Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

Support of the collaborative inquiry learning process: influence of support on task and team regulation

Regulation of the learning process is an important condition for efficient and effective learning. In collaborative learning, students have to regulate their collaborative activities (team regulation) next to the regulation of their own learning process focused on the task at hand (task regulation). In this study, we investigate how support of collaborative inquiry learning can influence the use of regulative activities of students. Furthermore, we explore the possible relations between task regulation, team regulation and learning results. This study involves tenth-grade students who worked in pairs in a collaborative inquiry learning environment that was based on a computer simulation, Collisions, developed in the program SimQuest. Students of the same team worked on two different computers and communicated through chat. Chat logs of students from three different conditions are compared. Students in the first condition did not receive any support at all (Control condition). In the second condition, students received an instruction in effective communication, the RIDE rules (RIDE condition). In the third condition, students were, in addition to receiving the RIDE rules instruction, supported by the Collaborative Hypothesis Tool (CHT), which helped the students with formulating hypotheses together (CHT condition). The results show that students overall used more team regulation than task regulation. In the RIDE condition and the CHT condition, students regulated their team activities most often. Moreover, in the CHT condition the regulation of team activities was positively related to the learning results. We can conclude that different measures of support can enhance the use of team regulative activities, which in turn can lead to better learning results

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Collaborative development of the Arrowsmith two node search interface designed for laboratory investigators.

Arrowsmith is a unique computer-assisted strategy designed to assist investigators in detecting biologically-relevant connections between two disparate sets of articles in Medline. This paper describes how an inter-institutional consortium of neuroscientists used the UIC Arrowsmith web interface http://arrowsmith.psych.uic.edu in their daily work and guided the development, refinement and expansion of the system into a suite of tools intended for use by the wider scientific community

An agile business process and practice meta-model

Business Process Management (BPM) encompasses the discovery, modelling, monitoring, analysis and improvement of business processes. Limitations of traditional BPM approaches in addressing changes in business requirements have resulted in a number of agile BPM approaches that seek to accelerate the redesign of business process models. Meta-models are a key BPM feature that reduce the ambiguity of business process models. This paper describes a meta-model supporting the agile version of the Business Process and Practice Alignment Methodology (BPPAM) for business process improvement, which captures process information from actual work practices. The ability of the meta-model to achieve business process agility is discussed and compared with other agile meta-models, based on definitions of business process flexibility and agility found in the literature. (C) 2017 The Authors. Published by Elsevier B.V

Empirical modelling principles to support learning in a cultural context

Much research on pedagogy stresses the need for a broad perspective on learning. Such a perspective might take account (for instance) of the experience that informs knowledge and understanding [Tur91], the situation in which the learning activity takes place [Lav88], and the influence of multiple intelligences [Gar83]. Educational technology appears to hold great promise in this connection. Computer-related technologies such as new media, the internet, virtual reality and brain-mediated communication afford access to a range of learning resources that grows ever wider in its scope and supports ever more sophisticated interactions. Whether educational technology is fulfilling its potential in broadening the horizons for learning activity is more controversial. Though some see the successful development of radically new educational resources as merely a matter of time, investment and engineering, there are also many critics of the trends in computer-based learning who see little evidence of the greater degree of human engagement to which new technologies aspire [Tal95]. This paper reviews the potential application to educational technology of principles and tools for computer-based modelling that have been developed under the auspices of the Empirical Modelling (EM) project at Warwick [EMweb]. This theme was first addressed at length in a previous paper [Bey97], and is here revisited in the light of new practical developments in EM both in respect of tools and of model-building that has been targetted at education at various levels. Our central thesis is that the problems of educational technology stem from the limitations of current conceptual frameworks and tool support for the essential cognitive model building activity, and that tackling these problems requires a radical shift in philosophical perspective on the nature and role of empirical knowledge that has significant practical implications. The paper is in two main sections. The first discusses the limitations of the classical computer science perspective where educational technology to support situated learning is concerned, and relates the learning activities that are most closely associated with a cultural context to the empiricist perspective on learning introduced in [Bey97]. The second outlines the principles of EM and describes and illustrates features of its practical application that are particularly well-suited to learning in a cultural setting

Towards engineering ontologies for cognitive profiling of agents on the semantic web

Research shows that most agent-based collaborations suffer from lack of flexibility. This is due to the fact that most agent-based applications assume pre-defined knowledge of agents’ capabilities and/or neglect basic cognitive and interactional requirements in multi-agent collaboration. The highlight of this paper is that it brings cognitive models (inspired from cognitive sciences and HCI) proposing architectural and knowledge-based requirements for agents to structure ontological models for cognitive profiling in order to increase cognitive awareness between themselves, which in turn promotes flexibility, reusability and predictability of agent behavior; thus contributing towards minimizing cognitive overload incurred on humans. The semantic web is used as an action mediating space, where shared knowledge base in the form of ontological models provides affordances for improving cognitive awareness