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Mathematics
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Active Methodologies for the Promotion of Mathematical Learning
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Active Methodologies for the Promotion of Mathematical Learning

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 132682

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. Dr. Francisco D. Fernández-Martín

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Guest Editor
Department of Developmental and Educational Psychology, University of Granada, 18071 Granada, Spain
Interests: program evaluation; plurilingual education; peer learning; entrepreneurship education; bullying behavior; service learning; civic engagement; inclusive education; counseling; elderly education; special educational needs
Special Issues, Collections and Topics in MDPI journals
Dr. José-María Romero-Rodríguez

E-Mail Website
Guest Editor
Head of Association for Research and Promotion of Education in the Digital Society – PROMOEDUCA, Granada, Spain
Interests: educational technology; teacher training; higher education; sustainability education; social networks; educational innovation; active methodologies; Internet risks; mobile learning.
Special Issues, Collections and Topics in MDPI journals
Dr. Gerardo Gómez-García

E-Mail Website
Guest Editor
Department of Didactics and School Organization, University of Granada, Granada, Spain
Interests: E-Learning; Innovation; ICT; Digital Literacy; Flip Teaching; Fake News; Informational Literacy
Dr. Magdalena Ramos Navas-Parejo

E-Mail Website
Guest Editor
Department of Didactics and School Organization, Faculty of Educational Sciences, University of Granada, 18011 Granada, Spain
Interests: active methodologies; information and communication technologies (ICT) in education; reading promotion for educational inclusion
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, the way of teaching has been in a process of transition. Multiple active methodologies have proliferated, with the aim of changing the concept we have had of teaching so far. These advocate for a student who plays a leading role in the process of building learning, while a teacher acts as that figure who facilitates and glimpses the paths to learning. To be able to carry out this type of teaching in an optimal way, it is necessary for the teaching and research community to be correctly trained in its pedagogical principles and in the tools that boost its implementation. Among them, it is of vital importance that information and communication technologies (ICT) be adequately handled. The use of active methodologies (project-based learning, problem-based learning, service learning, flipped classroom, mobile learning, etc.) or innovative pedagogical approaches (simulation, role-playing, gamification, etc.) promotes an improvement in the motivation of students as well as their skills. This aspect is especially important in the area of mathematics, whose contents are characterized by their abstraction and, therefore, highlights the need for its dynamization in classrooms of different educational stages.

Based on these ideas, the present issue of the journal Mathematics entitled “Active Methodologies for the Promotion of Mathematical Learning” aims to bring together studies and research as well as theoretical contributions that exemplify and support good educational practices in which active methodologies have been used in the mathematics classroom. Scientific contributions will be accepted under the following mathematics: active methodologies (project-based learning, problem-based learning, flipped classroom, gamification, mobile learning); active learning approaches (simulation and role-playing, learning through video games, active use of social networks to improve mathematical content, educational video etc.); application of emerging technological resources in the mathematics classroom (augmented reality, virtual reality, robotics, etc.); works from a systematic or theoretical approach.

Overseeing this Special Issue are the Guest Editors Francisco D. Fernández-Martín PhD from the Department of Developmental and Educational Psychology of the University of Granada, José-María Romero-Rodríguez (Head of Centre) MEd from the Association for Research and Promotion of Education in the Digital Society—PROMOEDUCA, Gerardo Gómez-García MEd from Department of Didactics and School Organization of the University of Granada and Magdalena Ramos Navas-Parejo, MEd from Department of Didactics and School Organization of the University of Granada. All with extensive publishing experience and multiple publications of high impact linked to teaching innovation and improvement of its quality. We look forward to seeing this Special Issue come to fruition, together with your contributions and perspectives on this topic.

