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Special Issues
Recent Advances in Mathematics Education
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Recent Advances in Mathematics Education

A special issue of European Journal of Investigation in Health, Psychology and Education (ISSN 2254-9625).

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 14160

Special Issue Editors

Prof. Dr. Michael Voskoglou

E-Mail Website
Guest Editor
Graduate Technological Educational Institute (T.E.I.) of Western Greece, School of Technological Applications, 263 34 Patras, Greece
Interests: fuzzy sets and logic; Markov chains; abstract and linear algebra; artificial intelligence; mathematics education
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Joanna Mamona-Downs

E-Mail Website
Guest Editor
Mathematics Department, University of Patras, 263 34 Patra, Greece
Interests: understanding of the main concepts of real analysis; problem solving in mathematics; problem posing in mathematics; the fine differences and interconnections of problem solving and proof in mathematics

Special Issue Information

Dear Colleagues,

The Special Issue ‘Recent Advances in Mathematics Education’ will focus on contemporary research outcomes and quality review papers regarding the teaching and learning of mathematics at all levels of education.

The proposed topics of this issue include, but are not limited to, the following:

(I) Themes of general interest

  • Theories and methods of teaching and learning mathematics
  • Problem solving and problem posing
  • Mathematical modelling
  • Argumentation and proof (pertaining to mathematical subjects)
  • Computers and artificial intelligence in mathematics education

(II) Elementary Education

  • Teaching and learning of arithmetic, geometry and statistics
  • Special education

(III) Secondary Education

  • Teaching and learning of algebra, geometry, calculus, probability and statistics

For Algebra: Themes as the transition from arithmetic to algebra, the difficulties brought by symbolization and the ways that students justify mathematical statements and propositions in the (new for them) symbolic environment.

For Geometry: Themes as the paradigm of Euclidean geometry and the effect of its gradual elimination on students’ ability to justify, prove and visualize.

For Calculus: Methods of teaching that enable a deep understanding of the basic concepts and principles of calculus.

For Probability and Statistics: Methods of teaching and usefulness in everyday life.

  • Other mathematical topics in secondary education (logic, number theory, etc.)
  • Education of mathematically gifted students: proposals with respect to the design of mathematical tasks that aim to assess and foster the mathematical giftedness and creativity of these students.

(IV) Tertiary Education

  • Bridging the gap between mathematics taught at school and the subject as evolved at university level, especially the transition from calculus to analysis.
  • Difficulties (and proposals on how to tackle them) concerning the fundamentals of number theory, combinatorics, abstract algebra and graph theory.
  • Teaching new approaches of mathematics (fuzzy sets and systems, chaos theory and fractals, etc.)

Prof. Dr. Michael Voskoglou
Prof. Dr. Joanna Mamona-Downs
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. European Journal of Investigation in Health, Psychology and Education 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 1400 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 learning
  • smart learning systems
  • problem solving
  • problem posing
  • mathematical modelling
  • analogical and case-based reasoning
  • critical thinking
  • computational thinking
  • mathematical proof

Published Papers (6 papers)

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Editorial

Jump to: Research

2 pages, 196 KiB  
Editorial
Introduction to the Special Issue on Recent Advances in Mathematics Education
by Michael Gr. Voskoglou and Joanna Mamona-Downs
Eur. J. Investig. Health Psychol. Educ. 2022, 12(10), 1498-1499; https://doi.org/10.3390/ejihpe12100103 - 04 Oct 2022
Viewed by 1168
Abstract
The Special Issue with the title “Recent Advances in Mathematics Education” presents contemporary research outcomes regarding the teaching and learning of Mathematics at all levels of Education [...] Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)

