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Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy

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

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 32886

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Prof. Dr. Antonio Rodríguez Fuentes

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Department of Didactics and School Organization, University of Granada, 52005 Melilla, Spain
Interests: Didactics and School Organization; Special Education; Communication difficulties Oral and written; communication Accessibility

Prof. Dr. José Luis Gallego Ortega

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Department of Didactics and School Organization, University of Granada, 18071 Granada, Spain
Interests: special education; attention to diversity; oral communication; oral language

Special Issue Information

Dear Colleagues,

The basic academic skills are reading, writing, and calculation. These are unquestionably necessary skills in school systems. Through very diverse methodologies and the combination of all kinds of personal, didactic, and technological resources, their development must be sought in all students. However, all students do not start, acquire, and develop these skills equally, but each collective and each student needs to find their own rhythm, path, and result. Special Needs Education (SNE) and/or Barriers to Learning and Participation (BLP) in communication and calculation require an attention to diversity by means of universal design for learning and the curriculum adaptation. The obligation of educational sciences and educational institutions is to guarantee and improve teaching in the above manner so that all students can acquire written communication and calculation. Only very exceptional cases will not manage to acquire or develop them to the extent desired. Let us focus on the first and not the last. That is the purpose of this monograph.

Prof. Dr. Antonio Rodríguez Fuentes
Prof. Dr. José Luis Gallego Ortega
Guest Editors

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Keywords

Inclusive Education
Special Needs Education (SNE)
Barriers to Learning and Participation (BLP)
Attention to Diversity
Universal Design for Learning (UDL)
Curriculum Adaptations
Didactics of Mathematics
Didactics of Oral Language
Didactics of Written Language (reading and writing)
Technologies for Communication
Technologies for Mathematics
Information and Communication Technologies (ICT)
Learning and Knowledge Technologies (LKT)
Neuroeducation

Published Papers (13 papers)

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Research

18 pages, 2357 KiB

Open AccessArticle

Statistical Validation of the “ECODIES” Questionnaire to Measure the Digital Competence of Colombian High School Students in the Subject of Mathematics

by Ana Bertha Betín de la Hoz, Antonio Rodríguez-Fuentes, María Jesús Caurcel Cara and Carmen del Pilar Gallardo Montes

Mathematics 2023, 11(1), 33; https://0-doi-org.brum.beds.ac.uk/10.3390/math11010033 - 22 Dec 2022

Cited by 1 | Viewed by 1384

Abstract

Education in the 21st century faces the challenge of digitalization; therefore, the acquisition and development of digital skills in students is indispensable, not only for their learning processes but also for their lives. This study aims to validate the test “ECODIES”, which was used to assess the level of development of digital competence in students in a public high school in Bogotá (Colombia). The test is based on the DigCom model and was administered to a sample of 777 students aged between 11 and 18. The results obtained in the exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and reliability analysis show the quality of the test. Therefore, in this study it is concluded that “ECODIES” is a test with the reliability and validity to assess digital competence in the Colombian context; in this way, we hope to gain enough research about this topic to contribute to the development of digital competence in Colombian students. We conducted an instrumental study for the analysis of the psychometric properties of the questionnaire. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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22 pages, 1748 KiB

Open AccessArticle

Neurodidactics of Languages: Neuromyths in Multilingual Learners

by Antonia Navarro Rincón, María José Carrillo López, César Augusto Solano Galvis and Laura Isla Navarro

Mathematics 2022, 10(2), 196; https://0-doi-org.brum.beds.ac.uk/10.3390/math10020196 - 09 Jan 2022

Viewed by 2809

Abstract

From the perspective of neuroscience applied to education and the teaching of foreign languages, this exploratory study analyzes the beliefs and conceptions about the functioning of the brain and language learning in students enrolled in Education degrees at the Melilla campus of the University of Granada. The sample consisted of 397 participants. The data collection was carried out by means of a questionnaire designed for this purpose, consisting of questions related to the context and linguistic background of the respondents and to educational neuromyths regarding language learning. The data were analyzed using the SPSS version 27 statistical software, and univariate and bivariate analyses were carried out according to the three grouping dimensions: (a) brain functioning, (b) multiple intelligences and learning styles, and (c) language learning. The results indicate the prevalence of neuromyths related to general concepts, which determine the learning comprehension. This corroborates the findings of research studies in other contexts. Although the participants do not show a prevalence of neuromyths regarding foreign language learning, presumably due to their experiences in multilingual contexts, which constitutes the main contribution of this study. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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25 pages, 1031 KiB