Prof. Dr. Francisco D. Fernández-Martín
Dr. José-María Romero-Rodríguez
Dr. Gerardo Gómez-García
Dr. Magdalena Ramos Navas-Parejo
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 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

  • mathematical education
  • active methodologies
  • educational innovation
  • flipped classroom
  • mobile learning
  • gamification
  • information and communication technologies
  • emerging technologies
  • good practices in mathematics education

Published Papers (19 papers)

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17 pages, 4071 KiB  
Article
Improving the Teaching of Real Valued Functions Using Serious Games. Binary Who Is Who?
by Sagrario Lantarón, Mariló López, Susana Merchán and Javier Rodrigo
Mathematics 2021, 9(11), 1239; https://doi.org/10.3390/math9111239 - 28 May 2021
Cited by 1 | Viewed by 2074
Abstract
The study presented makes an original, new and exhaustive analysis of the adaptation of a classical board game which has been named Binary Who is Who? This proposal shows a very useful tool for the consolidation of mathematical concepts related to the study [...] Read more.
The study presented makes an original, new and exhaustive analysis of the adaptation of a classical board game which has been named Binary Who is Who? This proposal shows a very useful tool for the consolidation of mathematical concepts related to the study of real-valued functions that are treated in the different levels of the teaching of mathematics (first and second year of superior secondary studies and the first years of some university degrees). The use of games as a means for learning is the authors’ proposal. The aim is to offer teachers the chance of using the games as a method of teaching mathematical concepts, as well as a motivating instrument for them. This game has been created to be played face-to-face in the classroom and it has also been programmed to create a video game which allows the students to play virtually. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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19 pages, 4385 KiB  
Article
EXPLORIA, a New Way to Teach Maths at University Level as Part of Everything
by Pantaleón D. Romero, Nicolas Montes, Sara Barquero, Paula Aloy, Teresa Ferrer, Marusela Granell and Manuel Millán
Mathematics 2021, 9(10), 1082; https://doi.org/10.3390/math9101082 - 11 May 2021
Cited by 4 | Viewed by 2438
Abstract
The main objective of this article has been to evaluate the effect that the implementation of the EXPLORIA project has had on the Engineering Degree in Industrial Design and Product Development. The EXPLORIA project aims to develop an integrated competence map of the [...] Read more.
The main objective of this article has been to evaluate the effect that the implementation of the EXPLORIA project has had on the Engineering Degree in Industrial Design and Product Development. The EXPLORIA project aims to develop an integrated competence map of the learning process, where the subjects are no longer considered as isolated contents, by elaborating an integrated learning process where the competences and learning outcomes of the subjects are considered as a whole, global and comprehensive learning. The EXPLORIA project connects the competencies of the different STEAM subjects that make up the degree, designing a learning process as a logical, sequential and incremental itinerary. Through concepts on which the foundations of design are based—shape, volume, colour, space and structure—the competencies of the different subjects are defined in incremental learning levels: understanding, applying, experimenting and developing, all taken from Bloom’s taxonomy. Mathematics is linked to the rest of learning through active learning methodologies that make learning useful. This new methodology changes the student’s affective domain towards mathematics in which positive emotions are transformed into positive attitudes that will improve the learning result and therefore, the students’ academic results. To validate it, at the end of the paper, the academic results compared with previous years are shown, as well as an ad hoc survey of the students’ assessment of the new teaching methodology. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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15 pages, 484 KiB  
Article
Formative Assessment of Pre-Service Teachers’ Knowledge on Mathematical Modeling
by Jhony Alexander Villa-Ochoa, Jonathan Sánchez-Cardona and Paula Andrea Rendón-Mesa
Mathematics 2021, 9(8), 851; https://doi.org/10.3390/math9080851 - 14 Apr 2021
Cited by 2 | Viewed by 2539
Abstract
This document reports how formative assessment strategies promote the knowledge of modeling of pre-service mathematics teachers. This knowledge is understood from content and vehicle points of view. Formative assessment strategies were designed and experimented with 14 participants in a mathematical modeling course offered [...] Read more.
