Abstract: One of the promises of ITSs and ILEs is that they will teach and assist learning in an intelligent manner. Historically this has tended to mean concentrating on the interface, on the representation of the domain and on the representation of the student’s knowledge. So systems have attempted to provide students with reifications both of what is to be learned and of the learning process, as well as optimally sequencing and adjusting activities, problems and feedback to best help them learn that domain. We now have embodied (and disembodied) teaching agents and computer-based peers, and the field demonstrates a much greater interest in metacognition and in collaborative activities and tools to support that collaboration. Nevertheless the issue of the teaching competence of ITSs and ILEs is still important, as well as the more specific question as to whether systems can and should mimic human teachers. Indeed increasing interest in embodied agents has thrown the spotlight back on how such agents should behave with respect to learners. In the mid 1980s Ohlsson and others offered critiques of ITSs and ILEs in terms of the limited range and adaptability of their teaching actions as compared to the wealth of tactics and strategies employed by human expert teachers. So are we in any better position in modelling

Over the past several years, a community of researchers has been using and refining a particular framework for research and curriculum development in undergraduate mathematics education. The purpose of this paper is to share the results of this work with the mathematics education community at large by describing the current version of the framework and giving some examples of its application. Our framework utilizes qualitative methods for research and is based on a very specific theoretical perspective that is being developed through attempts to understand the ideas of Piaget concerning reflective abstraction and reconstruct them in the context of college level mathematics. Our approach has three components. It begins with an initial theoretical analysis of what it means to understand a concept and how that understanding can be constructed by the learner. This leads to the design of an instructional treatment that focuses directly on trying to get students to make the constructions cal...

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Traditional approaches to developing user models, especially for computer-based learning environments, are notoriously difficult and time-consuming because they rely heavily on expert-elicited knowledge about the target application and domain. Furthermore, because the expert-elicited knowledge used in the user model is application and domain specific, the entire model development process must be repeated for each new application. In this thesis, we outline a data-based user modeling framework that uses both unsupervised and supervised machine learning in order to reduce the development costs of building user models, and facilitate transferability. We apply the framework to build user models of student interaction with two different learning environments (the CIspace Constraint Satisfaction Problem Applet for demonstrating an Artificial Intelligence algorithm, and the Adaptive Coach for Exploration for mathematical functions), and using two different data sources (logged interface and eye-tracking data). Although these two experiments are limited by the fact that we do not have large data sets, our results provide initial evidence that (i) the framework can automatically identify meaningful student interaction behaviors, and (ii) the user models built via the framework can recognize new student behaviors online. In addition, the similar results obtained from both of our experiments show framework transferability across applications and data types. iii

Workplace learning has developed as a field both of practice and of research over the past decade. The increase in interest is due in part to heightened awareness that workplace knowledge and skills contribute to enterprise and national competitiveness, but it is also due to an increased focus on the connections to be made between theory and practice as part of an education or training experience. At the same time, new learning technologies have enhanced delivery of instruction and learning materials in workplaces. This article reviews some of the conceptualizations of workplace learning and its cognitive bases. It also examines workplaces as learning environments and considers the special challenges involved in the flexible delivery of training to workplaces.

ion, everyday examples, construction of objects, and naming There is a curious statement on page 163. In advocating a "tool-based" approach Confrey and Costa acknowledge that it would share a central feature with the ideas they are criticizing, to wit, "asserting the importance of structure". But then they say, "However, (in a tool-based approach) rather than demanding departure from activity, the act of seeing similarities in structure across different contexts would be the basis for abstraction." Again, I have said enough about inaccuracies such as the assertion that the people Confrey and Costa are talking about advocate a "departure from activity". What I am concerned about here is the basis for abstraction that Confrey and Costa advocate. I think that focusing on structure is very different from seeing similarities across contexts. Indeed, I can find no other interpretation of the latter phrase than that there are some ideas which have an independent existence, and that they are ...

Almost a century ago the noted English author H.G. Wells said, "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." The teaching and learning of introductory statistics in the behavioral sciences continues to generate much debate on content and pedagogy amidst on-going reform. Facilitating change where appropriate also necessitates an understanding of instructors’ motivation for their approach. This pilot study explored approaches to teaching introductory statistics, and instructors ’ rationale for their approach. Emphasis on concept, calculation and both were reported by 30 (70%), 4 (9%) and 9 (21%) respectively. Teaching approaches were characterized as mechanistic, pragmatic and holistic. These findings can be used to design subgroup-specific interventions for current and prospective instructors of statistics.

Li, an 11 year old boy, participated in the implementation of a mixed-media design for the binomial that combines activities pertaining to theoretical probability (combinatorial analysis) and empirical probability (simulated experiments). This design was engineered to accommodate, corroborate, yet elaborate on students ’ heuristic inferences, and student reasoning was elicited through semi-structured clinical interviews. Applying a cultural–semiotic approach to the analysis of Li’s case study, I discuss a universal pedagogical tradeoff articulated as tension between constructivist and sociocultural perspectives on mathematics education. Li fluctuates between two interpretations of a sample space: event-based attention grounded in intuitive perceptual judgment of a random generator yet oblivious to permutations; and outcome-based attention supporting normative mathematization yet initially unsynthesized with intuition. These apparently vying perspectives are reconciled, if problematically, when Li notices that the entire sample space indexes an expected distribution qualitatively aligned with his perceptual intuition. At a theoretical level, I argue, constructivist and sociocultural perspectives, too, can be reconciled, if problematically, by accepting that mathematical phenomena are phenomenologically akin to scientific phenomena and thus mathematical learning is an inductive process of synthesizing (Schön, 1981) heuristic-based perceptual judgments and artifact-based mediated analytic procedures.

Abstract—This paper discusses the use of explorative data mining tools that allow the educator to explore new relationships between reported learning experiences and actual activities, even if there are multiple dimensions with a large number of measured items. The underlying technology is based on the so-called Compendium Platform for Reproducible Computing

This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one of several such perspectives, practices or areas of study. Use of the definite article ‘the ’ suggests to some the arrogation of definitiveness to the account given. 1 In other words, it is the dominant or otherwise unique account of philosophy of mathematics education. However, an alternative reading is that ‘the ’ refers to a definite area of enquiry, a specific domain, within which one account is offered. So the philosophy of mathematics education need not be a dominant interpretation so much as an area of study, an area of investigation, and hence something with this title can be an exploratory assay into this area. This is what I intend here. Moving beyond the first word, there is the more substantive question of the reference of the term ‘philosophy of mathematics education’. There is a narrow sense that can be applied in interpreting the words ‘philosophy ’ and ‘mathematics education’. The philosophy of some area or activity can be understood as its aims or rationale. Mathematics education understood