Reasoning With Conditionals About Everyday and Mathematical Concepts in Primary School

A research link between conditional reasoning and mathematics has been reported only for late adolescents and adults, despite claims about the pivotal importance of conditional reasoning, i.e., reasoning with if-then statements, in mathematics. Secondary students' problems with deductive reasoning in mathematics have been documented for a long time. However, evidence from developmental psychology shows that even elementary students possess some early conditional reasoning skills in familiar contexts. It is still an open question to what extent conditional reasoning with mathematical concepts differs from conditional reasoning in familiar everyday contexts. Based on Mental Model Theory (MMT) of conditional reasoning, we assume that (mathematical) content knowledge will influence the generation of models, when conditionals concern mathematical concepts. In a cross-sectional study, 102 students in Cyprus from grades 2, 4, and 6 solved four conditional reasoning tasks on each type of content (everyday and mathematical). All four logical forms, modus ponens (MP), modus tollens (MT), denial of the antecedent (DA), and affirmation of the consequent (AC), were included in each task. Consistent with previous findings, even second graders were able to make correct inferences on some logical forms. Controlling for Working Memory (WM), there were significant effects of grade and logical form, with stronger growth on MP and AC than on MT and DA. The main effect of context was not significant, but context interacted significantly with logical form and grade level. The pattern of results was not consistent with the predictions of MMT. Based on analyses of students' chosen responses, we propose an alternative mechanism explaining the specific pattern of results. The study indicates that deductive reasoning skills arise from a combination of knowledge of domain-general principles and domain-specific knowledge. It extends results concerning the gradual development of primary students' conditional reasoning with everyday concepts to reasoning with mathematical concepts adding to our understanding of the link between mathematics and conditional reasoning in primary school. The results inspire the development of educational interventions, while further implications and limitations of the study are discussed

Belief Revision, Self-Construction and Systemic Certainty

L’influence des processus engagés dans l’élaboration personnelle d’une relation conditionnelle (si P alors Q) sur la révision des croyances est examinée ici au moyen d’un système d’auto présentation segmentée implémenté sur ordinateur. A certains sujets, il était dit que la relation si P alors Q était toujours vraie ; aux autres, il leur était proposé d’explorer le système afin qu’ils établissent par eux-mêmes cette même relation, avec un degré de certitude très élevé. Les résultats montrent que les sujets révisent plus leur croyance en la relation conditionnelle lorsque cette croyance leur est imposée que lorsqu’ils ont à l’élaborer. Et malgré le fait que l’on observe un degré très élevé de certitude de la croyance issue de cette élaboration, la révision de cette croyance paraît très nettement dépendre (1) du nombre de fois qu’a été explorée la relation conditionnelle, et (2) du nombre de fois qu’a été exploré l’unique élément qui variait dans le système. Ces résultats suggèrent que la certitude est une construction à plusieurs niveaux qui implique une évaluation des paramètres du système dans lequel une croyance est issue.The extent to which belief revision is affected by a process of self-construction of a conditional (if P then Q) relation was examined using a computer generated system. Some participants were told that it was always true that if P then Q, while others were allowed to explore the system in order to self-construct this same relation to a high degree of certainty. Results show that the tendency to modify a conditional belief was smaller when this belief was self-constructed than when it was simply communicated. Interestingly, despite very high levels of subjective certainty that accompanied self-construction, belief revision was strongly affected by (1) the quantity of direct experience with the conditional relation, and (2) the quantity of direct experience with the single variable element in the system. This suggests that certainty is a multi-leveled construct that included an evaluation of the parameters of the system into which a belief is embedded

Belief Revision, Self-Construction and Systemic Certainty

L’influence des processus engagés dans l’élaboration personnelle d’une relation conditionnelle (si P alors Q) sur la révision des croyances est examinée ici au moyen d’un système d’auto présentation segmentée implémenté sur ordinateur. A certains sujets, il était dit que la relation si P alors Q était toujours vraie ; aux autres, il leur était proposé d’explorer le système afin qu’ils établissent par eux-mêmes cette même relation, avec un degré de certitude très élevé. Les résultats montrent que les sujets révisent plus leur croyance en la relation conditionnelle lorsque cette croyance leur est imposée que lorsqu’ils ont à l’élaborer. Et malgré le fait que l’on observe un degré très élevé de certitude de la croyance issue de cette élaboration, la révision de cette croyance paraît très nettement dépendre (1) du nombre de fois qu’a été explorée la relation conditionnelle, et (2) du nombre de fois qu’a été exploré l’unique élément qui variait dans le système. Ces résultats suggèrent que la certitude est une construction à plusieurs niveaux qui implique une évaluation des paramètres du système dans lequel une croyance est issue.The extent to which belief revision is affected by a process of self-construction of a conditional (if P then Q) relation was examined using a computer generated system. Some participants were told that it was always true that if P then Q, while others were allowed to explore the system in order to self-construct this same relation to a high degree of certainty. Results show that the tendency to modify a conditional belief was smaller when this belief was self-constructed than when it was simply communicated. Interestingly, despite very high levels of subjective certainty that accompanied self-construction, belief revision was strongly affected by (1) the quantity of direct experience with the conditional relation, and (2) the quantity of direct experience with the single variable element in the system. This suggests that certainty is a multi-leveled construct that included an evaluation of the parameters of the system into which a belief is embedded

Social Exclusion: More Important to Human Females Than Males

Theoretical models based on primate evidence suggest that social structure determines the costs and benefits of particular aggressive strategies. In humans, males more than females interact in groups of unrelated same-sex peers, and larger group size predicts success in inter-group contests. In marked contrast, human females form isolated one-on-one relationships with fewer instrumental benefits, so social exclusion constitutes a more useful strategy. If this model is accurate, then human social exclusion should be utilized by females more than males and females should be more sensitive to its occurrence. Here we present four studies supporting this model. In Study 1, using a computerized game with fictitious opponents, we demonstrate that females are more willing than males to socially exclude a temporary ally. In Study 2, females report more actual incidents of social exclusion than males do. In Study 3, females perceive cues revealing social exclusion more rapidly than males do. Finally, in Study 4, females’ heart rate increases more than males’ in response to social exclusion. Together, results indicate that social exclusion is a strategy well-tailored to human females’ social structure.Human Evolutionary Biolog

“A very orderly retreat”: Democratic transition in East Germany, 1989-90

East Germany's 1989-90 democratisation is among the best known of East European transitions, but does not lend itself to comparative analysis, due to the singular way in which political reform and democratic consolidation were subsumed by Germany's unification process. Yet aspects of East Germany's democratisation have proved amenable to comparative approaches. This article reviews the comparative literature that refers to East Germany, and finds a schism between those who designate East Germany's transition “regime collapse” and others who contend that it exemplifies “transition through extrication”. It inquires into the merits of each position and finds in favour of the latter. Drawing on primary and secondary literature, as well as archival and interview sources, it portrays a communist elite that was, to a large extent, prepared to adapt to changing circumstances and capable of learning from “reference states” such as Poland. Although East Germany was the Soviet state in which the positions of existing elites were most threatened by democratic transition, here too a surprising number succeeded in maintaining their position while filing across the bridge to market society. A concluding section outlines the alchemy through which their bureaucratic power was transmuted into property and influence in the “new Germany”