This document reports how formative assessment strategies promote the knowledge of modeling of pre-service mathematics teachers. This knowledge is understood from content and vehicle points of view. Formative assessment strategies were designed and experimented with 14 participants in a mathematical modeling course offered to pre-service teachers in a Colombian university. Thematic analysis was conducted on lesson plans built by pre-service teachers. In those plans, they evinced knowledge of class management, mathematics teaching, problem solving, and modeling teaching. Finally, the collective construction of assessment rubrics is highlighted. Its contributions and limitations as a formative assessment tool are reported. The role played by the advisors’ feedback and support to pre-service teachers is also presented. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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40 pages, 633 KiB  
Article
Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis
by Esperanza Lozada, Carolina Guerrero-Ortiz, Aníbal Coronel and Rigoberto Medina
Mathematics 2021, 9(7), 745; https://doi.org/10.3390/math9070745 - 31 Mar 2021
Cited by 11 | Viewed by 4494
Abstract
In this paper, we develop a review of the research focused on the teaching and learning of ordinary differential equations with the following three purposes: to get an overview of the existing literature of the topic, to contribute to the integration of the [...] Read more.
In this paper, we develop a review of the research focused on the teaching and learning of ordinary differential equations with the following three purposes: to get an overview of the existing literature of the topic, to contribute to the integration of the actual knowledge, and to define some possible challenges and perspectives for the further research in the topic. The methodology we followed is a combination of a systematic literature review and a bibliometric analysis. The contributions of the paper are given by the following: shed light on the latest research in this area, present a characterization of the actual research lines regarding the teaching and learning of ordinary differential equations, present some topics to be addressed in the next years and define a starting point for researchers who are interested in developing research in this field. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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19 pages, 1631 KiB  
Article
Application in Augmented Reality for Learning Mathematical Functions: A Study for the Development of Spatial Intelligence in Secondary Education Students
by Francisco del Cerro Velázquez and Ginés Morales Méndez
Mathematics 2021, 9(4), 369; https://doi.org/10.3390/math9040369 - 13 Feb 2021
Cited by 34 | Viewed by 9364
Abstract
Spatial intelligence is an essential skill for understanding and solving real-world problems. These visuospatial skills are fundamental in the learning of different Science, Technology, Engineering and Mathematics (STEM) subjects, such as Technical Drawing, Physics, Robotics, etc., in order to build mental models of [...] Read more.
Spatial intelligence is an essential skill for understanding and solving real-world problems. These visuospatial skills are fundamental in the learning of different Science, Technology, Engineering and Mathematics (STEM) subjects, such as Technical Drawing, Physics, Robotics, etc., in order to build mental models of objects or graphic representations from algebraic expressions, two-dimensional designs, or oral descriptions. It must be taken into account that spatial intelligence is not an innate skill but a dynamic skill, which can be enhanced by interacting with real and/or virtual objects. This ability can be enhanced by applying new technologies such as augmented reality, capable of illustrating mathematical procedures through images and graphics, which help students considerably to visualize, understand, and master concepts related to mathematical functions. The aim of this study is to find out whether the integration of the Geogebra AR (Augmented Reality) within a contextualized methodological environment affects the academic performance and spatial skills of fourth year compulsory secondary education mathematics students. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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14 pages, 715 KiB  
Article
Improving the Teaching of Hypothesis Testing Using a Divide-and-Conquer Strategy and Content Exposure Control in a Gamified Environment
by David Delgado-Gómez, Franks González-Landero, Carlos Montes-Botella, Aaron Sujar, Sofia Bayona and Luca Martino
Mathematics 2020, 8(12), 2244; https://doi.org/10.3390/math8122244 - 19 Dec 2020
Cited by 7 | Viewed by 3454
Abstract
Hypothesis testing has been pointed out as one of the statistical topics in which students present more misconceptions. In this article, an approach based on the divide-and-conquer methodology is proposed to facilitate its learning. The proposed strategy is designed to sequentially explain and [...] Read more.
