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Education Sciences
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Visualisation in Mathematics Education
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Visualisation in Mathematics Education

A special issue of Education Sciences (ISSN 2227-7102). This special issue belongs to the section "Curriculum and Instruction".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 4484

Special Issue Editors

Prof. Dr. Andreas Eichler

E-Mail Website
Guest Editor
Institute for Mathematics, University of Kassel, 34127 Kassel, Germany
Interests: statistics education; teaching mathematics with technology; transition from school to university; teachers beliefs
Prof. Dr. Lars Holzäpfel

E-Mail Website
Guest Editor
Department of Mathematics, University of Education, 79117 Freiburg, Germany
Interests: mathematics education; educational psychology; teacher training

Special Issue Information

Dear Colleagues, 

Visualisation of mathematical concepts or mathematical objects is an “integral part of the doing of mathematics” (Presmeg, 2002, ix) and thus an important part of teaching and learning mathematics. Moreover, Duval suggests that visualisation of mathematical concepts is “at the core of understanding in mathematics” (Duval, 2002, p. 312). In mathematics education research, it is widely accepted that representations and visualisations could have a considerable impact on students’ learning (Arcavi, 2003). Accordingly, visualisation has been a crucial topic in mathematics education research. For example, visualisation was the subject of a four-year discussion group at PME that resulted in an overview of this topic in 2002 (Hitt, 2002). Further, a Topic Study Group at the International Conference on Mathematics Education in 2016 focussed on visualisation as a specific form of representation of mathematical objects. Different special issues of journals in mathematics education emphasised visualisation (e.g., ZDM, 46, 1, 2014). Visualisation is also a crucial topic in general educational research as the two Special Interest Groups of the EARLI (Comprehension of text and graphics and Instructional design) imply.

This Special Issue addresses the topic of visualisation in mathematics education. A specific focus is on empirical research about facilitating effects of visualisation for improving mathematical understanding.

If you are interested in, please submit a 250-word abstract by 31 May 2022 to guest editor and assistant editor ().

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215–241.

Duval, R. (2002). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt (Ed.), Representations and mathematics visualization: Papers presented in this Working Group of PME-NA, 1998-2002 (pp. 311–336). Mexico: Cinestav - IPN.

Hitt, F. (Ed.) (2002). Representations and mathematics visualization: Papers presented in this Working Group of PME-NA, 1998-2002. Mexico: Cinestav - IPN.

Presmeg, N.C. (2002). Preface. In F. Hitt (Ed.), Representations and mathematics visualization. North American Chapter of the International Group for the Psychology of Mathematics Education, (pp. ix–xvi).

Prof. Dr. Andreas Eichler
Prof. Dr. Lars Holzäpfel
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a double-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Education Sciences is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematics education
  • visualisation
  • empirical studies
  • learning mathematics
  • representation

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Published Papers (2 papers)

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Research

17 pages, 5492 KiB  
Article
Using the Van Hiele Theory to Explain Pre-Service Teachers’ Understanding of Similarity in Euclidean Geometry
by Mduduzi Mbatha and Sarah Bansilal
Educ. Sci. 2023, 13(9), 861; https://doi.org/10.3390/educsci13090861 - 23 Aug 2023
Viewed by 1278
Abstract
Helping learners to develop a solid grasp of geometric concepts poses a challenge for teachers. Therefore, it is important that teachers have a sound understanding of the geometry they teach. The aim of this qualitative study was to explore pre-service teachers’ (PST’s) understanding [...] Read more.
Helping learners to develop a solid grasp of geometric concepts poses a challenge for teachers. Therefore, it is important that teachers have a sound understanding of the geometry they teach. The aim of this qualitative study was to explore pre-service teachers’ (PST’s) understanding of the concept of similarity in Euclidean geometry and to use van Hiele’s theory to explain misconceptions evidenced by the PSTs. Data in this study were collected from 34 first-year PSTs studying for a Bachelor of Education degree in high school mathematics. The authors analysed the written responses to a 13-item worksheet and also conducted interviews with seven of the participants. The analysis of the data was guided by van Hiele’s theory which was used to identify misconceptions amongst PST’s who had not yet developed the appropriate reasoning skills linked to particular van Hiele levels of geometric thought. It was found that these students used reasoning that is characteristic of the elementary levels to make judgments. Many PST’s faced challenges with similarity notation and the process of proving the similarity between two figures. This study recommends that PST’s should be given more opportunities to connect visual and analytic representations of similarity. Full article
(This article belongs to the Special Issue Visualisation in Mathematics Education)
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29 pages, 14656 KiB  
Article
Designing Visualisations for Bayesian Problems According to Multimedia Principles
by Theresa Büchter, Nicole Steib, Katharina Böcherer-Linder, Andreas Eichler, Stefan Krauss, Karin Binder and Markus Vogel
Educ. Sci. 2022, 12(11), 739; https://doi.org/10.3390/educsci12110739 - 25 Oct 2022
Cited by 4 | Viewed by 2216
Abstract
Questions involving Bayesian Reasoning often arise in events of everyday life, such as assessing the results of a breathalyser test or a medical diagnostic test. Bayesian Reasoning is perceived to be difficult, but visualisations are known to support it. However, prior research on [...] Read more.
Questions involving Bayesian Reasoning often arise in events of everyday life, such as assessing the results of a breathalyser test or a medical diagnostic test. Bayesian Reasoning is perceived to be difficult, but visualisations are known to support it. However, prior research on visualisations for Bayesian Reasoning has only rarely addressed the issue on how to design such visualisations in the most effective way according to research on multimedia learning. In this article, we present a concise overview on subject-didactical considerations, together with the most fundamental research of both Bayesian Reasoning and multimedia learning. Building on these aspects, we provide a step-by-step development of the design of visualisations which support Bayesian problems, particularly for so-called double-trees and unit squares. Full article
(This article belongs to the Special Issue Visualisation in Mathematics Education)
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