International Electronic Journal of Mathematics Education

The evolution of mathematics coincided with advancements in its teaching. The 19&lt;sup&gt;th&lt;/sup&gt; and 20&lt;sup&gt;th&lt;/sup&gt; centuries marked a pedagogical revolution in mathematics education. This paper argues that Bruner’s (1966) model, Gagné’s (1985) taxonomy, innovative teaching methods emphasizing research and problem-solving, and the inclusion of data analysis topics have shaped modern mathematics education. Additionally, the paper explores transformative trends, emphasizing mathematics literacy and the integration of virtual reality (VR) and artificial intelligence (AI) in education. This evolution emphasizes practical, contextually relevant approaches. VR enhances engagement and comprehension of abstract concepts, while AI offers personalized learning experiences, fostering deeper understanding and skill development.

Mara Cotič

Daniel Doz

Matija Jenko

Amalija Žakelj

Mathematics education: What was it, what is it, and what will it be?

数学教育：它曾经是什么，现在是什么，未来又将会是什么？

The purpose of this study is to conduct a bibliometric analysis of the research published in the field of mathematics misconception from 1947 to 2023, to determine the general knowledge structure and participation in research publication. An analytical approach was used based on Scopus database data. This study used mixed methods; quantitative method to summarize the articles using bibliometric analysis, and qualitative method to analyze the content of the most cited papers on mathematics misconception. The results showed that research publications on mathematics misconceptions have increased over time. The majority of the researchers and educational institutions who published papers about mathematics misconceptions were from the USA, England, and Turkey. The most used keywords were teaching, students, and education. The qualitative analysis identified (23) common mathematics misconceptions, which were grouped into four categories: general mathematics misconception, algebraic mathematics misconception, trigonometric mathematics misconception, and calculus mathematics misconception.

Rana J.Y. Aleifat

Ahmad A.S. Tabieh

A bibliometric analysis of scientific articles on mathematics misconceptions

数学误解科学文章的文献计量分析

Understanding part-whole relations is crucial in early mathematics education. However, both analogue and digital learning environments often lack systematic approaches to foster part-whole understanding. With the rising popularity of educational apps, it is essential to evaluate how they implement learning of part-whole relations. Accordingly, this review aims to evaluate whether educational math apps provide a systematic approach to learn part-whole relations. Therefore, we first developed a framework for evaluating apps with a focus on opportunities for learning part-whole relations. Second, we applied this framework to evaluate n =&lt;i&gt; &lt;/i&gt;18 apps. Results indicated that none of the reviewed apps implemented a systematic approach to learn part-whole relations from hands-on to more abstract compositions/decompositions including number triples up to ten. In contrast, the automating of number compositions/decompositions is most frequently targeted. These findings underscore the importance of selecting educational apps carefully and integrating principles from effective learning environments and digital learning research into future app design.

Caroline Marx

Stephanie Roesch

Korbinian Moeller

Christiane Benz

From the whole to its parts – A systematic analysis of affordances for learning part-whole-relations in digital apps

从整体到部分——数字应用中学习整体-部分关系的功能系统分析

Knowing functions and functional thinking have recently moved from just knowledge for older students to incorporating younger students, and functional thinking has been identified as one of the core competencies for algebra. Although it is significant for mathematical understanding, there is no unified view of functional thinking and how different aspects of the concept are used as a theoretical base. In this paper, we analyse different definitions used in empirical studies. First, we did a systematic research review resulting in 19 empirical studies focusing on functional thinking with an appropriate theoretical underpinning. The definitions were analysed using an AI tool. After that, we analysed the results using intrinsic mathematical properties of how functions can be defined in mathematics to identify core aspects of the definitions. According to the analysis, two definitions capture most of the key aspects of functional thinking, and most empirical studies use these key concepts. These two definitions treat functional thinking as products or products and processes. One definition used in one empirical study stands out by theoretically operationalizing functional thinking as a process. As such, different ontological assumptions are made in the studies; however, in some cases, having the same epistemological outcome. From a methodological point of view, the cosine similarity matrix was a useful tool for an ontological analysis, but a qualitative analysis is still needed to make meaning of it.

Lovisa Sumpter

Anneli Blomqvist

What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

功能思维是什么？在语义本体分析中使用余弦相似度矩阵

The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public institution in Barranquilla, Colombia. The diagnostic test revealed difficulties in the concept of linear function and the modelling of situations. Therefore, a laboratory was implemented with eight activities focused on the concept of linear function, variation situations, generalization and conversion between different representations of the linear function (verbal, numerical, tabular, graphical, and algebraic). The results showed a significant advance in the variational thinking of the students, who managed to establish connections between different representations, procedural, metaphorical and better understand the meanings of the linear function. Also, the type of mathematical tasks used promote mathematical connections and variational thinking about the linear function and applications.

Karina Nuñez-Gutierrez

Camilo Andrés Rodríguez-Nieto

Lisseth Correa-Sandoval

Vicenç Font Moll

High school Colombian students’ variational thinking triggered by mathematical connections in a laboratory on linear functions

哥伦比亚高中生在直线函数实验室中通过数学联系引发的变异思维

This paper describes the design, implementation, and results of a training action with prospective primary education teachers, focusing on the creation of problems involving proportional and algebraic reasoning. Prospective teachers must solve a proportionality problem using both arithmetic and algebraic procedures, and then vary it to motivate proto-algebraic activity. Results show that participants successfully solved the task and created significant problems, which mostly motivated the expected algebraic activities. However, it can be observed that aspects of proportional reasoning or representations typical of proto-algebraic levels were not considered, which could have generated greater richness in the variety of problems created.

Abbreviation	Int. Electron. J. Math. Educ.
Journal Impact	0.49
Quartiles(Global)	EDUCATION, SCIENTIFIC DISCIPLINES(Q4)

Publication Information	Publisher: Modestum LTD，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2020，Proportion of original research papers: 93.55%，Self Citation Rate:， Gold OA Rate: 100.00%

International Electronic Journal of Mathematics Education

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Mathematics education: What was it, what is it, and what will it be?

A bibliometric analysis of scientific articles on mathematics misconceptions

From the whole to its parts – A systematic analysis of affordances for learning part-whole-relations in digital apps

What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

High school Colombian students’ variational thinking triggered by mathematical connections in a laboratory on linear functions

A bibliometric analysis of scientific articles on mathematics misconceptions

From the whole to its parts – A systematic analysis of affordances for learning part-whole-relations in digital apps

What is functional thinking? Using cosine similarity matrix in a semantic ontological analysis

High school Colombian students’ variational thinking triggered by mathematical connections in a laboratory on linear functions

Problem creation to articulate proportional and algebraic reasoning