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Mathematics
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Designing Tasks within Dynamic and Interactive Mathematics Learning Environments
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Designing Tasks within Dynamic and Interactive Mathematics Learning Environments

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 22449

Special Issue Editor

Dr. Anna Baccaglini-Frank

E-Mail Website
Guest Editor
Associate Professor, Department of Mathematics, University of Pisa, Pisa, Italy
Interests: technology-enhanced learning; design-based research for the development of mathematical activities for all grade levels; educational interventions for students manifesting persistent difficulties in mathematical learning

Special Issue Information

Dynamic and interactive mathematics learning environments (DIMLEs) have become the protagonists of an increasing body of research and are currently being used by many mathematics educators in a variety of contexts. Indeed, as digital technology evolves, a variety of new educational spaces and forms for the mathematics classroom open up, and novel ideas and approaches emerge. This Special Issue specifically addresses new design issues, principles, and choices grounded within the Mathematics Education research tradition that have been adopted and studied recently, possibly also in response to the online distance learning emergency created by the COVID-19 pandemic. Papers submitted to this Special Issue should focus in particular on: how mathematical tasks can be designed so that specific features of the DIMLE used (including multi-touch inputs or haptic interfaces) can be capitalized upon to transform learners’ experiential knowledge into conceptual mathematical knowledge, and how the design of tasks in DIMLEs shapes relationships within mathematical classrooms (including virtual classrooms). The Special Issue also welcomes literature reviews providing insights into the issues above.

Dr. Anna Baccaglini-Frank
Guest Editor

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 single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Digital technology
  • Distance learning
  • Dynamic and interactive mathematics learning environments
  • Mathematics education
  • Task design

Published Papers (7 papers)

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Research

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16 pages, 19889 KiB  
Article
Implementation of Mobile Learning in Mathematics Instruction for Elementary Second Graders
by Tzu-Hua Wang, Chien-Hui Kao and Tsai-Ju Wang
Mathematics 2021, 9(14), 1603; https://doi.org/10.3390/math9141603 - 07 Jul 2021
Cited by 3 | Viewed by 2617
Abstract
In this study, a mobile learning system (MLS) was developed and adopted to facilitate elementary second-grade students to learn mathematics. A quasi-experimental design was adopted. There were two learning models, including the typical instruction group (TI group) and MLS group. The learning content [...] Read more.
In this study, a mobile learning system (MLS) was developed and adopted to facilitate elementary second-grade students to learn mathematics. A quasi-experimental design was adopted. There were two learning models, including the typical instruction group (TI group) and MLS group. The learning content is the topic of multiplication. A total of 93 s-grade students from four classes in a public elementary school in Northern Taiwan participated in this research. Participants were randomly divided into the MLS group (47 participants: 22 boys and 25 girls) and the TI group (46 participants: 26 boys and 20 girls). Participants in the MLS group received mathematics instruction in the MLS, whereas those in the TI group received direct instruction in typical classrooms. All students took the pretest and posttest of mathematics learning achievement test and mathematics learning interest scale assess their improvement of learning achievement and learning interest after the learning activities. The findings revealed that students in the MLS group had significantly better improvement in their mathematics learning interest and mathematics learning achievement than those in the TI group. In addition, students in the MLS group had significantly better performance in answering items of comprehension and application levels in the mathematics learning achievement test. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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27 pages, 6456 KiB  
Article
Enhancing the Skill of Geometric Prediction Using Dynamic Geometry
by Elisa Miragliotta and Anna E. Baccaglini-Frank
Mathematics 2021, 9(8), 821; https://doi.org/10.3390/math9080821 - 09 Apr 2021
Cited by 5 | Viewed by 1978
Abstract
This study concerns geometric prediction, a process of anticipation that has been identified as key in mathematical reasoning, and its possible constructive relationship with explorations within a Dynamic Geometry Environment (DGE). We frame this case study within Fischbein’s Theory of Figural Concepts and, [...] Read more.
This study concerns geometric prediction, a process of anticipation that has been identified as key in mathematical reasoning, and its possible constructive relationship with explorations within a Dynamic Geometry Environment (DGE). We frame this case study within Fischbein’s Theory of Figural Concepts and, to gain insight into a solver’s conceptual control over a geometrical figure, we introduce a set of analytical tools that include: the identification of the solver’s geometric predictions, theoretical and phenomenological evidence that s/he may seek for, and the dragging modalities s/he makes use of in the DGE. We present fine-grained analysis of data collected during a clinical interview as a high school student reasons about a geometrical task, first on paper-and-pencil, and then in a DGE. The results suggest that, indeed, the DGE exploration has the potential of strengthening the solver’s conceptual control, promoting its evolution toward theoretical control. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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21 pages, 3771 KiB  
Article
The Analysis of a Model–Task Dyad in Two Settings: Zaplify and Pencil and Paper
by Canan Güneş
Mathematics 2021, 9(5), 581; https://doi.org/10.3390/math9050581 - 09 Mar 2021
Cited by 1 | Viewed by 1631
Abstract
This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that [...] Read more.
This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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16 pages, 2266 KiB  
Article
Designing Tasks for Introducing Functions and Graphs within Dynamic Interactive Environments
by Samuele Antonini and Giulia Lisarelli
Mathematics 2021, 9(5), 572; https://doi.org/10.3390/math9050572 - 07 Mar 2021
Cited by 1 | Viewed by 2205
Abstract
In this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment [...] Read more.
In this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment and having the semiotic potential for embedding mathematical meanings of covariation of independent and dependent variables. After laying down the theoretical grounds, we formulate the design principles that emerged as the result of bringing the theory into a dialogue with the didactical aims. Finally, we present a teaching sequence, designed and implemented on the basis of the design principles and we show how students’ efforts in describing and manipulating the different graphs of functions can promote their production of specific signs that can progressively evolve towards mathematical meanings. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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30 pages, 661 KiB  
Article
Designing Tasks for a Dynamic Online Environment: Applying Research into Students’ Difficulties with Linear Equations
by Morten Elkjær and Uffe Thomas Jankvist
Mathematics 2021, 9(5), 557; https://doi.org/10.3390/math9050557 - 06 Mar 2021
Cited by 1 | Viewed by 3516
Abstract
Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic [...] Read more.
Despite almost half a century of research into students’ difficulties with solving linear equations, these difficulties persist in everyday mathematics classes around the world. Furthermore, the difficulties reported decades ago are the same ones that persist today. With the immense number of dynamic online environments for mathematics teaching and learning that are emerging today, we are presented with a perhaps unique opportunity to do something about this. This study sets out to apply the research on lower secondary school students’ difficulties with equation solving, in order to eventually inform students’ personalised learning through a specific task design in a particular dynamic online environment (matematikfessor.dk). In doing so, task design theory is applied, particularly variation theory. The final design we present consists of eleven general equation types—ten types of arithmetical equations and one type of algebraic equation—and a broad range of variations of these, embedded in a potential learning-trajectory-tree structure. Besides establishing this tree structure, the main theoretical contribution of the study and the task design we present is the detailed treatment of the category of arithmetical equations, which also involves a new distinction between simplified and non-simplified arithmetical equations. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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Review

