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 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.

María Burgos

Nicolás Tizón-Escamilla

Jorhan Chaverri

Problem creation to articulate proportional and algebraic reasoning

问题创设以阐明比例与代数推理

The study reported had the aimed to identify the mathematical connections made by a group of Mexican preservice mathematics teachers (PMTs) when solving tasks on systems of linear equations. We consider a mathematical connection as a true relationship that a person makes between two or more ideas, concepts, definitions, theorems, procedures, representations, and meanings with each other, with other disciplines or with real life. Four PMTs participated voluntarily in task-based interviews, providing the primary data for analysis. Thematic analysis was employed to analyze the data. The findings revealed that the preservice teachers made mathematical connections of procedural, implication, feature, meaning, and different representations. However, the findings also revealed that some preservice teachers faced challenges when attempting to solve the tasks, leading to difficulties in establishing certain mathematical connections.

Alberto León del Carmen

Wendoly León del Carmen

Javier García-García

Gerardo Salgado-Beltrán

Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations

职前数学教师在解决线性方程组任务时的数学联系

Beginning teachers benefit from preparation emphasizing supporting students with diverse needs and developing deeper understandings of algebraic connections. Our study aims to explore how instructors in secondary preparation programs and mathematics preservice teachers (M-PSTs) conceptualize and enact algebraic connections in required courses. Our dataset comprises instructor interviews and course materials from 48 courses across five universities, and 10 focus group interviews involving 37 M-PSTs. Employing constant comparison method, we analyzed data by creating a coding system for algebraic connections. Our findings highlight varying perspectives of M-PSTs and instructors related to encounters with algebraic connections, emphasis of algebraic connection types by both groups, and types emphasized as main objectives of courses in five secondary mathematics teacher education programs. We describe nine algebraic connection themes that were identified in this investigation. We discuss emergent implications for curriculum development, instructional practices, and foundational algebraic concepts in teacher preparation programs.

Hyunyi Jung

Jill Newton

Eryn M. Maher

Conceptualizing algebraic connections: Honoring voices from future mathematics teachers and the instructors who teach them

概念化代数联系：尊重未来数学教师及其指导教师的观点

Previous research has shown that mathematics teachers face difficulties teaching the derivative of a function at a point. One of these difficulties revolves around the lack of materials and specialized information on this topic that allows teachers to carry out this task. Seeking to contribute to overcoming this difficulty, we describe the design of an activity oriented towards the encounter of mathematics teachers with meanings and levels of understanding of the derivative of a function at a point. The design is theoretically founded on the concepts of learning and activity of the theory of objectification and incorporates relevant information in the analytical, analytical-numerical, and geometric meanings of the derivative as well as the intra, inter, and trans levels of understanding of the concept. Based on these references, we describe the tasks that make up our design. We see our design as contributing to the field of mathematics education regarding the promotion of in-service teachers’ learning from an historical-cultural educational perspective.

Alan Basilio Pizarro-Ayavire

Juan Luis Prieto-González

Rafael Enrique Gutiérrez-Araujo

Designing the &lt;i&gt;encounter&lt;/i&gt; of teachers with meanings and levels of understanding of the derivative

设计教师与导数的意义及理解层次的“相遇”

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?

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

Problem creation to articulate proportional and algebraic reasoning

Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations

Conceptualizing algebraic connections: Honoring voices from future mathematics teachers and the instructors who teach them

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

Problem creation to articulate proportional and algebraic reasoning

Mathematical connections made by preservice mathematics teachers when solving tasks about systems of linear equations

Conceptualizing algebraic connections: Honoring voices from future mathematics teachers and the instructors who teach them

Designing the <i>encounter</i> of teachers with meanings and levels of understanding of the derivative