Open AccessArticle

Epistemic Complexity of the Mathematical Object “Integral”

by Enrique Mateus-Nieves and Vicenç Font Moll

Mathematics 2021, 9(19), 2453; https://0-doi-org.brum.beds.ac.uk/10.3390/math9192453 - 02 Oct 2021

Cited by 3 | Viewed by 1740

Abstract

The literature in mathematics education identifies a traditional formal mechanistic-type paradigm in Integral Calculus teaching which is focused on the content to be taught but not on how to teach it. Resorting to the history of the genesis of knowledge makes it possible to identify variables in the mathematical content of the curriculum that have a positive influence on the appropriation of the notions and procedures of calculus, enabling a particularised way of teaching. Objective: The objective of this research was to characterise the anthology of the integral seen from the epistemic complexity that composes it based on historiography. Design: The modelling of epistemic complexity for the definite integral was considered, based on the theoretical construct “epistemic configuration”. Analysis and results: Formalising this complexity revealed logical keys and epistemological elements in the process of the theoretical constitution that reflected epistemological ruptures which, in the organisation of the information, gave rise to three periods for the integral. The characterisation of this complexity and the connection of its components were used to design a process of teaching the integral that was applied to three groups of university students. The implementation showed that a paradigm shift in the teaching process is possible, allowing students to develop mathematical competencies. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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24 pages, 1261 KiB

Open AccessArticle

Learning Effect in a Multilingual Web-Based Argumentative Writing Instruction Model, Called ECM, on Metacognition, Rhetorical Moves, and Self-Efficacy for Scientific Purposes

by Rosario Arroyo González, Eric Fernández-Lancho and Juan Antonio Maldonado Jurado

Mathematics 2021, 9(17), 2119; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172119 - 01 Sep 2021

Cited by 3 | Viewed by 2357

Abstract

The purpose of this study is to assess the learning effect of a multilingual web-based argumentative writing instruction model called the Ensayo Científico Multilingüe (ECM, Multilingual Scientific Essay) adapting the didactic model called Genre-based Writing Instruction (GBWI) in an experiment conducted over three months. For this purpose, a quasi-experimental research model was applied to 150 students in the experimental group and 150 in the control group, with two measurements, pre and post-test, for three dependent variables: (a) writing metacognition and its dimensions; (b) written argumentative self-efficacy; and (c) rhetorical moves and steps of an argumentative essay. The latter variable was measured by the content analysis method. Variables (a) and (b) were both measured with instruments validated in a population of 518 university students using structural equations. The findings demonstrate the positive effect of the ECM, which combines WBWI and GBWI in argumentative written learning in the students’ mother tongue in all variables measured, applying statistics such as the Shapiro–Wilk statistic, parametric contrast, and the Wilcoxon signed-rank test. In relation to the findings, with respect to the evaluated variables, it was discovered, specifically, that the rhetorical steps in which the students showed a significant improvement were innovations, quotes/research, definitions of concepts, refutations, definitive reasons, and bibliographical references. Likewise, the rhetorical steps that did not present significant differences following the application of the ECM were discovered, and they were: reason summary, formulation of premise, and reasons for. Furthermore, it can be stated that for the ECM there was an increase, above all, in awareness of the following metacognitive dimensions: (a) writing self-regulation; (b) writing planning; and (c) writing revision, as well as argumentative self-efficacy. The novelties of this research with respect to the precedents reside in that it offers valid and concrete results on the effect of a multilingual web design integrated into a well-defined didactic model of argumentative writing on writing metacognition and its dimensions, argumentative structuring and its rhetorical steps, and argumentative self-efficacy. The related studies consider only some of these variables, but not all of them together or their complexity. These results have allowed us to establish specific didactic–technological proposals for improving the ECM that are transferable to didactic designs to guide written argumentation at higher academic levels using multilingual web technologies and integrating the metacognitive, behavioral, and motivational dimensions of writing. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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14 pages, 19847 KiB

Open AccessArticle

Learning Ecologies in the Digital Era: A Challenge for Primary Education in Low-Income Contexts

by Celia Moreno-Morilla, Fernando Guzmán-Simón and Eduardo García-Jiménez

Mathematics 2021, 9(17), 2108; https://0-doi-org.brum.beds.ac.uk/10.3390/math9172108 - 31 Aug 2021

