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In this article, we resume discussions about the application of Differential and Integral Calculus in the Teaching of Chemical Kinetics in Teacher Training. Aspects aimed at demonstrating statements through the resolution of tasks in a course of studies and research as a strategy aimed at appropriating concepts in the domain of reaction kinetics, in the context of activities based specifically on the Anthropological Theory of the Didactic (ATD), based on epistemological models of reference and the dominant one around the object speed laws of chemical reaction. Along the way, the importance and reason for being of Integral and Differential Calculus techniques for teacher training and the formulation of didactic organizations that can serve as support for tasks in the exercise of the profession in high school were highlighted, highlighting the use of instruments of ICT, such as Excel, in the construction of these tasks. It was observed that throughout the course the students understood the steps proposed in the reference epistemological model by completing a crucial task, associated with the question that generated the course, which necessarily applies integration and differentiation techniques to obtain ordinary differential equations, associated with the technique analysis of the least squares method, for the kinetic characterization of a chemical system, a medicine in the simulation of the experimental determination of its expiration date. [ABSTRACT FROM AUTHOR]

This article aims to present a method of intervention in the classroom, specifically in the Differential and Integral Calculus course of a Mathematics Teaching degree, when working with students on the Intermediate Value Theorem. We base our approach on the studies by Bicudo (1991), Garnica (1992), and Garnica and Bicudo (1994) regarding a teaching methodology based on hermeneutic work with mathematical texts in the classroom. We describe the experience conducted and our understanding of the activity carried out. We present the questions posed by the students and the indications of their understanding of the ideas introduced in the studied theorem. [ABSTRACT FROM AUTHOR]

This article proposes a theoretical reflection on models and Calculus, pointing out preliminary notions and basic principles for building a reference epistemological model to teach this subject. To this end, we examine some models present in our daily lives to suggest a generalization of the term. Next, we present the representative model proposed by the anthropological theory of the didactic to subsequently define the dominant and the reference epistemological models as well as the didactic model of reference. Having overcome these definitions, we develop a brief history of the term to clarify what we understand today by Calculus and how it has been used over time. The results of the theoretical-bibliographical research will be valuable for didactic researchers in constructing a reference epistemological model for teaching Calculus. [ABSTRACT FROM AUTHOR]

In the research reported in this article, we seek to explore aspects of differential thinking and thinking-with-GeoGebra that emerge when high school students investigate activities on the calculation of areas and volumes. Initially, we discuss issues about mathematical thinking and differential thinking, proposing a perspective on differential thinking formed by four aspects: Notion of limit and continuity; Notion of infinitesimal; Defined integral concept; Visualgeometric design. From the methodological point of view, based on qualitative research, we developed teaching experiments with 6 pairs of students from the 10, 11 and 12 grades of High School, considering the elaboration of a task composed of 5 activities. In the article, based on the notion of sampling in qualitative research, we discuss the investigation developed by one pair of 12th grades about the activity entitled "The Problem of Volume". In the data analysis, we highlighted the role of visualization and experimentation-with-technologies in the development of students' thinking. In particular, we emphasize how the resources or potentialities of the software offered ways for students to articulate the four aspects that make up differential thinking in the proposed perspective. This study contributes to the production of knowledge about the use of digital technologies in Mathematics Education, in particular to the relation to the teaching of Calculus in High School. [ABSTRACT FROM AUTHOR]

This article contributes to the knowledge about the learning of systems of differential equations from the point of view of dynamical systems. It analyzes the evolution of the Schema of dynamic systems of two variables in university students, after finishing a course of dynamic systems designed with the Action Process Object Object Schema (APOE) theory as a support for the design of activities used throughout the course. In particular, this study focuses on how students give meaning to the strategies used to represent and interpret systems of differential equations and the relationships they establish between the structures that make up the Systems of Equations Schema and in particular the relationships between the function and its derivative through the different representations used to study them. This work also contributes to enrich the notion of Schema and interaction between Schemas of the APOE theory, as well as to the analysis of the relationships between the different concepts involved in and between the different representations of the solutions that play a role in the context of systems of differential equations and, importantly, in the understanding of parametric functions. [ABSTRACT FROM AUTHOR]