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Education Sciences
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Methods and Tools in Mathematics Education
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Methods and Tools in Mathematics Education

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

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 9958

Special Issue Editors

Dr. Francesca Ferrara

E-Mail Website
Guest Editor
Department of Mathematics, University of Torino, 10123 Torino, Italy
Interests: the role of tools in the teaching and learning of mathematics; mathematical embodiment; mathematical imagination; methodology in mathematics education
Dr. Giulia Ferrari

E-Mail Website
Guest Editor
Department of Mathematics, University of Torino, 10123 Torino, Italy
Interests: the role of bodily activities in mathematical meaning making; the use of technology for teaching and learning mathematics; diagrams and (digital) representations in mathematics; gender differences in mathematics

Special Issue Information

Dear Colleagues,

The purpose of this Special Issue is to focus on mathematics education research that addresses the role of methods and tools in mathematics teaching and learning, looking at success as related to mathematical activity, as well as related to learners’ engagement and motivation. Recently, growing attention has been drawn to the relevance of expressive technology (e.g., dynamic geometry environments, interactive microworlds, and software) in the circulation of affect in the mathematics classroom and to the emotional investment of learners. Expressive technology has been studied in terms of engagement and agency, as well as in terms of the quality of the mathematical experiences that learners can have. However, few studies center on the ways that these aspects of learning are distributed across a material activity with tools and are changed in relation to how students work during regular mathematics lessons. The role of the teacher is also an object of study, for example, in respect to teacher training programs or the mathematics classroom.

A contribution to the Special Issue may address any of the following aspects or go beyond these topics:

  • Theoretical approaches to the study of methods and tools in mathematics;
  • The use of (digital or not) tools in the teaching and learning of mathematics;
  • Methods and approaches to study tool use in mathematical activity;
  • The role of the teacher with respect to tools and methods in mathematics teaching.   

Dr. Francesca Ferrara
Dr. Giulia Ferrari
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
  • teaching and learning processes
  • methods
  • tools

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Published Papers (8 papers)