Viewed by 1606

Abstract

This research focused on the study of learning ecologies utilizing digital technology. The qualitative methodology used has allowed the analysis of the interactions children establish with digital technologies and the manner in which they construct a learning ecology. A total of 46 12-year-olds, their families, and their teachers participated in this study. The children’s schools and homes were in neighborhoods where structural situations of poverty and social and cultural marginality concurred. The children integrated researchers into their digital community, which allowed access to the events that the community was developing through digital technologies for two years. This information was complemented by the development of systematic observations and interviews with each participant. The participants’ multimodal linguistic and literacy practices were analyzed using a social semiotics approach. The results of the research describe and interpret the interactions that took place between participants and digital technologies. The research has identified the processes of recontextualization, transduction, and transcontextualization of the discourses developed in the frame of the participants’ learning ecologies. Digital ethnography has been revealed as an adequate method for studying learning ecologies. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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17 pages, 1254 KiB

Open AccessArticle

A Revisited Conceptual Change in Mathematical-Physics Education from a Neurodidactic Approach: A Pendulum Inquiry

by Julio Ballesta-Claver, María Fernanda Ayllón Blanco and Isabel Angustias Gómez Pérez

Mathematics 2021, 9(15), 1755; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151755 - 26 Jul 2021

Cited by 1 | Viewed by 2272

Abstract

Learning physics today contains a strong algebraic component, which does not contribute to making an effective conceptual change due to several misunderstandings and misconceptions that students have. Inquiry-based science education methodology (IBSE) is a solution, as well as model-based inquiry (MBI), but no agreement exists regarding which one is the best option. The contribution of both new neuroscientific and cognitive psychology advances is necessary. All these components can be arranged within a transdisciplinary discipline called Neurodidactics. This work presents a neurodidactic proposal to achieve an effective conceptual change. The study involves 171 undergraduate university students and is based on an experimental design (control and experimental groups) with pre- and post-test questionnaires. Results will show the importance of experimentation in mathematical-physics sessions, as well as the importance of visuospatial abilities and the inquiry component offered by the different resources used (virtual simulations and multimedia) in order to obtain a model. In addition, the role of transdisciplinary orientation and the importance of conceptual modeling was tested, obtaining an essential contribution to balance the normally non-significant algebraic approach of physics science, offering altogether a possible new path for scientific learning. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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16 pages, 347 KiB

Open AccessArticle

Mathematics Preservice Trainee Teachers’ Perceptions of Attention to Diversity in Initial Training as Secondary Education Teachers

by María Jesús Caurcel Cara, Emilio Crisol Moya and Carmen del Pilar Gallardo-Montes

Mathematics 2021, 9(14), 1697; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141697 - 19 Jul 2021

Cited by 2 | Viewed by 2017

Abstract

Research on teachers’ perceptions about diversity is key to understanding the different approaches to be implemented to build inclusive education. Within this framework, the perceptions and attitudes of 73 students in the Mathematics specialization of the University Master’s Degree in Teacher Training for Secondary Education, Bachillerato, Vocational Training and Language Teaching (Máster Universitario en Profesorado de Educación Secundaria Obligatoria, Formación Profesional y Enseñanza de Idiomas (MAES) at the University of Granada (Spain) were analyzed to determine their views about the initial training they received on attention to diversity during the Master’s program. The study is a descriptive and correlational-predictive transversal examination of the responses obtained from the “Questionnaire for preservice secondary education teachers on perceptions about attention to diversity” (Colmenero Ruiz and Pegalajar Palomino, 2015). The findings demonstrate that the students—preservice secondary education teachers—held favorable attitudes toward diversity and the principle of inclusion. The findings also show that contact with persons with disability influences perception of this population. The authors conclude that better training and knowledge of the elements that condition the teaching–learning process for high-quality attention to diversity predict better pedagogical preparation in matters of attention to diversity. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

11 pages, 296 KiB

Open AccessArticle

Teaching Attitudes towards Students with Disabilities

by José Luis Gallego-Ortega and Antonio Rodríguez-Fuentes

Mathematics 2021, 9(14), 1637; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141637 - 11 Jul 2021

