Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students

Neuro-fuzzy knowledge processing in intelligent learning environments for improved student diagnosis

In this paper, a neural network implementation for a fuzzy logic-based model of the diagnostic process is proposed as a means to achieve accurate student diagnosis and updates of the student model in Intelligent Learning Environments. The neuro-fuzzy synergy allows the diagnostic model to some extent "imitate" teachers in diagnosing students' characteristics, and equips the intelligent learning environment with reasoning capabilities that can be further used to drive pedagogical decisions depending on the student learning style. The neuro-fuzzy implementation helps to encode both structured and non-structured teachers' knowledge: when teachers' reasoning is available and well defined, it can be encoded in the form of fuzzy rules; when teachers' reasoning is not well defined but is available through practical examples illustrating their experience, then the networks can be trained to represent this experience. The proposed approach has been tested in diagnosing aspects of student's learning style in a discovery-learning environment that aims to help students to construct the concepts of vectors in physics and mathematics. The diagnosis outcomes of the model have been compared against the recommendations of a group of five experienced teachers, and the results produced by two alternative soft computing methods. The results of our pilot study show that the neuro-fuzzy model successfully manages the inherent uncertainty of the diagnostic process; especially for marginal cases, i.e. where it is very difficult, even for human tutors, to diagnose and accurately evaluate students by directly synthesizing subjective and, some times, conflicting judgments

Factors revealed while posing mathematical modelling problems by mathematics student teachers

The purpose of this study is to reveal factors considered by mathematics student teachers while posing modelling problems. The participants were twenty-seven mathematics student teachers and posed their modelling problems within their groups. The data were obtained from the modelling problems posed by the participants, their solutions on these problems and the groups’ reflective diaries regarding their problem posing and solution processes. The data were analyzed by using content analysis and the codes were constructed according to the problems’ contents. The participants' diaries were examined in terms of generated codes and the expressions supporting/relating the codes were determined. While designing the problems, the participants considered the factors such as being interesting, understandable, appropriateness to real life and modelling process, model construction, and usability of different mathematical concepts. Their solutions were generally handled in terms of usage of the mathematical statements, appropriateness to the modelling process and being meaningful for real life. Modelling training should be provided to enable the student teachers to develop modelling problems and their designs should be examined and the feedbacks should be given. © 2018 Eurasian Society of Educational Research. All Rights Reserved

Modelling human teaching tactics and strategies for tutoring systems

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 teaching than we were in the 80s? Are these criticisms still as valid today as they were then? This paper reviews progress in understanding certain aspects of human expert teaching and in developing tutoring systems that implement those human teaching strategies and tactics. It concentrates particularly on how systems have dealt with student answers and how they have dealt with motivational issues, referring particularly to work carried out at Sussex: for example, on responding effectively to the student’s motivational state, on contingent and Vygotskian inspired teaching strategies and on the plausibility problem. This latter is concerned with whether tactics that are effectively applied by human teachers can be as effective when embodied in machine teachers

Using the Internet to improve university education: Problem-oriented web-based learning and the MUNICS environment

Up to this point, university education has largely remained unaffected by the developments of novel approaches to web-based learning. The paper presents a principled approach to the design of problem-oriented, web-based learning at the university level. The principles include providing authentic contexts with multimedia, supporting collaborative knowledge construction, making thinking visible with dynamic visualisation, quick access to content resources via Information and Communication Technologies (ICT), and flexible support by tele-tutoring. These principles are used in the Munich Net-based Learning In Computer Science (MUNICS) learning environment, which is designed to support students of computer science to apply their factual knowledge from the lectures to complex real-world problems. For example, students can model the knowledge management in an educational organisation with a graphical simulation tool. Some more general findings from a formative evaluation study with the MUNICS prototype are reported and discussed. E.g., the students' ignorance of the additional content resources is discussed in the light of the well-known finding of insufficient use of help systems in software applicationsBislang wurden neuere Ansätze zum web-basierten Lernen in nur geringem Maße zur Verbesserung des Universitätsstudiums genutzt. Es werden theoretisch begründete Prinzipien für die Gestaltung problemorientierter, web-basierter Lernumgebungen an der Universität formuliert. Zu diesen Prinzipien gehören die Nutzung von Multimedia-Technologien für die Realisierung authentischer Problemkontexte, die Unterstützung der gemeinsamen Wissenskonstruktion, die dynamische Visualisierung, der schnelle Zugang zu weiterführenden Wissensressourcen mit Hilfe von Informations- und Kommunikationstechnologien sowie die flexible Unterstützung durch Teletutoring. Diese Prinzipien wurden bei der Gestaltung der MUNICS Lernumgebung umgesetzt. MUNICS soll Studierende der Informatik bei der Wissensanwendung im Kontext komplexer praktischer Problemstellungen unterstützen. So können die Studierenden u.a. das Wissensmanagement in einer Bildungsorganisation mit Hilfe eines graphischen Simulationswerkzeugs modellieren. Es werden Ergebnisse einer formativen Evaluationsstudie berichtet und diskutiert. Beispielsweise wird die in der Studie festgestellte Ignoranz der Studierenden gegenüber den weiterführenden Wissensressourcen vor dem Hintergrund des häufig berichteten Befunds der unzureichenden Nutzung von Hilfesystemen beleuchte

Using the Internet to improve university education

Up to this point, university education has largely remained unaffected by the developments of novel approaches to web-based learning. The paper presents a principled approach to the design of problem-oriented, web-based learning at the university level. The principles include providing authentic contexts with multimedia, supporting collaborative knowledge construction, making thinking visible with dynamic visualisation, quick access to content resources via information and communication technologies, and flexible support by tele-tutoring. These principles are used in the MUNICS learning environment, which is designed to support students of computer science to apply their factual knowledge from the lectures to complex real-world problems. For example, students may model the knowledge management in an educational organisation with a graphical simulation tool. Some more general findings from a formative evaluation study with the MUNICS prototype are reported and discussed. For example, the students' ignorance of the additional content resources is discussed in the light of the well-known finding of insufficient use of help systems in software applications

The effect of multiple knowledge sources on learning and teaching

Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel