Abstract
A teaching approach based on the global interpretation of figurative properties prioritizes the curve sketching and understanding from the conversions among algebraic, graphical and linguistic registers, more precisely the identification of basic units (graphical, symbolic and linguistic) and the verification of how they related with each other. Raymond Duval presents this approach in an outline work of a related linear function using a resource for the global interpretation of the parameters of the algebraic expression: , emphasizing the relationship between these parameters and the graphical visual variables: inclination direction, tracing angles with the axes, and tracing position relatively to the vertical axis origin. Other authors have proposed works under this perspective with a focus on High School. Among them: Moretti (2003), for the quadratic function; Silva (2008), for the exponential, logarithmic and trigonometric functions; Menoncini & Moretti (2017), for the modular function; Martins (2017), for curves whose expressions are in parametric form; Moretti, Ferraz & Ferreira (2008), for more complex functions of college teaching; and Pasa (2017), for polynomial functions of the second and third degree. In this article, we present these works, complementing Pasa & Moretti (2016), presenting the resources used in each of them that allow changing verifications which the graph changes generates in the algebraic expression and vice versa and the identification of the visual variables and units related to the modifications.
Highlights
A teaching approach based on the global interpretation of figurative properties prioritizes the curve sketching and understanding from the conversions among algebraic, graphical and linguistic registers, more precisely the identification of basic units and the verification of how they related with each other
Raymond Duval presents this approach in an outline work of a related linear function using a resource for the global interpretation of the parameters of the algebraic expression: y = ax + b, emphasizing the relationship between these parameters and the graphical visual variables: inclination direction, tracing angles with the axes, and tracing position relatively to the vertical axis origin
Among them: Moretti (2003), for the quadratic function; Silva (2008), for the exponential, logarithmic and trigonometric functions; Menoncini & Moretti (2017), for the modular function; Martins (2017), for curves whose expressions are in parametric form; Moretti, Ferraz & Ferreira (2008), for more complex functions of college teaching; and Pasa (2017), for polynomial functions of the second and third degree. We present these works, complementing Pasa & Moretti (2016), presenting the resources used in each of them that allow changing verifications which the graph changes generates in the algebraic expression and vice versa and the identification of the visual variables and units related to the modifications
Summary
In various areas of knowledge, curves sketching and its understanding are essential activities for interpreting graphs and phenomena. From the perspective of Raymond Duval’s theory of registers of semiotics representations, the whole analysis of the acquisition and construction of mathematical knowledge permeates three closely linked phenomena: the diversification on semiotics representations registers, the differentiation between representant and represented, or between form and content of a semiotic representation, and the coordination (conversion) between the different registers of semiotic representation These aspects, linked to noncongruence issues among the registers are, for this author, the sources of the difficulties in understanding mathematics. We present works with curves sketching of functions for high school contexts, complementary to those exposed in Pasa & Moretti (2016) In each paper, it is highlighted the articulation resources used and its examples in order to clarify the approach and verify changes that one register influences in the other
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