Cited by 6 | Viewed by 5020

Abstract

(1) Background: Inclusive education has been a recurring topic during the last decades. However, not every teacher is equally enthusiastic about how to implement it. Understanding these discrepancies can help to identify improvement procedures. Therefore, even though teachers’ beliefs and attitudes around inclusion have been thoroughly explored, it is necessary to delve further on this type of study to understand possible changes derived from the socio-educational transformations experimented by current societies. (2) Methods: This study examined the attitudes of 122 teachers, both Primary and Special Needs ones, working in rural and urban schools, regarding inclusion of students with disabilities. The data were collected from two scales: Attitude Survey Inclusive Education–Teachers (ASIE-T) and Scale for Measuring Pre-Service Teachers’ Perceptions about Inclusion the Sentiments, Attitudes and Concerns about Inclusive Education Revised (SACIE-R). A quantitative approach was employed, of descriptive and correlational type. Descriptive and inferential analyses were performed by means of parametric tests. Furthermore, the bivariate correlation technique Person’s r was carried out in order to verify the intensity among variables. The effect sizes are provided as Cohen’s d. (3) Results: The results revealed positive beliefs concerning inclusion and the existence of differences among teachers, depending on their specialisation and gender. The variables “age” and “stage of education” were not significant in terms of generating in terms of attitude generation. (4) Conclusions: Understanding the association between socio-demographic variables and stigma is crucial when it comes to accomplishing an inclusive and high-quality education. The general findings of this study contribute to justify the implementation of programmes to stimulate and encourage meaningful interactions between general education teachers and students with disabilities. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

11 pages, 442 KiB

Open AccessArticle

Effectiveness of a Long-Term Training Programme for Teachers in Attention-Deficit/Hyperactivity Disorder on Knowledge and Self-Efficacy

by Sonia Jarque Fernández, Laura Amado Luz, Marta Oporto Alonso and Marina Fernández-Andújar

Mathematics 2021, 9(12), 1414; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121414 - 18 Jun 2021

Cited by 3 | Viewed by 2754

Abstract

The active participation of teachers in the process of diagnosis and intervention of Attention-Deficit/Hyperactivity Disorder (ADHD) is relevant to helping mitigate future problems in children with ADHD. In training programmes, teachers usually implement strategies to improve the child’s functioning after participating in an ADHD management-training programme. However, they receive little psycho-educational training and coaching and have low-to-moderate levels of knowledge of the disorder, mostly in terms of training in classroom management strategies. This study analyses the effectiveness of training in increasing knowledge and perceived self-efficacy with regard to ADHD in 40 primary school teachers. Twenty of these teachers participated in a long-term psycho-educational training programme on the management of ADHD (intervention multimodal group), while the other 20 did not (control group). The results of the post-treatment phase revealed statistically significant differences between the two groups of teachers with regard to their knowledge (Z = −5.427; p = 0.000; d = 0.89) and perceived self-efficacy (Z = −5.150; p = 0.000; d = 0.79), in favour of the participants who had received training. Our findings have important implications for the design of training programmes for teachers in the management of ADHD in the classroom. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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10 pages, 243 KiB

Open AccessArticle

An Analytical Perspective of the Reliability of Multi-Evaluation in Higher Education

by Antonio Rodríguez Fuentes and José Luis Gallego Ortega

Mathematics 2021, 9(11), 1223; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111223 - 27 May 2021

Cited by 2 | Viewed by 1628

Abstract

It is urgent to evaluate the rest of the renewed elements within the university didactic action, overcoming the hegemony of traditional methods in which the professor constitutes as the sole evaluator. If autonomous and cooperative group-based learning is encouraged, self-assessment and co-assessment must also be promoted, apart from the traditional lecturing and evaluation by others. The assessing competence of Teacher Training degree students (n = 175) was researched, started with stratified sampling (in the second and fourth years), following a participant selection process in each group. The compiled data were subject to descriptive, inferential, and correlation analysis by means of statistical software. The results pointed to low execution levels as for the self-evaluation (individual and group), although a certain progress was identified in the four year students compared to those in their second year of study. A better execution in evaluation was observed in all students regarding co-assessment (among different work groups in the classroom) and assessment by others (towards the professor). The use of all types of assessment is proposed, having a certain awareness and training regarding self-evaluation, and counting with a full supervision and control over it. All in all, the advantages of multiple and democratic assessment surpass the drawbacks derived from them. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