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Research

17 pages, 5019 KiB  
Article
Bridging the Gap: An Epistemic Logical Model for Analysing Students’ Argumentation and Proof in Mathematics Education Research
by Miglena Asenova
Educ. Sci. 2024, 14(6), 673; https://doi.org/10.3390/educsci14060673 - 20 Jun 2024
Viewed by 807
Abstract
In this theoretical paper, an epistemic logical model for analysis of students’ argumentation and proof processes is presented. The model is conceived as a methodological tool addressed to the researcher in mathematics education that aims to shed light on the relations between argumentation [...] Read more.
In this theoretical paper, an epistemic logical model for analysis of students’ argumentation and proof processes is presented. The model is conceived as a methodological tool addressed to the researcher in mathematics education that aims to shed light on the relations between argumentation and proof, highlighting the continuities and discontinuities within and between them. It reconciles the epistemic logic approach, which takes into account the exploratory phases of a statement, linked to argumentative processes, and the deductive logic approach, which takes into account the phases linked to proof in a classical sense. The model is based on Vergnaud’s concepts- and theorems-in-action, on Duval’s distinction between the epistemic and logical value of verbalised propositions, and on elements of Oostra’s intuitionistic existential graphs, a kind of graphical topological logic rooted in Peircean thought, adapted to mathematics education research by considering also shifts in the classical existential graphs. After exposing the theoretical grounding the model is based on, some examples taken from the literature are examined to exemplify how it works. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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16 pages, 3511 KiB  
Article
Embedding Mathematics in Socio-Scientific Games: The Mathematical in Grappling with Wicked Problems
by Chronis Kynigos
Educ. Sci. 2024, 14(6), 630; https://doi.org/10.3390/educsci14060630 - 12 Jun 2024
Viewed by 806
Abstract
This paper discusses the ways in which digitally enabled transformation in mathematics education could envisage a role for rationality in post-normal science and wicked problems. The scene is set firstly by reviewing the ways in which digital media have been designed and used [...] Read more.
This paper discusses the ways in which digitally enabled transformation in mathematics education could envisage a role for rationality in post-normal science and wicked problems. The scene is set firstly by reviewing the ways in which digital media have been designed and used in transformative mathematics education as a rationale for thinking about such media for wicked problem education. The problem is set in epistemological terms: can normal science approaches contribute to post-normal science? By considering the basic arguments regarding wicked problem education, I focus on the discussion of a specific constructionist digital tool called ‘ChoiCo: Choices with Consequences’, designed to embed mathematical ideas and facilitate mathematical reasoning, yet be about grappling with wicked problems. The final section discusses student discourse to set the scene for what such reasoning might look like in the context of grappling with wicked problems. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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22 pages, 26919 KiB  
Article
The Promise of AI Object-Recognition in Learning Mathematics: An Explorative Study of 6-Year-Old Children’s Interactions with Cuisenaire Rods and the Blockplay.ai App
by Michael Rumbelow and Alf Coles
Educ. Sci. 2024, 14(6), 591; https://doi.org/10.3390/educsci14060591 - 30 May 2024
Viewed by 947
Abstract
We developed and trained a prototype AI-based object-recognition app, blockplay.ai, to recognise Cuisenaire rods placed on a tabletop, and speak the rods’ lengths. We challenged 6-year-olds in a primary school in England to play a ‘game’: can you make the app say the [...] Read more.
We developed and trained a prototype AI-based object-recognition app, blockplay.ai, to recognise Cuisenaire rods placed on a tabletop, and speak the rods’ lengths. We challenged 6-year-olds in a primary school in England to play a ‘game’: can you make the app say the two times table? Drawing methodologically on theories of embodiment, we analyse two videoclips, each of a child interacting with rods, the app and the task set by the researchers, as a dynamic, complex child-rods-app-task body-artefact system. Theoretically we draw on Davydovian concepts of learning as a concrete-to-abstract-to-new-concrete cycle, using abstract artefacts such as mathematical language to coordinate new perceptually-guided actions on concrete objects. In one videoclip the child’s pattern of actions are consistent with a change, within a few minutes, from perceiving and acting on rods as counters, to perceiving and acting on rods as lengths; in the other videoclip, this does not happen. We analyse the changes in patterns of interactions as shifts to new stable attractors in a dynamic child-rods-app-task body-artefact system, driven by tensions generated by unexpected concrete-to-abstract relationships. We end by looking forward to the range of possible uses of object-recognition technology in the learning of mathematics, for example, provoking algebraic awareness. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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20 pages, 7979 KiB  
Article
Didactical Materials Customizable to Suit Classroom Needs: A Valuable Resource for Teachers
by Silvia Sbaragli and Monica Panero
Educ. Sci. 2024, 14(5), 449; https://doi.org/10.3390/educsci14050449 - 24 Apr 2024
Viewed by 1020
Abstract
Can free, adaptable, and didactically validated materials have an impact on teachers’ practices and competences? This issue has been focused on by the researchers working on the MaMa—Matematica per la scuola elementare (MaMa—Mathematics for the primary school) project, commissioned by the Dipartimento dell’educazione, [...] Read more.
Can free, adaptable, and didactically validated materials have an impact on teachers’ practices and competences? This issue has been focused on by the researchers working on the MaMa—Matematica per la scuola elementare (MaMa—Mathematics for the primary school) project, commissioned by the Dipartimento dell’educazione, della cultura e dello sport (Department of education, culture and sport) of the Canton of Ticino (Switzerland). Since 2019, this project has been aiming to create materials for teaching and learning mathematics in primary school, in line with the curriculum. The innovative MaMa materials, which can be freely downloaded via the mama.edu.ti.ch platform, are addressed to both teachers and learners. In many cases, they are editable, so that they can be customized by each user to suit the different teaching contexts and pupils’ learning needs and be grouped into collections. Via the administration and analysis of a questionnaire, this article investigates how teachers use the materials, and whether they influence teachers’ practices and competences. The results of this pilot study show that MaMa materials are perceived from teacher–users as “materials for teacher education and development”, especially at the disciplinary level, supporting both the instructional design process and the appropriation/transformation of didactical resources to deal with the challenges of differentiation in the classrooms. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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22 pages, 12088 KiB  