Hypothesis testing has been pointed out as one of the statistical topics in which students present more misconceptions. In this article, an approach based on the divide-and-conquer methodology is proposed to facilitate its learning. The proposed strategy is designed to sequentially explain and evaluate the different concepts involved in hypothesis testing, ensuring that a new concept is not presented until the previous one has been fully assimilated. The proposed approach, which contains several gamification elements (i.e., points or a leader-board), is implemented into an application via a modern game engine. The usefulness of the proposed approach was assessed in an experiment in which 89 first-year students enrolled in the Statistics course within the Industrial Engineering degree participated. Based on the results of a test aimed at evaluating the acquired knowledge, it was observed that students who used the developed application based on the proposed approach obtained statistically significant higher scores than those that attended a traditional class (p-value < 0.001), regardless of whether they used the learning tool before or after the traditional class. In addition, the responses provided by the students who participated in the study to a test of satisfaction showed their high satisfaction with the application and their interest in the promotion of these tools. However, despite the good results, they also considered that these learning tools should be considered as a complement to the master class rather than a replacement. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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15 pages, 449 KiB  
Article
The Possibilities of Gamifying the Mathematical Curriculum in the Early Childhood Education Stage
by Verónica Marín-Díaz, Begoña E. Sampedro-Requena, Juan M. Muñoz-Gonzalez and Noelia N. Jiménez-Fanjul
Mathematics 2020, 8(12), 2215; https://doi.org/10.3390/math8122215 - 14 Dec 2020
Cited by 7 | Viewed by 2947
Abstract
The addition of gamification to the classroom as a methodological tool means that the teacher’s opinion about this has become an inflection point that can affect its use or not in the classroom. In this sense, the main objective of the present article [...] Read more.
The addition of gamification to the classroom as a methodological tool means that the teacher’s opinion about this has become an inflection point that can affect its use or not in the classroom. In this sense, the main objective of the present article is to explore the opinion of future Early Childhood education teachers on the use of this resource for the development of the mathematics curriculum at this education stage and to obtain an explanatory model that explains it. The design of the study utilized a descriptive perspective and a cross-sectional quantitative focus through a quantitative exploratory study. For data collection, an ad hoc questionnaire was utilized, which was administered to a sample of 232 teachers-in-training. The main result obtained was that the future early childhood education professionals considered that gamification could be a resource for the learning of specific mathematics contents, and this was shaped around a model of two elements. On one hand, the development of mathematical thinking, and on the other, the establishment of relationships between mathematical concepts. Lastly, we can conclude that elements such as age or gender do not determine the perception of the use of gamification in the early childhood education classroom. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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21 pages, 2770 KiB  
Article
Using Robotics to Enhance Active Learning in Mathematics: A Multi-Scenario Study
by Edgar Lopez-Caudana, Maria Soledad Ramirez-Montoya, Sandra Martínez-Pérez and Guillermo Rodríguez-Abitia
Mathematics 2020, 8(12), 2163; https://doi.org/10.3390/math8122163 - 04 Dec 2020
Cited by 24 | Viewed by 10259
Abstract
The use of technology, which is linked to active learning strategies, can contribute to better outcomes in Mathematics education. We analyse the conditions that are necessary for achieving an effective learning of Mathematics, aided by a robotic platform. Within this framework, the question [...] Read more.
The use of technology, which is linked to active learning strategies, can contribute to better outcomes in Mathematics education. We analyse the conditions that are necessary for achieving an effective learning of Mathematics, aided by a robotic platform. Within this framework, the question raised was “What are the conditions that promote effective active math learning with robotic support?” Interventions at different educational scenarios were carried in order to explore three educational levels: elementary, secondary, and high school. Qualitative and quantitative analyses were performed, comparing the control and treatment groups for all scenarios through examinations, direct observations, and testimonials. The findings point to three key conditions: level, motivation, and teacher training. The obtained results show a very favourable impact on the attention and motivation of the students, and they allow for establishing the conditions that need to be met for an effective relationship between the teacher and the technological tool, so that better learning outcomes in Mathematics are more likely to be obtained. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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24 pages, 863 KiB  
Article
Factors Influencing Mathematics Achievement of University Students of Social Sciences
by Alenka Brezavšček, Janja Jerebic, Gregor Rus and Anja Žnidaršič
Mathematics 2020, 8(12), 2134; https://doi.org/10.3390/math8122134 - 01 Dec 2020
Cited by 11 | Viewed by 19133
Abstract
The paper aims to investigate the main factors influencing the mathematics achievement of social sciences university students in Slovenia. A conceptual model was derived where three categories of variables were taken into account: attitude towards mathematics and math anxiety, engagement in learning activities, [...] Read more.