14 pages, 490 KiB

Open AccessArticle

Statistical Analysis of the Evolutive Effects of Language Development in the Resolution of Mathematical Problems in Primary School Education

by M. M. Rodríguez-Hernández, R. E. Pruneda and J. M. Rodríguez-Díaz

Mathematics 2021, 9(10), 1081; https://0-doi-org.brum.beds.ac.uk/10.3390/math9101081 - 11 May 2021

Cited by 3 | Viewed by 2032

Abstract

For primary school students, the difficulty in solving mathematical problems is highly related to language capacity. A correct solution can only be achieved after being able to deal with different abstract concepts through several stages: comprehension, processing, symbolic representation and relation of the concepts with the right mathematical operations. A model linking the solution of the mathematical problems (PS) with the mental representation (MR) of the problem statement, while taking into account the level of the students (which has influence in the linguistic abilities), is presented in this study. Different statistical tools such as the Analysis of Covariance (ANCOVA), ROC curves and logistic regression models have been applied. The relation between both variables has been proved, showing that the influence of MR in PS is similar in the different age groups, with linking models varying just in the constant term depending on the grade level. In addition, a cutoff in the mental representation test is provided in order to predict the student’s ability in problem resolution. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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17 pages, 645 KiB

Open AccessArticle

Assessment of Apps Aimed at Developing Basic Instrumental Skills in Autistic Children and Teenagers

by Carmen del Pilar Gallardo-Montes, María Jesús Caurcel Cara, Emilio Crisol Moya and Sonia Jarque Fernández

Mathematics 2021, 9(9), 1032; https://0-doi-org.brum.beds.ac.uk/10.3390/math9091032 - 02 May 2021

Cited by 6 | Viewed by 2783

Abstract

It is crucial for families and professionals to promote basic instrumental skills in children with autism, as these skills can help with comprehensive growth and development, and are a starting point in acquiring the essential tools needed for one to live an independent and successful life. These skills include oral language, reading, writing, and mathematics. Therefore, given that ICT and mobile applications (apps) are effective tools that offer suitable content, and are designed exclusively for people with this disorder, working on these skills with apps is an interesting option that is worthy of our attention. We analyzed 88 apps that focused on these skills, through a duly validated system of indicators, calculating frequencies, percentages, measures of central tendency and dispersion, and non-parametric contrast statistics. The app search was carried out in the Google Play Store, with the keyword “autism”, in English and in Spanish. Most of the apps focused on aspects linked to oral language and reading, but few were aimed at reading and mathematics. In addition to the apps’ lack of specialization in the last two skills, the vast majority did not specify the age group for which their content was intended. Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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27 pages, 371 KiB

Open AccessArticle

Coping with Challenges in Teaching Foreign Languages to Children with Mild Intellectual Disabilities: Stakeholders’ Perspectives

by Cristina Pérez-Valverde, Raúl Ruiz-Cecilia, Leopoldo Medina-Sánchez and Juan Ramón Guijarro-Ojeda

Mathematics 2021, 9(8), 906; https://0-doi-org.brum.beds.ac.uk/10.3390/math9080906 - 19 Apr 2021

Cited by 1 | Viewed by 2220

Abstract

In this qualitative study, we aim to gain insight into the stakeholders’ perspectives around the inclusion of a mild intellectual disability (MID) student of perinatal origin in the foreign language (FL) classroom, and their perspectives on the student’s working conditions, and the support needed to effectively develop this student’s basic FL skills. The research hypothesis holds that the stakeholders face numerous technical, contextual, and formative challenges which hinder the MID student’s learning conditions in the FL classroom. The study was carried out in a state secondary school of the metropolitan area of Granada (Spain). Different stakeholders participated in this study. As an instrument of research, we designed an in-depth interview with open questions. The data were perused, sifted, and interpreted by means of a content analysis methodology. The main results confirm the research hypothesis since stakeholders’ perspectives are positive towards the theoretical bases of inclusive education. Conversely, we observe that these perspectives are negative when it comes to the real and effective practice of inclusive education in the FL classroom, which would allow them to tailor their teaching methodology to the real needs of the MID student and the rest of students with special educational needs (SEN). Full article

(This article belongs to the Special Issue Inclusive Mathematics Education and Basic Academic Skills: Language and Numeracy)

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