Models and Tools for Math Education

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

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 16982

Special Issue Editors

Department of Didactics of Mathematics, University of Valencia, 46022 Valencia, Spain
Interests: problem solving; early mathematics education; educational robotics; ICT and education
Special Issues, Collections and Topics in MDPI journals
Department of Didactics of Mathematics, University of Valencia, 46100 Burjassot, Spain
Interests: image compression; applied mathematics; numerical analysis; mathematics education; educational robotics; ICT and education
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In their attempt to uncover the complexity of the teaching–learning processes of mathematics, education researchers have been looking for cognitive and instructional models from the first half of the twentieth century. The historical underpinnings of mathematics education research have resulted in different approaches ranging from the scientific disciplines of mathematics to psychology.

This Special Issue is devoted to discussing models and tools to explore mathematical thinking in educational contexts. Thus, empirical research involving innovative tools in all aspects of teaching and learning, theoretical models of mathematics education or instructional approaches based on technology and digital environments for mathematics teaching and learning are welcome. Discussions about models and tools (new or revisited) addressed at mathematics education, including cognitive, emotional, language-related, curriculum, and social dimensions of teaching and learning in educational contexts are also included in the scope of this issue.

Prof. Dr. Pascual D. Diago Nebot
Dr. Dionisio F. Yáñez
Guest Editors

Manuscript Submission Information

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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

  • ICT
  • theoretical review
  • teaching and learning
  • mathematics education
  • mathematics didactics
  • psychological approaches in mathematics education
  • digital environments in mathematics education, technological environments in mathematics education
  • models on mathematics education

Published Papers (9 papers)