The paper aims to investigate the main factors influencing the mathematics achievement of social sciences university students in Slovenia. A conceptual model was derived where three categories of variables were taken into account: attitude towards mathematics and math anxiety, engagement in learning activities, and attitude towards involving technology in learning mathematics. Data were collected for seven consecutive academic years and analysed using Structural Equation Modelling (SEM). The results showed a very high coefficient of determination for mathematics achievement (0.801), indicating that variables “Perceived Level of Math Anxiety”, “Self-Engagement in Mathematics Course at University”, and “Perceived Usefulness of Technology in Learning Mathematics”, together, explain 80.1% of the total variance. Based on our findings, we can conclude that teaching in secondary school is a crucial determinant for success in mathematics at university. It is essential to identify the best methods for secondary school math teachers which will help them give future students better entry-level knowledge for universities. These methods will, hopefully, also improve the level of mathematics self-confidence, as well as lower the level of math anxiety, which all considerably affect the performance of students in university mathematics. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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15 pages, 1493 KiB  
Article
Enhancing Computational Thinking through Interdisciplinary STEAM Activities Using Tablets
by Ľubomíra Valovičová, Ján Ondruška, Ľubomír Zelenický, Vlastimil Chytrý and Janka Medová
Mathematics 2020, 8(12), 2128; https://doi.org/10.3390/math8122128 - 27 Nov 2020
Cited by 17 | Viewed by 3897
Abstract
Computational thinking is a highly appreciated skill by mathematicians. It was forecasted that, in the next few years, half of the jobs in science, mathematics, technology and engineering (abbreviated as STEM, including arts as STEAM) will use some kind of computation. It is [...] Read more.
Computational thinking is a highly appreciated skill by mathematicians. It was forecasted that, in the next few years, half of the jobs in science, mathematics, technology and engineering (abbreviated as STEM, including arts as STEAM) will use some kind of computation. It is therefore necessary to enhance the learning of mathematics by collaborative problem-solving activities focused on both learning mathematics and developing computational thinking. The problems in science offer a reasonable context in which to investigate the common overarching concepts (e.g., measuring the length). An interdisciplinary STEAM collaborative problem-solving activity was designed and piloted with 27 lower secondary students aged 13.07 ± 1.21 years. Different levels of willingness to use the technology were observed and the factors influencing it were identified. We found that strong background knowledge implies high demands when controlling the used device. On the other hand, when a nice and user-friendly application was used, students did not need to perceive any control over it. After the intervention, the students’ views on the tablet changed and they reported more STEAM-related functions of the device. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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20 pages, 10709 KiB  
Article
Mathematical Modeling Projects Oriented towards Social Impact as Generators of Learning Opportunities: A Case Study
by Lluís Albarracín and Núria Gorgorió
Mathematics 2020, 8(11), 2034; https://doi.org/10.3390/math8112034 - 15 Nov 2020
Cited by 4 | Viewed by 4476
Abstract
This paper presents a case study carried out at an elementary school that led to a characterization of mathematical modeling projects aimed at generating social impact. It shows their potential as generators of mathematical learning opportunities. In the school project, upper-grade students (sixth [...] Read more.