Article
Learning Multiplication by Translating across Microworlds
by Sheena Tan, Sean Chorney and Nathalie Sinclair
Educ. Sci. 2024, 14(4), 423; https://doi.org/10.3390/educsci14040423 - 17 Apr 2024
Viewed by 874
Abstract
In this article, we explore students’ experiences of using two different digital microworlds of multiplication, which can be found in the multitouch application TouchTimes. We draw on Diagne’s notion of translation to frame our study, focusing on the learning that occurs in the [...] Read more.
In this article, we explore students’ experiences of using two different digital microworlds of multiplication, which can be found in the multitouch application TouchTimes. We draw on Diagne’s notion of translation to frame our study, focusing on the learning that occurs in the movement between the two microworlds. We study translation in terms of actions, strategies, perceptions, and preferences and highlight both the translatables and the untranslatables that emerged in the pair-based interviews that were conducted with grades 3–4 students. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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18 pages, 1563 KiB  
Article
How Learning to Speak the Language of a Computer-Based Digital Environment Can Plant Seeds of Algebraic Generalisation: The Case of a 12-Year-Old Student and eXpresser
by Anna E. Baccaglini-Frank, Eirini Geraniou, Celia Hoyles and Richard Noss
Educ. Sci. 2024, 14(4), 409; https://doi.org/10.3390/educsci14040409 - 14 Apr 2024
Viewed by 1279
Abstract
When learning in a digital interactive mathematics learning environment (DIMLE) designed to foster the development of specific mathematics content, students come to express their ideas through different languages and representations. We devise a method based on the Theory of Instrumental Genesis (TIG) to [...] Read more.
When learning in a digital interactive mathematics learning environment (DIMLE) designed to foster the development of specific mathematics content, students come to express their ideas through different languages and representations. We devise a method based on the Theory of Instrumental Genesis (TIG) to analyse aspects of a middle school student’s learning about algebraic generalisation in a DIMLE called “eXpresser”. Our analytic scheme allows us to capture changes in her instrumented schemes when accomplishing a certain task repeatedly, gradually modifying her interactions with the system. The results concern both insights into a specific mathematics learning journey in a DIMLE, and methodological progress at a more general level. Indeed, the method we devised and explored in this specific case can be applied to infer students’ schemes from their actions as they interact with other DIMLEs. This possibility yields great potential because more and more actions can now be recognized directly by software. This has important implications for computer-supported personalised learning, and AI in general. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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23 pages, 5119 KiB  
Article
An Integrated Methodological Approach for Documenting Individual and Collective Mathematical Progress: Reinventing the Euler Method Algorithmic Tool
by Chris Rasmussen, Megan Wawro and Michelle Zandieh
Educ. Sci. 2024, 14(3), 335; https://doi.org/10.3390/educsci14030335 - 21 Mar 2024
Viewed by 1145
Abstract
In this paper we advance a methodological approach for documenting the mathematical progress of learners as an integrated analysis of individual and collective activity. Our approach is grounded in and expands the emergent perspective by integrating four analytic constructs: individual meanings, individual participation, [...] Read more.
In this paper we advance a methodological approach for documenting the mathematical progress of learners as an integrated analysis of individual and collective activity. Our approach is grounded in and expands the emergent perspective by integrating four analytic constructs: individual meanings, individual participation, collective mathematical practices, and collective disciplinary practices. Using video data of one small group of four students in an inquiry-oriented differential equations classroom, we analyze a 10 min segment in which one small group reinvent Euler’s method, an algorithmic tool for approximating solutions to differential equations. A central intellectual contribution of this work is elaborating and coordinating the four methodological constructs with greater integration, cohesiveness, and coherence. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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22 pages, 7856 KiB  
Article
Resources and Praxeologies Involved in Teachers’ Design of an Interdisciplinary STEAM Activity
by Gabriella Pocalana, Ornella Robutti and Elena Ciartano
Educ. Sci. 2024, 14(3), 333; https://doi.org/10.3390/educsci14030333 - 20 Mar 2024
Cited by 2 | Viewed by 1402
Abstract
This study aimed to examine the collaborative design of an interdisciplinary STEAM activity conducted by lower-secondary school teachers of different disciplines. We adopted an approach based on a case study involving four teachers (art, music, technology, and mathematics/science teachers) designing an activity focused [...] Read more.
This study aimed to examine the collaborative design of an interdisciplinary STEAM activity conducted by lower-secondary school teachers of different disciplines. We adopted an approach based on a case study involving four teachers (art, music, technology, and mathematics/science teachers) designing an activity focused on the concept of symmetry. We gathered data through oral, semi-structured interviews with the teachers and through schematic representations of resource systems provided by the teachers themselves. Data analysis aimed to identify the different kinds of resources the teachers relied on, their utilization schemes, and the overarching meta-didactical praxeology adopted by the teachers for their collaborative design work. The theoretical model adopted for data analysis was a combination of the Documentational Approach to Didactics and the Meta-Didactical Transposition frameworks, originally introduced to study the work of researchers in the context of teacher professional development. An application of this model to the collaborative design work of teachers can provide a fresh insight into the relationship between teachers’ documentation work for the design of a STEAM activity, the practices that they adopt to address this shared task (praxis), and the shared justifying discourses (logos) for their praxis. Full article
(This article belongs to the Special Issue Methods and Tools in Mathematics Education)
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