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http://repositoriodigital.ipn.mx/handle/123456789/11385| Título : | DE LA ARITMÉTICA AL CÁLCULO. UN ESTUDIO TRANSVERSAL SOBRE LA RAÍZ CUADRADA |
| Autor : | Martínez Sierra, Gustavo Castañeda Alonso, Apolo |
| Fecha de publicación : | 16-ene-2013 |
| Descripción : | The present investigation leaves from one of the central objectives of Mathematics Education is to elaborate descriptions and explanations on the operation of the didactic system: knowledge - teacher - student Its reference frame is the line of denominated investigation development of the thought and variational language (Cantoral & Farfán, 1998). Within the investigations in this line special attention to the construction of the function notion has been lent (Farfán et al., 2002a, 2002b) Our subject of investigation arises from the answers of the students of university level on exercises that involve square root, for example: • When solving the equation x2=4 only answers that x=2, because "they remove" square root to both sides of the equality • They establish that 4 + 9 has four values that are obtained to combine the results 4 = ±2 and 9 = ±3 Our antecedents are those investigations relative to the function notion. On the matter, we will make use of the investigations at the time of explaining the construction of the notion of function, in special those that equip with particularitities their explanation, specially with respect to the important functions as they are it the logarithmic functions (Ferrari, 2001), exponential (Martinez, 2000) and trigonometrical. Taking into account the fundamental paper that it carries out the square root in the mathematical student in all the scholastic levels, from the basic ones to the college students, we considered important to deepen in these conceptions which show the own complexity of this mathematical concept. Thus, our investigation is centered in studying this concept from the point of view of the Arithmetic, later of algebra and at last Calculus, by means of the text book analysis from the basic level to the superior one, as well as the application of a questionnaire to students of Secondary and University Level Finally we will show that the conceptions that between the students remain are the following ones • They consider 2 100 = 50 • The square root of an elevated negative number to the square is himself (−2)2 = −2 • The plot of the function y2 = x is the same one that the one of y = x • The properties of the equality extend until the radication The square root generates specific conceptions own that remain in the students since they initiate its scholastic instruction in the basic level and until finishing a race By all the previous reasons, we propose to incorporate to the square root the group of important functions. |
| URI : | http://www.repositoriodigital.ipn.mx/handle/123456789/11385 |
| Otros identificadores : | http://hdl.handle.net/123456789/893 |
| Aparece en las colecciones: | Doctorado |
Ficheros en este ítem:
| Fichero | Descripción | Tamaño | Formato | |
|---|---|---|---|---|
| colin_2006.pdf | 1.83 MB | Adobe PDF | Visualizar/Abrir |
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