Diversity of student-built ideas about real numbers, irrational numbers, order and density
We present the analysis of the responses of high school and university students to four tasks that investigate how they understand what a number is in general and an irrational number, the order, the density and the supreme of an interval, in real numbers. We find a depth gradient in these ideas fro...
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| Formato: | Artículo revista |
| Lenguaje: | Español |
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Unión Matemática Argentina - Facultad de Matemática, Astronomía, Física y Computación
2022
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| Acceso en línea: | https://revistas.unc.edu.ar/index.php/REM/article/view/32442 |
| Aporte de: |
| Sumario: | We present the analysis of the responses of high school and university students to four tasks that investigate how they understand what a number is in general and an irrational number, the order, the density and the supreme of an interval, in real numbers. We find a depth gradient in these ideas from (i) a view of the integers as a model of number, distancing, or insecurity in front of these aspects of R, mainly in students with less studies in mathematics. In an intermediate zone, the (ii) conception of real numbers is identified with finite decimals and an explicit discretely, mainly in secondary and high school students (iii) a view in which the real numbers are identified with the rational numbers and as infinite potentially dense. Present mainly in first-year students of scientific careers. In the other extreme (iv) mainly advanced students of Mathematics, who understand the order, density, and property of the supreme in the real numbers. We show that to encourage students to appropriate the real number, teachers must anticipate in the last years of high school and the first years of university to work on these complex notions, to facilitate the transition from school mathematics to advanced mathematics. |
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