Exploring University Mexican Students’ Quality of Intra-Mathematical Connections When Solving Tasks About Derivative Concept

Abstract

The quality of the intra-mathematical connections made by Mexican university students when solving tasks on the derivative was characterized. The typology of mathematical connections and the quality levels of mathematical connections were used. Interviews were conducted based on eight tasks applied to three case studies. The results showed that the quality of the intramathematical connections: different representations, procedural, implication, part-whole and meaning of the students, is found mostly at level 2 (consistent and argued mathematical connections) and only one student presented inconsistencies to find the correctness equation of the tangent line to the curve at a point (quality level 0 connection). Likewise, the metaphorical connection was identified when a student mentioned the metaphorical expression "the graph has no holes", which suggests the conceptual metaphor "the graph is a path" referring to the continuity of a function. We believe that quality level 2 mathematical connections ensure understanding, and the quality level 0 mathematical connections are the reasons why students have difficulty understanding the derivative.

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

“…Studies on mathematical connections have focused mainly on identifying the connections made by high school students, undergraduate students in mathematics, pre-service mathematics teachers and inservice mathematics teachers (García-García & Dolores-Flores, 20182020;Rodríguez-Nieto et al, 2021a, 2022a, 2021b, 2021c, worrying about answering questions aimed at the meaning of mathematical objects, what are the representations of mathematical objects, logical relationships of implication and part-whole, features of the concepts, but have not focused on the reasons, arguments, justifications that support a connection. It is important to mention that, in Rodríguez-Nieto et al (2021d) the mathematical connections were detailed in terms of OSA, without deeply emphasizing the arguments that a subject construct.…”

Literature review on networking of theories developed in mathematics education context

“…Just as research has been carried out on networking or theoretical connections, there have also been works focused on mathematical connections, which is a relevant topic in mathematics education because the establishment of connections contributes to the understanding of mathematical concepts (De Gamboa et al, 2020Gamboa et al, , 2021. Most of the research work on establishing connections has been carried out on key calculus concepts such as the derivative (Rodríguez-Nieto et al, 2021a, 2021b, 2021c, 2022, the derivative and its relationship with the integral (García-García & Dolores-Flores, 2019, 2021), the rate of change ; and on functions, such as exponential and logarithmic function (Campo-Meneses & García-García, 2020;Campo-Meneses et al, 2021), quadratic function (Businskas, 2008). In addition, among others, connections between geometric concepts (Caviedes et al, 2019) and ethnomathematical connections in daily practices (Pabón-Navarro et al, 2022;Rodríguez-Nieto, 2021).…”

Evaluating the Design of Mathematics Courses Available on the Blackboard Platform at Prince Sattam bin Abdulaziz University According to Quality Matters Standards

“…There is no doubt that mathematics achievement increases by revealing the connections between the topics of one course, or the connections between the various math courses (García-García & Dolores-Flores, 2017;Rodríguez-Nieto et al, 2021). This is reinforced by QM standards.…”