Abstract
This study investigated the role of each strategy in explaining sixth graders’ (12-13 years old students’) non-routine problem solving success and discriminating between successful and unsuccessful students. Twelve non-routine problems were given to 123 pupils. Answers were scored between 0 and 10. Bottom and top segments of 27% were then determined based on total scores. All scripts of pupils in these segments were then re-scored with regard to strategy use. Multiple regression analysis showed that strategies explain 65% of the problem solving success. Order of importance of strategies are as follows: make a drawing, look for a pattern, guess and check, make a systematic list, simplify the problem, and work backward. According to discriminant analysis results, strategies which play a significant role in distinguishing top and bottom students are look for a pattern, make a drawing, simplify the problem, guess and check and work backward, respectively. Key words: Sixth graders, mathematics education, non-routine problems, non-routine problem solving, problem solving strategies.
Highlights
In the history of mathematics and in mathematics teaching, problem-solving always plays an important role, since all creative mathematical work demands actions of problem-solving (Burchartz and Stein, 2002)
A large body of literature about mathematical problem-solving shows that non-routine problems are the kind of problems which are most appropriate for developing mathematical problem-solving and reasoning skills, as well as development of the ability to apply these skills to real-life situations (Cai, 2003; London, 2007)
Correlation coefficients which belong to work backward and make a systematic list strategies (.30 and .11) indicate that there is a positive but weak relationship between each of these strategies and problem solving success
Summary
In the history of mathematics and in mathematics teaching, problem-solving always plays an important role, since all creative mathematical work demands actions of problem-solving (Burchartz and Stein, 2002). Mathematics education communities commonly agree that teaching problem solving means teaching non-routine problems as well as routine problems. A large body of literature about mathematical problem-solving shows that non-routine problems are the kind of problems which are most appropriate for developing mathematical problem-solving and reasoning skills, as well as development of the ability to apply these skills to real-life situations (Cai, 2003; London, 2007). Routine problems can be solved using methods familiar to students by replicating previously learned methods in a step-by-step fashion, non-routine problems are problems for which there is no predictable, well-rehearsed approach or pathway explicitly suggested by the task, task instructions, or worked-out examples (Woodward et al, 2012). Non-routine problem solving strategies can be defined Nonroutine problems require reasoning and higher-order thinking skills and often go beyond procedural skills (Kolovou et al, 2009).
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