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Research

14 pages, 3901 KiB  
Article
Assessing a Didactic Sequence for Computational Thinking Development in Early Education Using Educational Robots
by Adrián Pérez-Suay, Ismael García-Bayona, Steven Van Vaerenbergh and Ana B. Pascual-Venteo
Educ. Sci. 2023, 13(7), 669; https://doi.org/10.3390/educsci13070669 - 30 Jun 2023
Viewed by 1218
Abstract
Computational thinking (CT) is increasingly incorporated into curricular planning across various educational levels in numerous countries. Presently, CT is being integrated into preschool and primary education. To effectively implement CT at the classroom level, the design and study of techniques and tasks are [...] Read more.
Computational thinking (CT) is increasingly incorporated into curricular planning across various educational levels in numerous countries. Presently, CT is being integrated into preschool and primary education. To effectively implement CT at the classroom level, the design and study of techniques and tasks are crucial. This research empirically evaluates a didactic sequence using programmable educational robots for problem-solving challenges rooted in mathematical concepts. The study consists of two sets of activities: computational localisation of elements on a regular grid, where students program robots to navigate, and problem-solving tasks involving sum calculations using distinct pre-operational strategies. The study sample is a class of 16 students at the preschool level. The results indicate an increasing complexity in the success of the designed sequence, with the ’counting all’ strategy demonstrating higher efficacy. These promising findings highlight the potential for further research, aiming to establish a strong foundation for early educational levels through the integration of CT via programmable robots and engaging problem-solving challenges. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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14 pages, 712 KiB  
Article
Acceptance and Intentions of Using Dynamic Geometry Software by Pre-Service Primary School Teachers
by Steven Van Vaerenbergh, Adrián Pérez-Suay and Pascual D. Diago
Educ. Sci. 2023, 13(7), 661; https://doi.org/10.3390/educsci13070661 - 28 Jun 2023
Viewed by 941
Abstract
In this paper, we empirically verify the validity of the extended Technology Acceptance Model (TAM) for the use of Dynamic Geometry Software (DGS) in teaching geometry, as proposed by Pittalis. The model includes the notion of “perceived pedagogical-learning fit” in addition to the [...] Read more.
In this paper, we empirically verify the validity of the extended Technology Acceptance Model (TAM) for the use of Dynamic Geometry Software (DGS) in teaching geometry, as proposed by Pittalis. The model includes the notion of “perceived pedagogical-learning fit” in addition to the traditional belief and attitude variables of TAM. We employ a structural equation modeling approach to capture the relationships between the different latent constructs. With a sample of 135 pre-service primary school teachers as participants, our study provides valuable insights into the factors influencing the adoption of DGS in geometry teaching. The results reveal that the extended TAM serves as a suitable framework to evaluate the intentions of teachers to use DGS in teaching geometry. However, we also observe some discrepancies in the predictive power of various latent factors when compared to the original study. These findings not only contribute to our understanding of the factors affecting the adoption of DGS in geometry teaching but also provide valuable insights for future research and practice. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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14 pages, 419 KiB  
Article
Assessing the Relevance of Information Sources for Modelling Student Performance in a Higher Mathematics Education Course
by Adrián Pérez-Suay, Ricardo Ferrís-Castell, Steven Van Vaerenbergh and Ana B. Pascual-Venteo
Educ. Sci. 2023, 13(6), 555; https://doi.org/10.3390/educsci13060555 - 28 May 2023
Viewed by 1223
Abstract
In recent years, most educational institutions have integrated digital technologies into their teaching–learning processes. Learning Management Systems (LMS) have gained increasing popularity, particularly in higher education, due to their ability to manage teacher–student interactions. These systems store valuable information which describes students’ behaviour [...] Read more.
In recent years, most educational institutions have integrated digital technologies into their teaching–learning processes. Learning Management Systems (LMS) have gained increasing popularity, particularly in higher education, due to their ability to manage teacher–student interactions. These systems store valuable information which describes students’ behaviour throughout a course. These data can be utilised to construct statistical models that represent learner behaviour within an online LMS platform. In this study, we aim to compare different sources of information and, more ambitiously, to provide insights into which source of information is most valuable for inferring student performance. The considered sets of information come from (i) the Moodle LMS; (ii) socio-economic data about students acquired from a survey; and (iii) subject marks achieved throughout the course. To determine the relevance of the incorporated information, we use artificial intelligence (AI) methods, and we report the importance measures of four state-of-the-art methods. Our findings indicate that the selected methodology is suitable for making inferences about student performance while also shedding light on model decisions through explainability. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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18 pages, 3182 KiB  
Article
An Approach to the Teacher Educator’s Pedagogical Content Knowledge for the Development of Professional Noticing in Pre-Service Teacher Education
by Andrés Pérez-Montilla and Mónica Arnal-Palacián
Educ. Sci. 2023, 13(6), 544; https://doi.org/10.3390/educsci13060544 - 25 May 2023
Cited by 2 | Viewed by 1169
Abstract
This study endeavors to illustrate how research on the professional development of mathematics teachers can help to enhance and nurture the professional knowledge of mathematics teacher educators (MTEs), thus becoming a potential source of professional growth for MTEs. To achieve this, a professional [...] Read more.
This study endeavors to illustrate how research on the professional development of mathematics teachers can help to enhance and nurture the professional knowledge of mathematics teacher educators (MTEs), thus becoming a potential source of professional growth for MTEs. To achieve this, a professional task was administered to 38 prospective secondary teachers from two Spanish public universities to explore their level of development in professional noticing. Specifically, the study focused on their skill of attending to children’s strategies in relation to transformations between semiotic representations as well as their awareness of the role of the semiotic register in task design. Drawing from the responses provided for the task, we offer a range of insights regarding expected or desirable Pedagogical Content Knowledge (MTEPCK) aimed at fostering the development of professional noticing, such as several challenges to be overcome by pre-service teachers or the identification of three potential levels of progression in their skill to attend to children’s strategies. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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16 pages, 2282 KiB  
Article
Exploring Gamification Approaches for Enhancing Computational Thinking in Young Learners
