Abstract
This paper describe the change patterns in the process of awareness, evaluation, and regulation of mathematics students in solving mathematical problems. The patterns of change is reveled done by observation of the emergence of activity and indicators awareness, evaluation, and regulation of students. Student metacognition activities and indicators are outlined in 5 activities with 30 indicators of awareness process, 5 activities with 23 indicators of evaluation process, and 4 activities with 19 indicators of regulation process. The subjects of the study were students of mathematics education who had taken Differential Calculus and subjects were given mathematical problems. Mathematical problem solving is done through think-aloud. In addition to think-aloud research subjects were given metacognition questionnaires, observed using observation sheets, and interviews. The data include student work, think-aloud, metacognition questionnaire, interview, and observation were analyzed using fixed comparison method. The result show that the change pattern of awareness, evaluation, and regulation processes of mathematics students were categorized into complete sequenced metacognition process, complete unsequenced metacognition and incomplete metacognition.
Highlights
It can be concluded that the change pattern of awareness, evaluation, and regulation of mathematics students in solving mathematical problems can be categorized into complete sequenced metacognition, complete unsequnced metacognition, and incomplete metacognition
Complete sequenced metacognition in awareness process patterned the students rethinking what is known from the mathematical problem, rethinking the question in mathematical problems and relating it to similar problems that have been resolved before, rethinking about something that has not been resolved in the past when solving the problem Mathematically, rethinking the step that must be done to solve a given mathematical problem, rethinking the description of the answer to the mathematical problem given
In the evaluation process the student rethinks the method used in solving the mathematical problem, rethinking the sequence of steps to be taken when solving the mathematical problem, re-examining the mathematical problems, which have been resolved, rethinking the correct answers to mathematical problems, and rethinking failure done in answering mathematical problems in the previous way
Summary
One's cognition consists of knowledge and cognition processes. The process of cognition consists of remembering, understanding, application, analysis, evaluation, and creating, (Anderson & Kratwohl, 2001). In relation to the metacognition processes, Davidson & Stenberg (1988) and Yoong (2007) state that metacognition is important for problem solving during the learning process. In another way, metacognition is important to know one's thinking process during problem solving (Cromley, 2005)
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