Demonstration Process Skills: From Explanation to Validation in a Precalculus Laboratory Course

Abstract

We present results of a research developed with first semester students from a Colombian Public University based on classroom intervention in a precalculus laboratory course mediated by an interactive mathematical software. We characterize and exemplify the cognitive skills of explanation, justification, argumentation and validation, using a methodological tool of analysis that integrates the ckç model of Balachef and Margolinas to Toulmin's model. This tool allows us to identify some elements that characterize each of these skills and allow us to offer a structure of analysis that we present as a proposal for the design of activities in research, based on classroom interventions that promote the development of demonstration skills.

Curricular proposal to address diversity in mathematics class: A design on sequences and patterns

“…(a) The curriculum framework poses the question: 'How to organize synchronized swimming competencies?' and presents a table that shows the purposes of activities at each depth level, linked with mathematical processes, addressing the guidelines from MEN (1998), and the insights provided by various authors on their development (Fiallo & Parada, 2018;Fiallo et al, 2021;Parada et al, 2023).…”

Communication skills enabled in a pre-calculus course using dynamic geometry software

“…Some strategies used to solve calculus problems may be careful reading of the statement in which the variables at stake are identified and what is being asked is understood, description of relationships between the different representations, and translation into a convenient mathematical language to answer the question, as well as providing concrete examples that give meaning to the problem statement, as also highlighted by Fiallo et al (2021).…”

“…During the mathematical education process, it is essential to invite students to justify their strategies and procedures, Fiallo et al (2021). For this, it is necessary to provide an environment that stimulates them to explain the why?…”