George Pólya was mathematician in Hennery. Throughout his writings, when presenting his heuristic, Pólya paid homage to Pappus (circa 300AD), whose concept of usually glossed as the art of solving problems. The practical roots of Pólya’s heuristic and pedagogical approach were apparently developed during the 1910s, and were already quite evident in Pólya (1919), his first writings on problem solving and pedagogy, and in Pólya and Szegő (1925).
Pólya’s heuristic is a model of human problem solving; it is a model for understanding creative expression of invention and discovery; it is a model of active teaching. Many interpretations of Pólya’s heuristic include only four stages of problem solving. Unlike other problem solving models that describe a handful of how-to steps or stages of problem solving, to be learned mnemonically and to be applied systematically and independently by the student, Pólya’s model provides far more: the teacher has an important and active role in the learning and teaching process.
Pólya’s heuristic comprises three levels or layers, from abstract to general guidance to descriptive application, outlining the relationship between the teacher and the student. First, it is framed by four “phases” of invention and discovery, or, if you will, creative problem solving: Understanding the problem devising a plan carrying out the plan looking back.