INDEPENDENCE IN MATHEMATICAL THINKING OF GRADE XI STUDENTS OF BENGKULU STATE HIGH SCHOOL IN SOLVING COMBINATION PROBLEMS

Abstrak

This study aimed to analyze in depth the students' independent thinking ability in solving combination problems in combinatorics material. The research method used was a qualitative case study, involving 24 high school students in grade XI who were selected purposively based on the criteria of never having studied the concept of combination formally and never having faced similar problems. The research instrument consisted of specially designed combination story problems and semi-structured interview guidelines to explore students' cognitive processes. Analysis was carried out on four aspects of ability, namely: (1) the ability to state problems in other forms, (2) the ability to form a solution strategy, (3) the ability to apply strategies for solving, and (4) the ability to verify the results obtained. The results of the study stated: (1) problems were stated in the form of number symbols and diagrams, using narrative sentences, drawing circles, forming sets, and using symbols B1 to B6; (2) the solution strategies used included: counting with the help of symbols, counting directly without symbols, and counting alternately; (3) solutions were found by using a variable symbol and set approach; (4) no students verified their solution results. These findings confirmed that although the majority of students demonstrated independent thinking in problem-solving and strategy development, only a small proportion consistently implemented the strategy, and none verified the results. The implications of this research could serve as a reference for designing more effective learning strategies to develop students' independent thinking skills in mathematics, particularly in combinatorics. Keywords: Combination, Independent Thinking, Problem-Solving