This paper presents a case study carried out at an elementary school that led to a characterization of mathematical modeling projects aimed at generating social impact. It shows their potential as generators of mathematical learning opportunities. In the school project, upper-grade students (sixth grade, 11-year-olds) studied the way in which the rest of the students at the institution traveled from their homes to school. Its purpose was to identify risk points from the standpoint of road safety and to develop a set of recommendations so that all the children could walk safely to school. In our study, we identified, on the one hand, the mathematical learning opportunities that emerged during the development of the project and, on the other, the mathematical models created by the students. We discuss the impact of the project on the different groups in the school community (other students, parents, and teachers). We conclude with a characterization of the mathematical modeling projects oriented towards social impact and affirm that they can be generators of mathematical learning opportunities. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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13 pages, 497 KiB  
Article
Influence of Musical Learning in the Acquisition of Mathematical Skills in Primary School
by Aurelio Chao-Fernández, Dorinda Mato-Vázquez and Rocío Chao-Fernández
Mathematics 2020, 8(11), 2003; https://doi.org/10.3390/math8112003 - 10 Nov 2020
Cited by 1 | Viewed by 3933
Abstract
In this research we analyze the influence of musical activities in the acquisition of mathematical knowledge and skills of a sample, 50 students from both a public and a private school in A Coruña (Spain), at a cognitive level. Based on a quantitative [...] Read more.
In this research we analyze the influence of musical activities in the acquisition of mathematical knowledge and skills of a sample, 50 students from both a public and a private school in A Coruña (Spain), at a cognitive level. Based on a quantitative study with a quasi-experimental design, we evaluated students’ knowledge acquisition; we worked with musical activities related to mathematics in the experimental group (EG), and with traditional mathematical activities in the control group (CG). We used a questionnaire that the teachers completed before and after putting the activities into practice, after collecting—writing daily field notes—the mathematical knowledge acquired by the students. The results indicate that there are significant differences between the pretest and the posttest, between CG and EG, but there are no differences between public and concerted schools. In short, it is concluded that music represents an excellent tool in mathematical learning. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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14 pages, 408 KiB  
Article
Learning Mathematics with Emerging Methodologies—The Escape Room as a Case Study
by Arturo Fuentes-Cabrera, María Elena Parra-González, Jesús López-Belmonte and Adrián Segura-Robles
Mathematics 2020, 8(9), 1586; https://doi.org/10.3390/math8091586 - 15 Sep 2020
Cited by 36 | Viewed by 5980
Abstract
Nowadays, different methodologies are booming in the field of education, and active gamification-based methodologies such as the Escape Room are an example of these methodologies, which is the base of this research. The purpose of this research is to analyze the effectiveness of [...] Read more.
Nowadays, different methodologies are booming in the field of education, and active gamification-based methodologies such as the Escape Room are an example of these methodologies, which is the base of this research. The purpose of this research is to analyze the effectiveness of the use of an Escape Room as an active methodology to learn mathematics. A quantitative research method was performed through an experimental design. Two study groups were set up. With the control group, a traditional training methodology was used, and with the experimental group, an innovative one was used through an Escape room experience. A total of 62 students of the 3rd level of Secondary Education from an educational center in Ceuta (Spain) participated. Results show how the experience developed through the escape room improved achievement, motivation and autonomy in a significant way. It has also reduced learning anxiety significantly. It is concluded that the use of the Escape room in Mathematics improves learning achievement, anxiety, motivation and autonomy, with gender being a variable to be taken into account, especially in motivation and autonomy. Therefore, the escape room has a greater potential than a traditional methodology in Mathematics. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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13 pages, 537 KiB  
Article
Measuring Arithmetic Word Problem Complexity through Reading Comprehension and Learning Analytics
by Maria T. Sanz, Emilia López-Iñesta, Daniel Garcia-Costa and Francisco Grimaldo
Mathematics 2020, 8(9), 1556; https://doi.org/10.3390/math8091556 - 10 Sep 2020
Cited by 8 | Viewed by 3017
Abstract
Numerous studies have addressed the relationship between performance in mathematics problem-solving and reading comprehension in students of all educational levels. This work presents a new proposal to measure the complexity of arithmetic word problems through the student reading comprehension of the problem statement [...] Read more.