Research

Jump to: Editorial

13 pages, 595 KiB  
Article
Mathematics Teachers’ Encouragement of Their Students’ Metacognitive Processes
by Wajeeh Daher and Iman Hashash
Eur. J. Investig. Health Psychol. Educ. 2022, 12(9), 1272-1284; https://doi.org/10.3390/ejihpe12090088 - 01 Sep 2022
Cited by 6 | Viewed by 1939
Abstract
Researchers have conducted little research into teachers’ practices to encourage their students’ metacognition. The present research attempted to address this issue quantitatively by suggesting a questionnaire that measured teachers’ encouragement of students’ planning, monitoring, regulating, and evaluating. We present the results of the [...] Read more.
Researchers have conducted little research into teachers’ practices to encourage their students’ metacognition. The present research attempted to address this issue quantitatively by suggesting a questionnaire that measured teachers’ encouragement of students’ planning, monitoring, regulating, and evaluating. We present the results of the validity and reliability of the questionnaire. In addition, using a one-sample t-test, the results of the research revealed “normal”, “good”, and “very good” levels of teachers’ encouragement of their students’ metacognitive practices. The present research utilized an independent-sample t-test to investigate the significance of the difference in teachers’ metacognitive practices due to gender and to academic qualification. The results indicated that the metacognitive practices for male and female teachers were significantly different in planning and regulating, while the differences were not significant in monitoring and evaluating. In addition, the research results indicated that the participating teachers’ practices related to students’ metacognitive processes did not differ significantly due to the teachers’ academic qualification. When utilizing a one-way ANOVA test to investigate the significance of the difference in teachers’ metacognitive practices due to years of experience, this difference was not significant for any of the factors of metacognitive practices. Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)
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10 pages, 828 KiB  
Article
Personal Need for Structure and Fractions in Mathematical Education
by Valéria Švecová, Ľubomír Rybanský and Gabriela Pavlovičová
Eur. J. Investig. Health Psychol. Educ. 2022, 12(5), 448-457; https://doi.org/10.3390/ejihpe12050033 - 29 Apr 2022
Cited by 3 | Viewed by 1798
Abstract
The research was aimed at finding relations between mathematical knowledge and cognitive individual variable. We realized the experiment with 162 students of the Constantine the Philosopher University in Nitra, Slovakia. We had two variables—the personal need for structure (PNS) as a cognitive-individual variable [...] Read more.
The research was aimed at finding relations between mathematical knowledge and cognitive individual variable. We realized the experiment with 162 students of the Constantine the Philosopher University in Nitra, Slovakia. We had two variables—the personal need for structure (PNS) as a cognitive-individual variable and knowledge of the fraction as a mathematical variable. The relationships between the factors of the personal need for structure scale and the knowledge of fractions were determined by the IRT model. We have proven a negative correlation between the successful solving of fraction test and score in the PNS scale. This means that the higher the success rate of solving the fraction tasks, the lower the overall score on the personal need for structure scale and its subfactors. Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)
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11 pages, 496 KiB  
Article
The Language of “Rate of Change” in Mathematics
by Evgenios Avgerinos and Dimitra Remoundou
Eur. J. Investig. Health Psychol. Educ. 2021, 11(4), 1599-1609; https://doi.org/10.3390/ejihpe11040113 - 06 Dec 2021
Cited by 2 | Viewed by 2431
Abstract
Language is an essential aspect of teaching and learning mathematics. It is necessary for communication, the transmission of concepts and ideas, and the formation of meaning of mathematical concepts. In mathematics, besides symbols, which are usually common among different languages, words and expressions [...] Read more.
Language is an essential aspect of teaching and learning mathematics. It is necessary for communication, the transmission of concepts and ideas, and the formation of meaning of mathematical concepts. In mathematics, besides symbols, which are usually common among different languages, words and expressions are used, which may invoke different concept images to students in various languages. Some words are used in mathematics and in everyday language with different meanings, while others are used only in mathematics or in mathematics and other disciplines in similar but non-identical ways. In Mathematical Analysis, the used vocabulary is gradually enhanced, and the concepts are defined in a more formal way. In the current study, the language used regarding mathematics of change is examined, focusing on “rate of change”, and its relation to misconceptions among students. Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)
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18 pages, 1991 KiB  
Article
From Formulas to Functions through Geometry: A Path to Understanding Algebraic Computations
by Alice Barana
Eur. J. Investig. Health Psychol. Educ. 2021, 11(4), 1485-1502; https://doi.org/10.3390/ejihpe11040106 - 19 Nov 2021
Cited by 5 | Viewed by 2555
Abstract
The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to algebra and giving [...] Read more.
The teaching of algebra at the secondary school level has faced a great revolution during the last 50 years. While previously, it was focused on technicisms and pure syntactic rules, the most modern trends recommend using a functional approach to algebra and giving more prominence to conversions among different representation registers than treatments as simplifications and expansions. Nowadays, the daily practice in teaching algebra is still influenced by the traditional approach, and there is a need to offer teachers examples of activities that can give meaning to algebraic computations. This study proposes a set of interactive activities for eighth grade students, with a functional approach to formulas in a geometric context. The goal of the study is to investigate how similar activities can help students to develop multiple approaches to problems, understand algebraic formulas, and discern which main problems they face. The activities were tested with about 300 students, and qualitative and quantitative data were analyzed to answer the research questions. Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)
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19 pages, 2017 KiB  
Article
Mathematics Classroom Assessment: A Framework for Designing Assessment Tasks and Interpreting Students’ Responses
by Eleni Demosthenous, Constantinos Christou and Demetra Pitta-Pantazi
Eur. J. Investig. Health Psychol. Educ. 2021, 11(3), 1088-1106; https://doi.org/10.3390/ejihpe11030081 - 18 Sep 2021
Cited by 3 | Viewed by 2608
Abstract
Classroom assessment could contribute substantially to improving students’ mathematics learning. The process of classroom assessment involves decisions about how to elicit evidence, how to interpret it, and how to use it for teaching and learning. However, the field still needs to further explore [...] Read more.
Classroom assessment could contribute substantially to improving students’ mathematics learning. The process of classroom assessment involves decisions about how to elicit evidence, how to interpret it, and how to use it for teaching and learning. However, the field still needs to further explore how assessment tasks could guide forthcoming instructional adjustments in the mathematics classroom. Towards the endeavor of unpacking the classroom assessment, we present a framework that provides a lens to capture the interplay between the design of mathematics assessment tasks and the analysis of students’ responses. To do so, we relied on existing frameworks of mathematics assessment tasks, and on issues that pertain to the design of tasks. The proposed framework consists of three types of mathematics assessment tasks, their respective competencies, and the characterization of students’ responses. The framework is exemplified with students’ responses from a fourth-grade classroom, and is also used to sketch different students’ profiles. Issues regarding the interpretation of students’ responses and the planning of instructional adjustments are discussed. Full article
(This article belongs to the Special Issue Recent Advances in Mathematics Education)
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