1,720,963 research outputs found
Transition tasks for building bridges between dynamic digital representations and Cartesian graphs of functions
No full textThis study focuses on a case study that highlights the mathematical discourse developed by two pairs of students when dealing with a specific transition task, i.e., an activity leading to the construction of a graph of a function based on the exploration of another representation of the same function. Such a task was designed to work on the “transition beyond” that involves moving from the graph of a function in a dynamic geometry environment to the Cartesian graph of the same function in the paper-and-pencil environment. In this case study, I analyze in fine-grained detail the discourse developed by two pairs of high-school students (ages 15–16) and describe how they translate the dynamism of the proposed representation into the paper-based context. The analysis aims at investigating the potentialities of transition tasks for supporting the building of bridges between multiple representations of the same function. The analysis also showcased the important role dragging routines played for making the transition
Designing tasks for introducing functions and graphs within dynamic interactive environments
Full text linkIn this paper, we elaborate on theoretical and methodological considerations for designing a sequence of tasks for introducing middle and high school students to functions and their graphs. In particular, we present didactical activities with an artifact realized within a dynamic interactive environment and having the semiotic potential for embedding mathematical meanings of covariation of independent and dependent variables. After laying down the theoretical grounds, we formulate the design principles that emerged as the result of bringing the theory into a dialogue with the didactical aims. Finally, we present a teaching sequence, designed and implemented on the basis of the design principles and we show how students’ efforts in describing and manipulating the different graphs of functions can promote their production of specific signs that can progressively evolve towards mathematical meanings
Analisi del discorso di classe sul riconoscimento di altezze di un triangolo
Full text linkL’articolo presenta l’analisi del discorso matematico degli studenti di una classe II di scuola secondaria di primo grado, intrapreso durante una lezione sul riconoscimento di altezze di un triangolo. La lezione si è svolta dopo un percorso didattico durante il quale il discorso sull’oggetto matematico altezza si è costruito a partire da diverse realizzazioni possibili. Obiettivo principale di questo studio è documentare quali tra queste realizzazioni del significante altezza compaiono nel discorso di classe, descriverne le caratteristiche e osservare quali continuità o discontinuità presentano rispetto alle realizzazioni più comuni descritte dalla letteratura in didattica della matematica. L’analisi del discorso, accompagnata dalla costruzione e confronto tra l’albero di realizzazione atteso e l’albero della classe, consentiranno di mettere in luce sia la ricchezza del discorso di classe sia le interazioni tra realizzazioni diverse. Infine, si discuteranno le implicazioni teoriche e didattiche dello studio
From multiple discourses to algebraic discourse
No full textThis study is framed within a commognitive perspective and is based on the theoretical stance that subsuming is a key discursive process for relating different representations, providing an alternative way of learning compared to memorizing meaningless procedures. We designed activities in digital learning environments to promote this subsuming process in the context of school algebra. We analyze the story of Aldo and Giulio, two high school students, showing how this process can feature and how algebraic discourse can emerge as a possible subsuming discourse
Did you know you can draw a huge number of infinite heights? The students’ realization tree of the heights of a triangle
No full textIn this paper we report on the analyses of the mathematical discourse of 7th grade students about the solution of a task on the recognition of the heights of a triangle. our aim is to describe through the commognitive lens the realizations that appear in the mathematical discourse of the classroom and to observe possible interactions between them. For this purpose, we construct and compare the expected and the actual students' realization trees, showing the richness of the realizations addressed by the participants in the mathematical discourse
A developing discourse on transitions between different realizations of the same function
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