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Featured researches published by Lenni Haapasalo.


Journal für Mathematik-Didaktik | 2000

Two Types of Mathematical Knowledge and Their Relation

Lenni Haapasalo; Djordje Kadijevich

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.


Journal of Computer Assisted Learning | 2001

Linking procedural and conceptual mathematical knowledge through CAL

Djordje Kadijevich; Lenni Haapasalo

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.


International Journal of Mathematical Education in Science and Technology | 2012

Real and virtual robotics in mathematics education at the school–university transition

Peter Samuels; Lenni Haapasalo

LOGO and turtle graphics were an influential movement in primary school mathematics education in the 1980s and 1990s. Since then, technology has moved forward, both in terms of its sophistication and pedagogical potential; and learner experiences, preferences and ways of thinking have changed dramatically. Based on the authors’ previous work and a literature review, this article revisits the subject of enhancing mathematics education through educational robotics kits and virtual robotic animations by proposing their simultaneous deployment at the school–university transition. The rationale for such an application is argued and an evaluation framework for these technologies is proposed. Two educational robotic kits and a virtual environment supporting robotic animations are evaluated both in terms of their feasibility of deployment and their educational effectiveness. Finally, the evaluation of learning experiences when deploying the proposed pedagogical approach is discussed.


Archive | 2015

Investigating Mathematical Beliefs by Using a Framework from the History of Mathematics

Lenni Haapasalo; Bernd Zimmermann

In the theoretical part of the article a framework of eight activities and motives is sketched (calculate, apply, construct, argue, order, find, play, evaluate), which proved to be successful along the history of mathematics. Furthermore, some arguments are presented and discussed why this framework is useful for studying mathematical beliefs. The empirical part is about two case studies using this network carried out in Joensuu (FIN) and Jena (GER). The goal of the first study was to compare mathematical beliefs of student mathematics teachers in Finland and Germany. The second part is about the influence of using a handheld calculator on the belief of a pupil. The first study reveals that neither in Finland nor in Germany the school mathematics seems to give much support for these activities, in Finland university mathematics even less. The only exception is calculating, for which the both institutions seem to give overdose. On the other hand, the finding of the second study that voluntary playing with progressive technology, even during a short period of time, might shift mathematical beliefs in a positive way.


Teaching Mathematics and Computer Science | 2017

Reappraising Learning Technologies from the Viewpoint of the Learning of Mathematics

Lenni Haapasalo; Peter Samuels

Within the context of secondary and tertiary mathematics education, most so-called learning technologies, such as virtual learning environments, bear little relation to the kinds of technologies contemporary learners use in their free time. Thus they appear alien to them and unlikely to stimulate them toward informal learning. By considering learning technologies from the perspective of the learner, through the analysis of case studies and a literature review, this article asserts that the expectation of these media might have been over-romanticised. This leads to the recommendation of five attributes for mathematical learning technologies to be more relevant to contemporary learners’ needs: promoting heuristic activities derived from human history; facilitating the shift from instrumentation to instrumentalisation; facilitating learners’ construction of conceptual knowledge that promotes procedural knowledge; providing appropriate scaffolding and assessment; and reappraising the curriculum.


Computers in Education | 2008

Factors that influence student teacher's interest to achieve educational technology standards

Djordje Kadijevich; Lenni Haapasalo


Archive | 2007

Adapting Mathematics Education to the Needs of ICT

Lenni Haapasalo


Teaching Mathematics and Its Applications | 2005

Using technology in applications and modelling

Djordje Kadijevich; Lenni Haapasalo; Jozef Hvorecky


Computers in Education | 2011

Responding to the challenges of instrumental orchestration through physical and virtual robotics

Lenni Haapasalo; Peter Samuels


The Professional Education and Development of Teachers of Mathematics - The 15th ICMI Study | 2009

Learning to Teach Mathematics: Expanding the Role of Practicum as an Integrated Part of a Teacher Education Programme

Christer Bergsten; Barbro Grevholm; Franco Favilli; Nadine Bednarz; Jérôme Proulx; D. Mewborn; P. Johnson; T. Rowland; A. Thwaites; P. Huckstep; Lucie DeBlois; Jean-François Maheux; O. Chapman; L. M. Rosu; B. Arvold; U. Gellert; G. Krummheuer; J. Skott; K. G. Garegae; P. A. Chakalisa; Djordje Kadijevich; Lenni Haapasalo; J. Hvorecky; A. Carneiro Abrahão; A. T. de Carvalho Correa de Oliveira; Jarmila Novotná; M. Hofmannová; D. Tirosh; P. Tsamir

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Djordje Kadijevich

Serbian Academy of Sciences and Arts

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Lasse Eronen

University of Eastern Finland

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