Special Issue "Recent Advances in Mathematics Education"

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 papers will be 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 quarterly 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 1000 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.

• mathematical learning
• smart learning systems
• problem solving
• problem posing
• mathematical modelling
• analogical and case-based reasoning
• critical thinking
• computational thinking
• mathematical proof

Title: The “Language” of Rate of Change in Mathematics Education
Authors: Prof. Evgenios Avgerinos and Dimitra Remoundou
Abstract: Language is an essential aspect of teaching and learning mathematics. It is necessary for communicating, transmission of concepts and ideas and formation of meaning of mathematical concepts. In mathematics, besides symbols, which are usually common in 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 in relation to misconceptions of students.
Keywords: Calculus; Rate of change; Language of mathematics; Mathematics education

Title: Analyzing Examination Problems of Students of Mathematics Following a Didactics of Mathematics Course
Author: Dr. Andreas Poulos
Abstract: The projected submission will present an analysis of mathematics undergraduates’ answers in an exam paper for the course ‘Didactics of Mathematics’ at a Greek University. The course was on Problem Solving, based on Polya’ s tradition. We will focus on three exam questions; each exam question is from a different exam paper, taken at different examination periods by about 100 students. The main research questions are the following: 1. Whether the theoretical background on Problem Solving, fostered in the course, strengthened students actual problem-solving strategies. 2. How is the student’s total score on the final exam in the Mathematics Didactics course related to the student’s performance on the Problem- Solving exam questions. 3. Is it justified for a student studying in a Mathematics Department, at University, not to be able to solve problems at the level of the given questions?
Keywords: Didactics of Mathematics; Problem Solving; Evaluation of Exam Papers

Title: Relationships between Domain General and Domain Specific Creativity: Focusing on Mathematics
Authors: Roza Leikin. Adi Araki, Estee Mann, Lior Miller
Abstract: Mathematical giftedness is usually associated with concepts of general giftedness and mathematical expertise (Leikin et al., 2017). We employ distinction between general giftedness (G) and excellence in mathematics (EM) to examine relationships between general ability, mathematical ability, general creativity and mathematical creativity. The study includes a sample of 101 students who study in two academic institutions in Israel who completed Raven test, SAT-M test along with mathematical and pictorial Multiple Solution Tasks (MST) ). We find that general giftedness has a meaningful effect on students' mathematical creativity, while mathematical expertise strengthened this effect with respect to flexibility component of creativity. This study gives strength to the definition of mathematical expertise based on general giftedness. We also found walk relationship between general and mathematical creativity and support the proponents of domain specific nature of creativity.