Pre-service Mathematics Teacher's Mathematical Connections in the Context of Problem-Solving About the Derivative

Pastells

2022

Ethnomathematics, STEAM Education, and the Globalized Approach are articulated to analyze mathematical connections in daily practices. For this, the networking strategies were considered (understand the theoretical approaches; contrast-compare; coordinate-combine; synthesize-local integration). In the coordination and comparison, the complementarities between the approaches were evidenced and based on these, an empirical phenomenon was analyzed on the connections in daily practices carried out by five artisans who worked in the elaboration of kites, cabinets, masks, and drawers, agriculture, and masonry. From the integration strategy, three results were identified: (i) intra-disciplinary connections, which make it possible to present mathematics as an integrated whole, rather than as a set of isolated knowledge; (ii) interdisciplinary connections, between knowledge from different disciplines that feed into each other; and (iii) connections between the mathematics practiced by cultural groups with institutionalised mathematics that are, at the same time, globalized because they relate mathematics to the socio-cultural context.

Networking Between Ethnomathematics, STEAM Education, and the Globalized Approach to Analyze Mathematical Connections in Daily Practices

Pastells

2022

Literature review on networking of theories developed in mathematics education context

Moll

Rodríguez-Vásquez

2022

The research aim is made a literature review on research focused on networking of theories developed in mathematics education field with several mathematical concepts. On the other hand, to illustrate what a networking of theories consists of, a synthesis of an articulation between the extended theory of connections (ETC) and the onto-semiotic approach (OSA) was presented using the study of the mathematical connections built by a university student on the derivative concept as an example. A qualitative study was developed in two stages: (1) Three phases were followed: search for information in various search engines and databases (ERIC, Google Scholar, etc.), organization and analysis of the documentation, finding works on articulation of theories focused on various mathematical concepts such as derivative. (2) A synthesis of the theoretical articulation ETC-OSA is presented, emphasizing the analysis of an episode over the derivative. It is concluded that the research reviewed on the articulation of theories about a certain phenomenon or teaching of content represents an important contribution to improving its understanding. In addition, this research provides a theoretical input or detailed panorama of background organized chronologically so that the community interested in this research line can use it for future studies.

Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories

Cervantes-Barraza

Moll

2023

Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “<i>if a function is derivable at a point then it is continuous at that point</i>”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.