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El álgebra es el idioma de la Matemática, es una rama de ella, en la que se utilizan letras y símbolos para representar generalizando relaciones aritméticas.
Se diferencia de la Aritmética, por el uso de abstracciones, como por ejemplo el uso de letras para representar números desconocidos o varios números.
En cuanto al álgebra escolar es concebida como el lenguaje para comunicar ideas, o generalizaciones de matemática, expresándolas mediante símbolos.

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Es la rama de la matemática que se encarga de las generalizaciones, de la abstracción utilizando combinaciones de operaciones, números y letras que cumplen con ciertas condiciones.
En el caso del álgebra escolar podría decirse que es una aritmética generalizada, ya que parte de ella para poder descontextualizar el procedimiento/calculo  para transformarlo en  en una expresión general aplicable a cualquier valor numérico.
Carla

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El álgebra es un lenguaje, es una forma de representar y generalizar relaciones presentes en la matemática. Se involucran en ella diversas variables que se relacionan   mediante las operaciones aritméticas para formar una expresión significativa.  El pensamiento algebraico implica pensar lógicamente en números, aplicar en ellos un razonamiento analítico para dar un paso hacia la abstracción. Estos aspectos hacen que el algebra también se constituya como una herramienta para modelizar distintas situaciones y resolver problemas de diferentes disciplinas.

En la cultura escolar las nociones acerca del álgebra suelen ser concebidas por ideas o concepciones que provienen de los libros escolares, currículos es sus distintos niveles de concreción, NAP etc. las cuales son tomadas como modelos de referencia para el abordaje del algebra escolar.

Eliana.