期刊名称：Center for Educational Policy Studies Journal
印刷版ISSN：1855-9719
电子版ISSN：2232-2647
出版年度：2013
卷号：3
期号：4
页码：5-8
出版社：University of Ljubljana
摘要：Many researchers have dealt with, and continue to deal with, problemsolving, definitions of the notion of a problem, the roles of problem solvingin mathematics with regard to the development of procedural and conceptualknowledge, and differentiating between investigation and problem solving. Ingeneral, a problem in mathematics is defined as a situation in which the solverperceives the situation as a problem and accepts the challenge of solving it butdoes not have a previously known strategy to do so, or is unable to recall sucha strategy. The best known strategies in mathematics are inductive reasoningand deductive reasoning. Inductive reasoning involves, on the basis of observationsof individual examples, deriving a generalisation with a certain levelof credibility (in mathematics, if the generalisation is not proven we must nottake it as true, as always applicable). With deductive reasoning, on the otherhand, we derive examples on the basis of a broadly accepted generalisation thatserve to illustrate the generalisation. Both forms of reasoning are importantin mathematical thinking. In addition to these two forms of reasoning – deductiveand inductive – certain authors in the field of mathematics use othercollocations, such as inductive inference, and reasoning and proof. In the majorityof cases, researchers investigating problem solving associate the issuesof problem solving with inductive reasoning. Research in the field of problemsolving is focused on the cognitive processes associated with strategies used byenquirers (students of all levels) in solving selected problems, as well as on thesignificance of inductive reasoning for the development of the basic conceptsof algebra. By analysing the process of solving problems, we gain insight intothe strategies used by solvers, on the basis of which we can draw conclusionsabout the success of specific strategies in forming generalisations. An importantfinding in this regard is that not all strategies are equally efficient, and thatthe context of a problem can either support or hinder generalisation. However,selecting a good mathematical problem is not the only criteria for successfulgeneralisation. Another important factor is the social interaction between thesolvers of the problem, which means that when solving a problem, in additionto the dimension subject-object (solver-problem), it is also necessary to takeinto account the dimension subject-subject (solver-solver, solver-teacher).
