Abstract
The objective of the present article is to present the research generated regarding the research interrogation: in activities conducted with students, how does the simulator make the sine present in its different forms of possible technical work, and the understanding of its historicity? This research was based on studies regarding how phenomenology views cyberspace in its philosophical and technological aspects, and how mathematical thought is constituted under the Husserlian perspective, which inspired the articulations put into the architecture of the research presented, and the way the information was collected and later hermeneutically analyzed. Finally, it presents the understanding that digital simulators are not necessarily sources of meaning for instituted mathematical objects. Computational interfaces, however elaborate, may miss something of the intrinsic cogitationes of mathematical thought, which constitute the syntheses of mathematical knowledge and its historicity.
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Research group Fenomenologia em Educação Matemática. E-mail address: fem.sepq.org.br/.
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High school in the Brazilian educational system comprises basic education with a duration of 9 years. In most cases it caters to students aged 15–18.
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Formal ontology is a term used by Husserl, in his doctoral thesis Philosophie der Arithmetik. Then, the term designated natural numbers, in their symbolic characteristics, as drivers of the numerical system, which comprises integers, rational, irrational, negative, and complex numbers, the latter composed of elements later named by Husserl imaginary entities. Later, the concept of formal ontology was expanded and gained the status of being: “the study of a system and its internal structure in terms of derivable relations, in domains where there is a language in which the noema is presented as an assertion system” (Kluth, 2005, p. 126, author’s translation) Noema is here is defined as the intended mathematical object.
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Phenomenological reduction is a mode of reflection; an attitude that aims to neutralize any and all ingenuity. Moura (1989) points to the naivety of the natural attitude by stating: “If the natural attitude is that through which the investigation is directed towards the objects, the phenomenological attitude is distinguished from it first of all by the “anti-natural habitus of reflection” (LUI)./111). The phenomenological attitude is determined only by the conversion of the acts themselves into objects, acts that remain anonymous in the “natural attitude.” (p. 116, author’s translation).
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Noetic and noematic have meanings in phenomenology when seen in the relation of man to the world, in the noesis–noema relationship. This relation tells of the human supposition which is the intentional act of consciousness—concerning noesis and the object of supposition—the noema, which is a correlate object of the world, which is understood as the natural, constituted, and being constituted world.
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The word epoché means highlighting something we want to know. This evidence builds when we initially disconnect from what is already known about it. It can be said that to make epochpe is to make this something an intentional object of reflection.
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For Gadamer (1997) there are only experiences to the extent that something is experienced or intended in them. This intentionality, because it is operative, gives the experience a lasting character. Thus, it is not restricted to the immediacy of the fact, but reveals itself as a phenomenon when learned in corporeality. It is the concrete element upon which the meaning of the world is constituted for us.
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Kluth, V.S. (2020). Phenomenological Study of a Digital Simulator of the Sine Function Contextualized in a Teaching and Learning Activity. In: Viggiani Bicudo, M. (eds) Constitution and Production of Mathematics in the Cyberspace. Springer, Cham. https://doi.org/10.1007/978-3-030-42242-4_6
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