Numerous studies have addressed the relationship between performance in mathematics problem-solving and reading comprehension in students of all educational levels. This work presents a new proposal to measure the complexity of arithmetic word problems through the student reading comprehension of the problem statement and the use of learning analytics. The procedure to quantify this reading comprehension comprises two phases: (a) the division of the statement into propositions and (b) the computation of the time dedicated to read each proposition through a technological environment that records the interactions of the students while solving the problem. We validated our approach by selecting a collection of problems containing mathematical concepts related to fractions and their different meanings, such as fractional numbers over a natural number, basic mathematical operations with a natural whole or fractional whole and the fraction as an operator. The main results indicate that a student’s reading time is an excellent proxy to determine the complexity of both propositions and the complete statement. Finally, we used this time to build a logistic regression model that predicts the success of students in solving arithmetic word problems. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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12 pages, 1609 KiB  
Article
Analysis of Factors Influencing Students’ Access to Mathematics Education in the Form of MOOC
by Dalibor Gonda, Viliam Ďuriš, Gabriela Pavlovičová and Anna Tirpáková
Mathematics 2020, 8(8), 1229; https://doi.org/10.3390/math8081229 - 27 Jul 2020
Cited by 15 | Viewed by 3747
Abstract
Restricting the movement of students because of COVID-19 requires expanding the offer of online education. Online education should reflect the principles of pedagogical constructivism to ensure the development of students’ cognitive and social competencies. The paper describes the preparatory course of mathematics, realized [...] Read more.
Restricting the movement of students because of COVID-19 requires expanding the offer of online education. Online education should reflect the principles of pedagogical constructivism to ensure the development of students’ cognitive and social competencies. The paper describes the preparatory course of mathematics, realized in the form of MOOC. This course was created and implemented based on the principles of pedagogical constructivism. The analysis of the respondents’ approach to MOOC revealed a difference between bachelor and master students in the use of MOOC. Bachelors found a strong correlation between their approach to MOOCs and the way they are educated in secondary schools. The results of the research point to the need of more emphasis should be placed on advancing the learner’s skills in navigating and analysing information. The questionnaire filled in by the participants also monitored the students’ access to learning. The results of the experiment confirmed the connection between the preferred approach to learning and students’ activities within the MOOC. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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13 pages, 461 KiB  
Article
B-Learning in Basic Vocational Training Students for the Development of the Module of Applied Sciences I
by Francisco-Javier Hinojo-Lucena, Juan-Manuel Trujillo-Torres, José-Antonio Marín-Marín and Carmen Rodríguez-Jiménez
Mathematics 2020, 8(7), 1102; https://doi.org/10.3390/math8071102 - 05 Jul 2020
Cited by 6 | Viewed by 2675
Abstract
Information and communication technologies are a step forward in education, as they have given rise to innovative methodologies, such as blended learning. This type of training can be applied at any stage or educational typology such as basic vocational training. The main objective [...] Read more.
Information and communication technologies are a step forward in education, as they have given rise to innovative methodologies, such as blended learning. This type of training can be applied at any stage or educational typology such as basic vocational training. The main objective of this article is to know the degree of effectiveness of this methodology in this stage, specifically in an applied science module. For this purpose, a quasi-experimental design has been applied with a control group and an experimental group with a total of 147 participants. The results show how those students who have worked through b-learning have experienced better results in all the dimensions of the study. In conclusion, the implementation of this methodology in basic vocational training brings benefits, such as motivation and autonomy in the teaching–learning processes of all students. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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16 pages, 507 KiB  
Article
E-Learning in the Teaching of Mathematics: An Educational Experience in Adult High School
by Antonio-José Moreno-Guerrero, Inmaculada Aznar-Díaz, Pilar Cáceres-Reche and Santiago Alonso-García
Mathematics 2020, 8(5), 840; https://doi.org/10.3390/math8050840 - 22 May 2020
Cited by 62 | Viewed by 19506
Abstract
Currently, the e-learning method, due to the period of confinement that is occurring due to COVID-19, has increased its use and application in the teaching and learning processes. The main objective of this research is to identify the effectiveness of the e-learning method [...] Read more.
