Ill-structured problems are contextualized, require learners to define the problems as well as determine the information and skills needed to solve them. The PISA and TIMSS show that Korean students have difficulty solving problems that connect mathematical concepts with everyday life. Ill-structured problems can also be considered as a way to improve students’ mathematical thinking capacity. Accordingly, they are able to abstract, generalize, and format problems of their daily lives. They learn to reorganize information, the better to focus thinking that leads to new understanding, and they evaluate alternatives in order to find the most appropriate solution.
Materials and methods:
The flowchart for the problem-solving learning process is:
[understanding problem] → [seeking solution] → [applying].
These study results showed that the mathematical abstraction levels and forms of the students can be improved by exposure to mathematical abstraction through a problem solving learning approach using ill-structured problems.
The analysis results of the mathematical abstraction levels and forms that the students showed during this study are also meaningful in regard to mathematics teaching and learning, and for the development of advanced mathematical thinking ability in schools.
Ill-structured problems with these characteristics can be used for the development of high-level mathematical thinking skills.