La historia de las matemáticas es, en gran medida, la historia de la resolución de problemas, la mayoría de los cuales, por no decir su casi totalidad, han sido engendrados dentro del propio ámbito de las matemáticas.
La naturaleza abstracta de las matemáticas conduce a que los métodos de resolución de problemas, profundamente vinculados con la lógica, alcance un alto nivel de generalidad, lo que permite aplicar su metodología a la resolución de problemas fuera del ámbito matemático.
No se trata pues de aplicar fórmulas matemáticas, sino formas y esquemas de razonamiento en la resolución de problemas.
El problema
La aparición de un problema está siempre vinculada a una cierta tensión emocional. Se trata de una reacción primaria de alerta asociada a situaciones de peligro. La primera reacción es por tanto emocional. Reconocer el problema es una segunda fase que no tiene porqué darse siempre y tiene una componente racional.
De lo primero que somos conscientes es de que nos enfrentamos a una situación nueva, de que hemos perdido cierta familiaridad con el entorno. Aparecen elementos que identificamos como conflictivos. Tenemos la sensación de que nos faltan datos y que no sabemos muy bien que hacer con los que ya tenemos.
Un sujeto o un colectivo no tiene un problema hasta que no lo reconoce como tal. De manera que el planteamiento problema suele tener una importante componente subjetiva.
Un problema reconocido por un colectivo puede tener diferente dimensión para cada uno de sus miembros, por lo que una solución general puede requerir de soluciones particulares.
Hay problemas deseados, que los genera o a los que se adscribe el propio individuo para mejorar una situación o como simple reto. En este caso el reconocimiento del problema es inmediato y lo que se quiere es resolver el problema, no eliminarlo. Otros son no deseados. El reconocimiento del problema puede ser más tardío y surge como necesidad, ya que tiene su origen en una tensión emocional que se desea eliminar. En este caso el sujeto antepone la desaparición del problema (si fuera posible) a su solución. En cualquier caso, la resolución de un problema requiere siempre de un esfuerzo.
Reconocer el problema.
Aunque es cierto que la mayoría de los problemas suelen ser consecuencia de determinados acontecimientos, no debe confundirse un problema con un acontecimiento. A diferencia del problema, el acontecimiento es ajeno a nuestra voluntad y no tenemos ninguna opción para intervenir en él. Al salir de la oficina está lloviendo. Carlos dice «Vaya problema». Está claro que el que llueva en ese momento es un acontecimiento. «Es que no tengo paraguas y me voy a mojar» eso sí es un problema. Pedro, que está a su lado le comenta «Yo me voy a casa de todas maneras. No me importa mojarme, incluso me gusta.» Frente a un mismo acontecimiento, Carlos tiene un problema, mientras que Pedro no lo tiene. El reconocimiento del problema tiene una componente claramente subjetiva.
Acontecimiento y problema tienen a veces una frontera difusa, lo que dificulta distinguir ambas naturalezas, la de acontecimiento y la de problema. En muchos casos establecer esta distinción es una decisión que se debe tomar para optimizar el correcto planteamiento del problema.
Frente a un mismo acontecimiento alguien puede sentirse víctima de las circunstancias y mantener una actitud pasiva. En cambio, otra persona reconoce que el acontecimiento a generado un problema y decide pasar a la acción para resolverlo. Cuando la tendencia es dar más protagonismo al acontecimiento que al problema es fácil prever de que el camino a seguir será el de la eliminación del problema antes que su solución.
Frente a una crisis económica (que es un acontecimiento), el cierre de una empresa puede ser contemplado como la eliminación de un problema, no su resolución. Hay que tener en cuenta que la posible eliminación de un problema suele ser fuente de problemas de difícil solución.
Cuando se trata de un colectivo, la naturaleza subjetiva del reconocimiento del problema puede plantear conflictos a la hora de implementar posibles soluciones, ya que algunos sujetos del colectivo pueden no haber reconocido el problema como tal.
La «magnitud» del problema no debe considerarse un parámetro válido. A diferencia del factor tiempo, no es algo que haga más apremiante el encontrar la solución. Esto es algo que debe tenerse en cuenta en los colectivos. No debe darse la situación de que unos sujetos consideren el problema como «muy importante» mientras otros lo valoren menos. En este sentido, un problema es un problema sin más. Las diferentes valoraciones no hacen más que camuflar la falta de reconocimiento del problema como tal.
Conclusión: no hay un gradiente en el reconocimiento del problema que oscile de mayor a menor. Es un SI o un NO.
Todos los sujetos que han reconocido el problema como tal se convierten, de alguna u otra forma, en sujetos activos de la solución. Debe ser así.
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