared. Sequences are also compared using another measure of randomness.Computer Science Departmen

Understanding of Randomness by Prospective Primary School Teachers

Current curricular guidelines for probability at Primary school level imply the need for a specific training of prospective teachers, which should be based on the previous assessment of their training needs. In order to contribute to this need, in this paper we present the analysis of responses by 157 Spanish prospective teachers to an open question, taken from previous research on subjective perception of randomness. The results show a mixture of correct and wrong conceptions, some of which parallel some historical conceptions of randomness. Teachers’ educators could start from these intuitions to help prospective teachers advance to a broader meaning of the concept, adequate for their future teaching responsibility

Spencer-Brown vs. Probability and Statistics: Entropy’s Testimony on Subjective and Objective Randomness.

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism

Employee Turnover Intention in the U.S. Fast Food Industry

Employee turnover in the U.S. fast food industry has been high, averaging rate 150% per annum. The purpose of the correlational design study was to examine the relationships between job satisfaction factors, job dissatisfaction factors, and employee turnover intentions among fast food employees to determine whether a statistically significant relationship exists between these variables. The population for the study consisted of 144 fast food restaurant employees working in the East Coast in the United States. The theoretical framework was Herzberg\u27s 2-factor motivation-hygiene needs theory, which describes job satisfaction factors and job dissatisfaction factors. Internet survey data of 144 participants were analyzed using Pearson-product correlation coefficients and multiple linear regressions analysis. The study findings revealed statistically significant relationships between job satisfaction factors and employee turnover intentions (p \u3c .01), and job dissatisfaction factors and employee turnover intentions (p \u3c .01). Among the job satisfaction factors, responsibility had a stronger relationship with employee turnover intentions (-.52) compared with other factors. Under job dissatisfaction factors, company policy had a stronger relationship with employee turnover intentions (-.52) compared with other factors. In addition, criterion variance of employee turnover intentions associated with combined job satisfaction factors was stronger (35%) than were the combined job dissatisfaction factors (31%). The study findings are designed to inform fast food restaurant managers in taking actions to reduce employee turnover, resulting in improved business financial sustainability and long-term growth

Learners' shifting perceptions of randomness.

This is a phenomenographic study of learners’ perceptions of randomness. Underpinning the study is a sense of randomness as a dynamic process, in which events emerge unpredictably from a generating process, into the determined past, through the curtain separating past from future. Previous research into perceptions of randomness has often used tasks in which people are asked to recognise randomness in a given sequence of outcomes. Other research has asked people to make up sequences of random outcomes. Such tasks do not carry the sense of randomness as dynamic. Interview tasks in this study were designed to present the dynamic sense of randomness using outcomes from random generators such as dice, coins and sampling bags in situ. Interviewees were invited to talk about their experiences of making sense of the emerging sequence of outcomes. The analysis of the interview transcripts addressed two related questions: • What do learners believe about randomness? • To what situations and circumstances do learners consider randomness to be an appropriate model? The first question encompasses learners’ expectations of a random generator and the methods, strategies and heuristics by which learners discern what is random from what is not. Drawing on local and global meanings of randomness identified by Pratt (1998), the thesis argues that learners’ perspectives on randomness shift rapidly and frequently between the local and global as the learners seek to interpret the observed outcomes. Learners’ interpretations of and beliefs about randomness are found to have significant impact upon the kinds of situations to which learners are able and willing to apply the model of randomness