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How to solve it

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How to solve it

  1. 1. HOW TO SOLVE IT? A New Aspect of Mathematical Method Cristhian Aldana Yarlequé Docente del Departamento Académico de Matemática y Física Universidad Nacional de San Cristóbal de Huamanga
  2. 2. INTRODUCCIÓN “ LA EDUCACIÓN COMIENZA CON LA VIDA Y TERMINA CON LA MUERTE” JOSÉ MARTI
  3. 3. <ul><li>A UN ESTUDIANTE LE FALTA ORIENTACIÓN, SE LE DEBE ORIENTAR… </li></ul><ul><li>HAY QUE IDENTIFICAR LAS CARENCIAS, FORTALEZAS Y POTENCIALIDADES DE LOS ALUMNOS PARA APLICAR ESTRATEGIAS QUE PERMITAN SOLUCIONAR DIFERENTES PROBLEMATICAS. </li></ul><ul><li>LA UNIVERSIDAD YA NO ES LA ACADEMIA QUE DA SÓLO CONTENIDOS, AQUÍ SE VINCULA YA CON LOS ENTORNOS. </li></ul><ul><li>SIGLO XXI: SOCIEDAD DEL CONOCIMIENTO </li></ul><ul><li>ENSEÑANZA – INVESTIGACIÓN – FORMACIÓN DE PROFESIONALES </li></ul>
  4. 4. <ul><li>UNIVERSIDAD MODERNA </li></ul><ul><li>PRODUCCIÓN DE CONOCIMIENTOS </li></ul><ul><li>INVESTIGACIÓN CIENTÍFICA </li></ul><ul><li>CREACIÓN DE CONOCIMIENTOS </li></ul>
  5. 5. Un gran descubrimiento resuelve un gran problema pero es un grano de descubrimiento en la solución de cualquier problema. Su problema puede ser modesto, pero si pone en duda su curiosidad y pone en juego sus facultades inventivas y si lo resuelve por sus propios medios, usted tendrá experiencias susceptibles que le generen un gusto por el trabajo mental y dejen su huella en la mente y el carácter para toda la vida. A NEW ASPECT OF MATHEMATICAL METHOD
  6. 6. Así, un profesor de matemáticas tiene una gran oportunidad. Pero si llena su tiempo asignado dotando a sus alumnos con operaciones de rutina que matan a su interés, obstaculiza su desarrollo intelectual, será una manera incorrecta de desarrollo mental. Pero si usted desafía la curiosidad de sus alumnos mediante el establecimiento de problemas de acuerdo con su conocimiento, y les ayuda a resolver sus problemas con preguntas estimulantes, será muy estimulante al pensamiento. A NEW ASPECT OF MATHEMATICAL METHOD
  7. 7. UNDERSTANDING THE PROBLEM First. What is the unknown? What are the data? What is the condition? (You have to It is possible to satisfy the condition? Is the condition sufficient to Understand the determine the unknown? Or is it insufficient? Or redundant? Or Contradictory?. Problem). Draw a figure. Introduce suitable notation. Separate the various parts of the condition. Can you write them down?   HOW TO SOLVE IT?
  8. 8.    DEVESING A PLAN SECOND (Find the connection between The data and the unknown A plan of the solution Consider auxiliary problems if An immediate connection cannot Be found. You should obtain eventuality a You may be obliged to Have you seen it before? Or have you seen the same problem in a slightly different form? Do you know a related problem? Do you know a theorem that could be useful? Look at the unknown! And try to think of a familiar problem having the same or a similar unknown. Here is problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible? Could you restate the problem? Could you restate it still differently? Go back To definitions. HOW TO SOLVE IT?
  9. 9. If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined how can it vary? Could you drive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or the data, or both if necessary, so that the new unknown and the new data are nearer to each other? Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem. HOW TO SOLVE IT?
  10. 10.   CARRYING OUT THE PLAN   THIRD: carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you Carry out your plan. Prove that it is correct? HOW TO SOLVE IT?
  11. 11. <ul><li>LOOKING BACK </li></ul><ul><li>  </li></ul><ul><li>FOURTH. Can you check the result? Can you check the argument? </li></ul><ul><li>Examine the solution can you derive the result differently? Can you see it at a glance? </li></ul><ul><ul><ul><li> Can you use the result, or the method, for some other problem </li></ul></ul></ul>HOW TO SOLVE IT?
  12. 12. MUCHAS GRACIAS

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