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24 pages, 1561 KiB  
Review
Mathematical Representation Competency in Relation to Use of Digital Technology and Task Design—A Literature Review
by Mathilde Kjær Pedersen, Cecilie Carlsen Bach, Rikke Maagaard Gregersen, Ingi Heinesen Højsted and Uffe Thomas Jankvist
Mathematics 2021, 9(4), 444; https://doi.org/10.3390/math9040444 - 23 Feb 2021
Cited by 5 | Viewed by 4413
Abstract
Representations are crucial to mathematical activity, both for learners and skilled mathematicians. Digital technologies (DT) to support mathematical activity offer a plethora of new possibilities, not least in the context of mathematics education. This paper presents a literature review on representations and activation [...] Read more.
Representations are crucial to mathematical activity, both for learners and skilled mathematicians. Digital technologies (DT) to support mathematical activity offer a plethora of new possibilities, not least in the context of mathematics education. This paper presents a literature review on representations and activation of students’ representation competency when using DT in mathematics teaching and learning situations. It does so with a starting point in task designs involving digital tools aiming to activate representation competency, drawing on the notion of Mathematical Digital Boundary Object (MDBO). The 30 studies included in the literature review are analyzed using Duval’s registers of semiotic representations and the representation competency from the Danish KOM framework. The results reveal a clear connection between the mathematical topics addressed and the types of representation utilized, and further indicate that certain aspects of the representation competency are outsourced when DT are used. To activate the representation competency in relation to the use of DT, we offer five suggestions for consideration when designing mathematical tasks. Finally, we raise the question of whether DT create new representations or merely new activities. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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20 pages, 1193 KiB  
Review
A Systematic Review on Task Design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs)
by Mustafa Cevikbas and Gabriele Kaiser
Mathematics 2021, 9(4), 399; https://doi.org/10.3390/math9040399 - 18 Feb 2021
Cited by 16 | Viewed by 4715
Abstract
Task design constitutes a growing core of research in mathematics education. In particular, task design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs) has become very popular, although it remains under-researched. This study aims to systematically analyze the current state of research on [...] Read more.
Task design constitutes a growing core of research in mathematics education. In particular, task design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs) has become very popular, although it remains under-researched. This study aims to systematically analyze the current state of research on task design in DIMLEs. The literature was searched through the Web of Science, and 10 articles were included in the review. Results show that the majority of research studies were undertaken in Asia, with a focus on secondary and higher education. Studies used design-based research, case study, and grounded theory. Most studies were carried out in the domain of geometry, followed by algebra and calculus. Most researchers used GeoGebra as a DIMLE. The studies used different frameworks and contributed to the literature by developing and testing design principles, problematizing task design, and extending existing frameworks. There are also some reported challenges concerning task design in DIMLEs, such as students’ negative attitudes and beliefs and being inexperienced or unfamiliar with DIMLEs. E-assessment issues also created problems, as well as students’ poor mathematical background and time-consuming activities for teachers and students. Overall, the results indicate that further studies are needed on task design in DIMLEs. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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