The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning

Previous research has shown that – due to the extensive attention spent to proportional reasoning in mathematics education – many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the ‘illusion of linearity’. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the over generalization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms oft he improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10^th and12^th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Writing reviews: perspectives from the editors of Educational Studies in Mathematics

Educational Studies in Mathematics -     

Leading the process of reculturing: Roles and actions of school leaders

In this article, we focus on the role and actions of individual school leaders in initiating and governing the process of reculturing. First, we elaborate on the core elements of the process of reculturing, referring to a complex learning process of finding a new balance between cognitions and emotions both individually and collectively. We then review the literature for issues related to school leaders’ roles and actions during reculturing. We argue that the role of leadership power largely has been left out of the picture so far while at the same time leadership power is so crucial for teachers’ roles and actions in educational innovation processes. To illustrate our line of thinking, we analyse the stories of three school leaders about their roles and actions during successful processes of reculturing and retrospectively analyse the role of leadership power during these processes, building on a framework of Hetebrij (2006) for judging the quality of power use.     

Overeducation and the returns to enterprise-related schooling

This paper examines the relation between overeducation and enterprise-related schooling. If overeducation and enterprise-related schooling are substitutes the social costs of Overeducation are less. We find that correctly allocated workers have the highest probability of participation in enterprise-related schooling, while undereducated workers have the lowest probability of participation. There is no evidence of overeducation and enterprise-related schooling being either substitutes or complements. If we do not correct for self-selection, the average return on a year of education for correctly allocated workers is higher than the average rate of return to education for under- and overeducated workers. If we correct for self-selection in the participation in enterprise-related schooling the rate of return to education increases. The rates of return to under- and overeducation increase as well. If we correct for self-selection the rate of return to a year of undereducation becomes higher than the rate of return to a year of actual education. For undereducated workers the wage gain of participation in enterprise-related schooling is higher than for a correctly allocated worker. A year of Overeducation decreases the wage gain of participation in enterprise-related schooling for participants.     

Learning relations of knowledge transfer (KT) and knowledge integration (KI) of doctoral students during online interdisciplinary training: an exploratory study

ABSTRACT

Interdisciplinary training for doctoral students is an emerging scenario in higher education. The learning relations of knowledge transfer (KT: transferring knowledge from one person to another) and knowledge integration (KI: integrating or synthesizing perspectives from different disciplines) built by doctoral students play an important role in the process of interdisciplinary training. This study explores how doctoral students from a wide range of disciplines build learning relations of KT and KI during online interdisciplinary training. A mixed-methods approach was applied. First, longitudinal social network analysis (SNA) was employed to investigate the patterns of KT and KI relations over a seven-month training period. Subsequently, interviews were conducted to triangulate the SNA findings. SNA results show that the establishment of KI relations is significantly less than that of KT. Qualitative results show three themes explaining the challenges of KI relations, including challenges of online settings, the design of the training modules, and student involvement. Practical implications are drawn for the improvement of online interdisciplinary training, such as suggestions to promote KI and strategies for group learning.     

Lexical decision and oral reading by poor and normal readers

The primary goal of this study was to compare a paper-and-pencil version of the lexical decision task, which can be administered groupwise, with reading aloud a differently ordered list of the same words and pseudowords. Participants were first and second graders (“normal readers”) and students from schools for children with learning difficulties. On the average, the latter “poor readers” scored at the same oral reading level as the normal readers, but were older. The correlation between both tasks appeared to be high and both tasks had comparable correlations with third variables, suggesting that performance is determined by the same processes. Because the lexical decision task showed little evidence for guessing, it may be an — even better — alternative for oral reading. No differences between participant groups were found that point to different reading strategies. Error analysis, however, indicates that the poor readers probably have a specific problem in the oral reading of pseudowords.     

Interactive Instruction to Prevent Attention Problems in Class

This article reports the development and implementation of a strategy designed to bring persistent attention problems in class (off-task behaviour) under the control of teachers and students. The strategy enables the teacher to recognise the demotivating meaning that a task situation can have for a student. By pinpointing this situation in short dialogues with the student, the teacher encourages the student to make his or her own task proposal with the intention of turning the task into a feasible challenge. The strategy was designed from a cognitive-motivational interpretation of attention problems, and it is given shape in four programs for elementary schools. The theoretical frame of reference, the characteristics of the strategy, and the implementation of the programs are set out. Furthermore, an evaluation study is reported. The results indicate that teachers using the strategy can deal more effectively with students who have task behaviour problems. The students' on-task behaviour in this study increased in units of time from 60–70%. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structured reflection breaks embedded in an online course – effects on learning experience,time on task and performance

The purpose of this article is to gain an insight into the effects of practicing short, frequent, and structured reflection breaks interspersed with the learning material in a computer-based course. To that end, the study sets up a standardized control trial with two groups of secondary school pupils. The study shows that while performance is not affected by these embedded “reflection rituals,” they significantly impact time on task and perceived learning. The study also suggests that the exposure to such built-in opportunities for reflection modifies the engagement with the content and fosters the claimed readiness for application of a similar reflective approach to learning in other occasions.     

Diverse-and-Dynamic Pathways in Educational and Interpersonal Identity Formation during Adolescence: Longitudinal Links With Psychosocial Functioning

This study aimed to examine the relations between educational and interpersonal identity trajectories and psychosocial functioning based on a three-factor identity process model. A total of 968 Japanese adolescents including 13- and 16-years-olds (49.7% female) participated in a four-wave longitudinal study. Latent class growth analysis extracted five identity trajectories in each educational and interpersonal identity domain and revealed (a) high prevalence of low commitment identity trajectories, (b) absence of the closure trajectory, and (c) changeable identity trajectories that have not been identified in Western context (i.e., the Netherlands). Furthermore, a latent change model revealed dynamic relations between identity trajectories and psychosocial functioning. These findings provide critical insights into the diverse and dynamic pathways of identity formation during adolescence in Japan.     

Travelogue of an Almohad Sherd: from Twelfth-Century al-Andalus to Fourteenth-Century Flanders*

Excavations in Sint-Lievens-Houtem (Flanders, Belgium), an important medieval pilgrimage village, uncovered a fourteenth-century refuse pit. This feature contained a fragment of a rare Andalusī moulded lustreware vessel, dating to the mid or second half of the twelfth century. The reconstruction of the vessel’s itinerary aids in understanding how an object travelled from Muslim Spain to Catholic Flanders and why it ended up under Sint-Lievens-Houtem’s marketplace, about two centuries after its production. Traditional explanations of Crusades or trade seem unlikely or do not account for the entire trajectory of the vessel. These narratives are therefore extended with the incorporation of the vessel in Sint-Lievens-Houtem’s church treasury. This biographical approach offers a valuable framework to interpret the increasing number of Islamic finds across Europe, the way by which they travelled north and the contexts in which they functioned.