Whilst the content in mathematical problem-solving consists of certain concepts, connections and procedures, the process describes the psychological processes that occur when solving a problem.
This course of action is described in Lompscher by various qualities, such as systematic planning, independence, accuracy, activity and agility.
Problem solving in mathematics education has been a prominent research field that aims at understanding and relating the processes involved in solving problems to students’ development of mathematical knowledge and problem solving competencies.
The accumulated knowledge and field developments include conceptual frameworks to characterize learners’ success in problem solving activities, cognitive, metacognitive, social and affective analysis, curriculum proposals, and ways to foster problem solving approaches.
In the survey, four interrelated areas are reviewed: (i) the relevance of heuristics in problem solving approaches—why are they important and what research tells us about their use?
(ii) the need to characterize and foster creative problem solving approaches—what type of heuristics helps learners think of and practice creative solutions?
Along with differences in motivation and the availability of expertise, it appears that intuitive problem solvers possess a particularly high mental agility, at least with regard to certain contents areas. by the capacity to change more or less easily from one aspect of viewing to another one or to embed one circumstance or component into different correlations, to understand the relativity of circumstances and statements.
It allows to reverse relations, to more or less easily or quickly attune to new conditions of mental activity or to simultaneously mind several objects or aspects of a given activity (Lompscher These typical manifestations of mental agility can be focused on in problem solving by mathematical means and can be related to the heurisms known from the analyses of approaches by Pólya et al. also Bruder Intuitive, that is, untrained good problem solvers, are, however, often unable to access these flexibility qualities consciously.
Taken together, what follows is a topical survey of ideas representing the diversity of views and tensions inherent in a field of research that is both dates back to the time of Archimedes and is said to have come out of one of the famous stories told about this great mathematician and inventor.
The King of Syracuse asked Archimedes to check whether his new wreath was really made of pure gold.