Currently, the e-learning method, due to the period of confinement that is occurring due to COVID-19, has increased its use and application in the teaching and learning processes. The main objective of this research is to identify the effectiveness of the e-learning method in the teaching of mathematics with adults who are in high school, in contrast to the traditional expository method. The study developed is quantitative, descriptive and correlational. The research design is quasi-experimental, with a control group and an experimental group. The results show that the use of the e-learning method has a positive influence on motivation, autonomy, participation, mathematical concepts, results and grades. It can be concluded that the e-learning method leads to improvement in adult students who are studying the mathematical subject in the educational stage of high school, provided that it is compared with the expository method. Therefore, this method is considered effective for its implementation in adults. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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Review

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10 pages, 649 KiB  
Review
Influence of Game-Based Learning in Mathematics Education on Students’ Affective Domain: A Systematic Review
by Peter Vankúš
Mathematics 2021, 9(9), 986; https://doi.org/10.3390/math9090986 - 28 Apr 2021
Cited by 20 | Viewed by 19587
Abstract
In modern education nowadays, the use of game-based learning as a teaching and learning method is popular in all school subjects, including mathematics. There are numerous studies dealing with the influences of this teaching method on the students’ achievements. Modern teaching theories consider [...] Read more.
In modern education nowadays, the use of game-based learning as a teaching and learning method is popular in all school subjects, including mathematics. There are numerous studies dealing with the influences of this teaching method on the students’ achievements. Modern teaching theories consider an important effect of education on the development of students’ affective domain, connected with the subject and its teaching. In this work, the author studies journal articles that the use game-based learning in mathematics to assess its effects on the students, with the aim to analyze its impact on students’ affective domain. To achieve this, a systematic review with the use of a PRISMA statement is applied. The data sources are 57 journal articles from the area of interest listed in the Web of Sciences and Scopus. The results indicate that 54% of the articles consider the affective domain in the measurement of the effects of game-based learning in mathematics education. These articles report mostly (84%) the positive influences of game-based learning on students’ motivation, engagement, attitudes, enjoyment, state of flow, etc. The rest of the articles show mixed results, with the authors’ conclusions possibly affected by flaws in the research instruments, selection of study groups, and game design, therefore, stressing the importance of these elements in future research on this topic. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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11 pages, 736 KiB  
Review
Impact of the Flipped Classroom Method in the Mathematical Area: A Systematic Review
by Francisco-Domingo Fernández-Martín, José-María Romero-Rodríguez, Gerardo Gómez-García and Magdalena Ramos Navas-Parejo
Mathematics 2020, 8(12), 2162; https://doi.org/10.3390/math8122162 - 04 Dec 2020
Cited by 21 | Viewed by 6505
Abstract
Currently, the use of technology has become one of the most popular educational trends in Higher Education. One of the most popular methods on the Higher Education stage is the Flipped Classroom, characterised by the use of both face-to-face and virtual teaching through [...] Read more.
Currently, the use of technology has become one of the most popular educational trends in Higher Education. One of the most popular methods on the Higher Education stage is the Flipped Classroom, characterised by the use of both face-to-face and virtual teaching through videos and online material, promoting more autonomous, flexible and dynamic teaching for students. In this work, we started to compile the main articles that used Flipped Classroom within the mathematical area in Higher Education, with the aim of analysing their main characteristics, as well as the impact caused on students. To do so, the method of systematic review was used, focusing on those empirical experiences published in Web of Sciences and Scopus. The results indicated that, in most cases, the implementation of Flipped Classroom led to an improvement in students’ knowledge and attitudes towards mathematical content and discipline. In addition, aspects such as collaborative work, autonomy, self-regulation towards learning or academic performance were benefited through this method. Full article
(This article belongs to the Special Issue Active Methodologies for the Promotion of Mathematical Learning)
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