Cultural Influences in Probabilistic Thinking

Concerns about students' difficulties in statistics and probability and a lack of research in this area outside of western countries led to a case study which explored form five (14 to 16 year olds) students' ideas in this area. The study focussed on probability, descriptive statistics and graphical representations. This paper presents and discusses the ways in which students made sense of probability constructs (equally likely and proportional reasoning) obtained from the individual interviews. The findings were interpreted in relation to cultural perspective. The findings revealed that many of the students used strategies based on cultural experiences (beliefs, everyday and school experiences) and intuitive strategies. While the results of the study confirm a number of findings of other researchers, the findings go beyond those discussed in the literature. The use of beliefs, everyday and school experiences was considerably more common than that discussed in literature. The paper concludes by suggesting some implications for teachers and researchers

Influence of culture on secondary school students' understanding of statistics: A Fijian perspective

Although we use statistical notions daily in making decisions, research in statistics education has focused mostly on formal statistics. Further, everyday culture may influence informal ideas of statistics. Yet, there appears to be minimal literature that deals with the educational implications of the role of culture. This paper will discuss the interaction between statistical cognition and culture, reporting on the effects of culture on secondary students’ statistical ideas. It will draw on examples from my work and that of a few others who have studied cultural influences on statistical ideas to explain how statistics is tied to cultural practices. The paper will consider the issues arising out of the literature and offer suggestions for meeting the challenges

Semantic indeterminacy in object relative clauses

This article examined whether semantic indeterminacy plays a role in comprehension of complex structures such as object relative clauses. Study 1 used a gated sentence completion task to assess which alternative interpretations are dominant as the relative clause unfolds; Study 2 compared reading times in object relative clauses containing different animacy configurations to unambiguous passive controls; and Study 3 related completion data and reading data. The results showed that comprehension difficulty was modulated by animacy configuration and voice (active vs. passive). These differences were well correlated with the availability of alternative interpretations as the relative clause unfolds, as revealed by the completion data. In contrast to approaches arguing that comprehension difficulty stems from syntactic complexity, these results suggest that semantic indeterminacy is a major source of comprehension difficulty in object relative clauses. Results are consistent with constraint-based approaches to ambiguity resolution and bring new insights into previously identified sources of difficulty. (C) 2007 Elsevier Inc. All rights reserved

Zero Shot Learning for Code Education: Rubric Sampling with Deep Learning Inference

In modern computer science education, massive open online courses (MOOCs) log thousands of hours of data about how students solve coding challenges. Being so rich in data, these platforms have garnered the interest of the machine learning community, with many new algorithms attempting to autonomously provide feedback to help future students learn. But what about those first hundred thousand students? In most educational contexts (i.e. classrooms), assignments do not have enough historical data for supervised learning. In this paper, we introduce a human-in-the-loop "rubric sampling" approach to tackle the "zero shot" feedback challenge. We are able to provide autonomous feedback for the first students working on an introductory programming assignment with accuracy that substantially outperforms data-hungry algorithms and approaches human level fidelity. Rubric sampling requires minimal teacher effort, can associate feedback with specific parts of a student's solution and can articulate a student's misconceptions in the language of the instructor. Deep learning inference enables rubric sampling to further improve as more assignment specific student data is acquired. We demonstrate our results on a novel dataset from Code.org, the world's largest programming education platform.Comment: To appear at AAAI 2019; 9 page

Multiobjective Tactical Planning under Uncertainty for Air Traffic Flow and Capacity Management

We investigate a method to deal with congestion of sectors and delays in the tactical phase of air traffic flow and capacity management. It relies on temporal objectives given for every point of the flight plans and shared among the controllers in order to create a collaborative environment. This would enhance the transition from the network view of the flow management to the local view of air traffic control. Uncertainty is modeled at the trajectory level with temporal information on the boundary points of the crossed sectors and then, we infer the probabilistic occupancy count. Therefore, we can model the accuracy of the trajectory prediction in the optimization process in order to fix some safety margins. On the one hand, more accurate is our prediction; more efficient will be the proposed solutions, because of the tighter safety margins. On the other hand, when uncertainty is not negligible, the proposed solutions will be more robust to disruptions. Furthermore, a multiobjective algorithm is used to find the tradeoff between the delays and congestion, which are antagonist in airspace with high traffic density. The flow management position can choose manually, or automatically with a preference-based algorithm, the adequate solution. This method is tested against two instances, one with 10 flights and 5 sectors and one with 300 flights and 16 sectors.Comment: IEEE Congress on Evolutionary Computation (2013). arXiv admin note: substantial text overlap with arXiv:1309.391

Computational Methods for Probabilistic Inference of Sector Congestion in Air Traffic Management

This article addresses the issue of computing the expected cost functions from a probabilistic model of the air traffic flow and capacity management. The Clenshaw-Curtis quadrature is compared to Monte-Carlo algorithms defined specifically for this problem. By tailoring the algorithms to this model, we reduce the computational burden in order to simulate real instances. The study shows that the Monte-Carlo algorithm is more sensible to the amount of uncertainty in the system, but has the advantage to return a result with the associated accuracy on demand. The performances for both approaches are comparable for the computation of the expected cost of delay and the expected cost of congestion. Finally, this study shows some evidences that the simulation of the proposed probabilistic model is tractable for realistic instances.Comment: Interdisciplinary Science for Innovative Air Traffic Management (2013