by Javier del Olmo-Muñoz, Andrea Bueno-Baquero, Ramón Cózar-Gutiérrez and José Antonio González-Calero
Educ. Sci. 2023, 13(5), 487; https://doi.org/10.3390/educsci13050487 - 11 May 2023
Cited by 2 | Viewed by 4470
Abstract
The integration of computational thinking (CT) in mathematics education is increasingly important due to its intersections with mathematical thinking and its role in the 21st century. Recent years have seen a growing interest in the use of innovative tools to enhance mathematics education, [...] Read more.
The integration of computational thinking (CT) in mathematics education is increasingly important due to its intersections with mathematical thinking and its role in the 21st century. Recent years have seen a growing interest in the use of innovative tools to enhance mathematics education, including the exploration of gamification techniques to improve student engagement. While previous research suggests that the inclusion of CT activities at an early age can positively impact students’ motivation and CT skills, the potential benefits of incorporating gamification techniques into CT instruction remain unexplored. In this study, we investigated the impact of shallow and deep gamification techniques on the CT skills and the intrinsic and extrinsic motivation of second-grade students in a blended teaching sequence that combined both unplugged and plugged CT activities. A quasi-experimental design was used with a control group and an experimental group. The findings suggest that both shallow and deep gamification techniques can be effective in improving CT skills in young students, but deep gamification may have a stronger impact on motivation. These results contribute to the growing body of literature on the integration of gamification techniques in CT instruction. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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16 pages, 6223 KiB  
Article
Dynamic and Multipurpose Teaching Models at the First International Exhibition of Mathematics Teaching Material
by Josefa Dólera-Almaida and Dolores Carrillo-Gallego
Educ. Sci. 2023, 13(3), 265; https://doi.org/10.3390/educsci13030265 - 02 Mar 2023
Cited by 1 | Viewed by 1321
Abstract
The International Commission for the Study and Improvement of Mathematical Education (1950) was interested in updating and developing teaching resources to address the pedagogical problems of mathematics teaching in the mid-1950s. As a result of this concern, the First International Exhibition of Mathematical [...] Read more.
The International Commission for the Study and Improvement of Mathematical Education (1950) was interested in updating and developing teaching resources to address the pedagogical problems of mathematics teaching in the mid-1950s. As a result of this concern, the First International Exhibition of Mathematical Teaching Material was held in Spain in 1957, an event that had great international repercussions. This work is situated in the field of the history of mathematics education, so the research method used is historical. The aim is to study those mathematical didactic models which, due to their dynamic and multipurpose nature, stood out at the Exhibition. The results show that these materials contributed favorably to the teaching of mathematics, as they made it possible to work on a wide variety of topics and provided numerous advantages over traditional material. The use of these models meant that the mathematical notions or ideas generally arose from the action that the child carried out with the material; they also made the student the main protagonist of their learning. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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19 pages, 539 KiB  
Article
Introduction to Computational Mathematics Using the Historical Solutions of the “Hundred Fowls” Problem
by Miguel Á. García-Moreno, Dionisio F. Yáñez and Pascual D. Diago
Educ. Sci. 2023, 13(1), 18; https://doi.org/10.3390/educsci13010018 - 23 Dec 2022
Viewed by 1148
Abstract
Through programming tasks, the skills and abilities used to solve mathematical problems are developed and improved. In this article we present a programming teaching trajectory using the solutions presented throughout the history of the “hundred fowls” problem. The proposed itinerary is graduated, meaning [...] Read more.
Through programming tasks, the skills and abilities used to solve mathematical problems are developed and improved. In this article we present a programming teaching trajectory using the solutions presented throughout the history of the “hundred fowls” problem. The proposed itinerary is graduated, meaning that it can be used for different educational stages. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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15 pages, 2124 KiB  
Article
Contextualized Mathematical Problems: Perspective of Teachers about Problem Posing
by Gilberto Chavarría-Arroyo and Veronica Albanese
Educ. Sci. 2023, 13(1), 6; https://doi.org/10.3390/educsci13010006 - 21 Dec 2022
Viewed by 2171
Abstract
This research describes the perspective of secondary school teachers on the selection, elaboration, and implementation of contextualized mathematical problems in secondary education in Costa Rica. An exploratory and descriptive quantitative study is carried out, applying a questionnaire to 67 in-service secondary school mathematics [...] Read more.
This research describes the perspective of secondary school teachers on the selection, elaboration, and implementation of contextualized mathematical problems in secondary education in Costa Rica. An exploratory and descriptive quantitative study is carried out, applying a questionnaire to 67 in-service secondary school mathematics teachers. The dimensions of the sources used by teachers, the difficulties encountered and the learners’ background considered for problem selection and elaboration are analyzed. In addition, the contexts present in the problems that teachers propose are classified. The results indicate that teachers use textbooks for the selection of mathematical problems. In addition, they give a favorable opinion regarding the use of realistic contexts in the creation of new problems. However, several of the proposed problems present fictitious or mathematical contexts. The highest percentage of the participants points out the need for training for the elaboration of contextualized mathematical problems. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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16 pages, 1061 KiB  
Article
Approach to the Formulation of the Variable Change Theorem
by Armando Morales Carballo, Edgardo Locia Espinoza, José M. Sigarreta Almira and Ismael G. Yero
Educ. Sci. 2021, 11(7), 357; https://doi.org/10.3390/educsci11070357 - 16 Jul 2021
Cited by 1 | Viewed by 1592
Abstract
This research proposes a didactic strategy to enrich the assimilation processes of the change of variable theorem in solving the definite integral. The theoretical foundations that support it are based on the contributions of social constructivism, problem solving, and treatment of theorems. The [...] Read more.
This research proposes a didactic strategy to enrich the assimilation processes of the change of variable theorem in solving the definite integral. The theoretical foundations that support it are based on the contributions of social constructivism, problem solving, and treatment of theorems. The practical validation of the strategy is carried out with students of the Higher Technical Level in Applied Mathematics at the Autonomous University of Guerrero. Full article
(This article belongs to the Special Issue Models and Tools for Math Education)
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