Djordje Kadijevich

Two Types of Mathematical Knowledge and Their Relation

The distinction between procedural knowledge and conceptual knowledge seems to be possible at a terminological level. However, real problems begin when this distinction is to be operationalized by acceptable tasks, and the relation between the two knowledge types is to be clarified. This article tries to resolve some of these problems by using a constructivist approach.ZusammenfassungDie Unterscheidung des prozeduralen und begrifflichen Wissens scheint auf terminologischer Ebene evident zu sein. Die wirklichen Schwierigkeiten beginnen dann, wenn explizite Beziehungen zwischen diesen zwei Kenntnisstypen oder angepasste Aufgaben gesucht sind. Dieser Artikel stellt einen Versuch dar, einige von diesen Problemen im Sinne des Konstruktivismus zu analysieren und zu lösen.

Linking procedural and conceptual mathematical knowledge through CAL

Despite its high educational relevance, relatively few CAL studies have examined whether their computer-based treatments search for and/or utilise any potential link between procedural and conceptual mathematical knowledge. This paper summarises some of the findings of studies of this kind, explains how these knowledge types may be linked and proposes two constructivist CAL environments which enable a desired link.

TPCK framework: assessing teachers' knowledge and designing courses for their professional development

Introduction Although the use of technology can empower teaching and learning, it is rarely used in classrooms (Ruthven, 2009). A major reason for that unfavorable state may be found in the fact that teachers lack sophisticated knowledge to support effective technology integration. This knowledge is indeed sophisticated as it, among other issues, calls for complex interplay involving three types of knowledge: content knowledge to teach, pedagogical knowledge to apply, and technology knowledge to empower the previous two. Because of this interplay, successful technology integration clearly requires teachers to develop a new body of knowledge, known under the name technological pedagogical content knowledge or just TPCK (Angeli & Valanides, 2009).

Technological Environments beyond the Classroom

This chapter discusses several options that technology can bring tomathematics teaching and learning, in providing access to many challenging virtual resources that become easily available to all learners. Recent studies point to new challenging learning opportunities that may be enhanced by technology by means of dynamic and interactive tools of modeling and experimenting. Finally, recent developments of flexible and sophisticated communication tools create numerous virtual spaces where people can meet, ask questions, discuss, and work collaboratively on challengingmathematical learning tasks.We present a broad view of existing worldwide practices and analyze concrete examples that deepen our understanding of the advantages and disadvantages related to integrating technology into challenging mathematical activities in and beyond the classroom. We conclude with several research paths that are opening in this relatively new field of study in mathematics education.

Towards a Wider Implementation of Mathematical Modelling at Upper Secondary and Tertiary Levels

Despite its unquestionable educational value, mathematical modelling has had so far mostly a marginal role in everyday mathematics education. To overcome such an inappropriate state, we should help mathematics educators realize the full power of computer-based mathematical modelling, develop suitable standards of such a modelling, and ensure their proper utilization.

Using ICT and Quality of Life: Comparing Persons with and Without Disabilities

Calls to promote greater participations of persons with disabilities in society usually deal with the use of various IC-based technologies. Many of initiatives also deal with the quality of life (QoL) of those persons and discuss possible impacts of ICT use on that quality. By comparing persons with and without disabilities, this study examined the extent to which (1) individuals used IC-based technologies, (2) their QoL was improved due to the use of those technologies, and (3) this use (USE) was related to that QoL improvement (IQoL). It was found that both USE and IQoL were lower for persons with disabilities, and that correlation between USE and IQoL was stronger for those persons. The study examines the role of education and its potential to improve the QoL for persons with disabilities as a result of better use of ICTs.

Neglected critical issues of effective CAS utilization

Abstract This paper examines two neglected critical issues of the effective utilization of Computer Algebra System (CAS). By using a number of examples from an upper secondary mathematics education, these issues deal with the instrumentalization of CAS, and support to students when solving tasks by CAS (i.e. CAS-based task design). Regarding this instrumentalization, the paper considers the extent to which it can be done with CAS tools at present, and discusses several critical issues in doing so with respect to tool, task and designer (learner). Concerning this support, the paper calls for a detailed task design that also includes the issues of acceptable solutions and scaffolding offered, which should be, in some detail, clarified and given in examination materials. Several challenges relating to the two critical issues are considered.

An approach to learning mathematics through knowledge engineering

This study deals with an AI approach to learning mathematics, which is realised through the development of expert system knowledge bases by using programming in logic and PROLOG. The paper presents this approach, and examines its theoretical values in the light of recent findings in computer science, mathematics education, didactics, psychology and philosophy. The examined values show evidence for the relevance of the approach to the computer-assisted learning of mathematics.

Challenges for IT-Enabled Formative Assessment of Complex 21st Century Skills

In this article, we identify and examine opportunities for formative assessment provided by information technologies (IT) and the challenges which these opportunities present. We address some of these challenges by examining key aspects of assessment processes that can be facilitated by IT: datafication of learning; feedback and scaffolding; peer assessment and peer feedback. We then consider how these processes may be applied in relation to the assessment of horizontal, general complex 21st century skills (21st CS), which are still proving challenging to incorporate into curricula as well as to assess. 21st CS such as creativity, complex problem solving, communication, collaboration and self-regulated learning contain complex constructs incorporating motivational and affective components. Our analysis has enabled us to make recommendations for policy, practice and further research. While there is currently much interest in and some progress towards the development of learning/assessment analytics for assessing 21st CS, the complexity of assessing such skills, together with the need to include affective aspects means that using IT-enabled techniques will need to be combined with more traditional methods of teacher assessment as well as peer assessment for some time to come. Therefore learners, teachers and school leaders must learn how to manage the greater variety of sorts and sources of feedback including resolving tensions of inconsistent feedback from different sources.

Inappropriate Use of Spreadsheets in the Finance Industry

Spreadsheets are major tools in the finance industry. In order to find out how these tools are used, we examined recently published research papers and interviewed seven experienced bankers. This examination showed that spreadsheets may be used insufficiently, uncritically, and erroneously. By focusing on the quality of data and models (to be) exploited, this paper presents main details of this business-risky use of spreadsheets. Implications for vocational education are included.