Session Information
24 SES 08 B, Problem Solving and Modeling
Paper Session
Contribution
There is a consensus today that metacognition plays an important role in effective learning of mathematics. Flavell (1976) defined metacognition as the knowledge and active regulation of one’s own cognitive processes. Nearly all definitions of metacognition have conceptualized around controlling and monitoring of one’s cognition, and self-regulating the solution processes (Mevarech,Tabuk & Sinai, 2006). For being qualified in mathematics, students must make use of cognitive resources in the sense of awareness and control over what to do and how to do it (Lucangeli and Cornoldi, 1997).
Metacognition takes part in mathematical problem solving, especially when students build an appropriate representation of the problem and check the outcome of the calculations (Verschaffel, 1999). Sarver (2006) declared that good problem solvers focus on the structural facets of a problem rather than its surface characteristics. They are more aware of their strengths and weaknesses. They monitor and evaluate the problem solving process more consistently compared to poor problem solvers. In essence, a growing body of evidence has shown that students have to be trained to self-monitor their learning as they solve problems (Mevarech & Kramarski, 1997). Educators’ main role is to teach students content and help them develop as learners. At this point, metacognition is important to achieve these goals, but instructors often feel lack of time or expertise to teach metacognition.
Nelson (1996) defined learning as a cyclic information flow between cognitive-level and meta-level through monitoring and control processes. At this point, self-questioning may be considered to have a crucial role on regulating these processes. Questioning is a comprehension-monitoring and regulating process; and serves as a self-checking process (Clardiello, 1998) and this characteristic is described as a metacognitive knowledge (Flavell, Miller & Miller, 1993). Questions have contributed to the development of meta-cognitive processes and mathematical achievement (Mevarech, 1999). As Schoenfeld (1985) declared that teaching students to ask self-addressed questions is important if they are to engage in problem solving situations. Researches indicated that self-questioning is one of the most effective monitoring and regulating strategy (King, 1994). Unfortunately, in many classrooms students are passive recipients of learning and stand away from asking questions in solving mathematics problems. This may be due to the lack of modeling that teachers demonstrate in how to ask relevant, directive and procedural questions. In mathematical problem solving situations, the questions should be designed to help students be aware of the problem-solving process and monitor their progress (Mevarech, 1999).
Based on the given theoretical framework, the purpose of the present study is twofold. The first research question is to investigate whether students who are trained to use enriched self-questioning perform better in word problem solving tasks. The second research question is to examine the development of students’ metacognitive processes. The study was designed to seek an understanding about effective methods for promoting self-questioning and metacognition. Thus, it aims to raise implications for the future design of metacognitive training programs.
Method
Expected Outcomes
References
Clardiello, A. V. (1998). Did you as a good question today? Alternative Cognitive and Metacognitive Strategies. Journal of Adolescent & Adult Literacy, 42(3), 210-219. American Educational Research Association (2003). Design-Based Research: An Emerging Paradigm for Educational Inquiry. Educational Researcher, 32 (1), 5-8. Flavell, J. H. (1976). Metacognitive aspects of problem solving, In L. B. Resnick (ed.), The Nature of Intelligence, pp. 231- 235, Hillsdale N. J.: Erlbaum. Flavell, J. H., Miller, P. H. & Miller, S. A. (1993). Cognitive Development (3rd ed.). Englewood Cliffs, NJ: Prentice Hall. King, A. (1994). Autonomy and question asking: The role of personal control in guided student-generated questioning. Learning and Individual Differences, 6, 163- 185. Lucangeli, D. and Cornoldi, C. (1997). Mathematics and metacognition: What is the nature of the relationship? Mathematical Cognition, 3 (2), 121- 139. Mevarech, Z. R.,Tabuk, A. & Sinai, O. (2006). Meta-cognitive Instruction in Mathematics Classrooms: Effects on the Solution of Different Kinds of Problems. In A. Desoete and M. Veenman (eds.), Metacognition in Mathematics Education, pp. 73- 81, New York: Nova Science Publishers, Inc. Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34, 365-394. Nelson, T. O. (1996). Consciousness and metacognition. American Psychologist, 51, 102- 116. Sarver, M. E., (2006). Metacognition and mathematical problem solving: Case studies of six seventh grade students, Unpublished Ph.D. dissertation, Montclair State University. Schoenfeld, A. H. (1985). How to solve it? 2nd ed. NJ: Princeton University Press. Verschaffel, L. (1999). Realistic Mathematical Modeling and Problem Solving in the Upper Elementary School: Analysis and Improvement, In J. H. M. Hamers, J. E. H. Van Luit and B. Csapo (eds.), Teaching and Learning Thinking Skills: Context of Learning, pp. 215- 240, Swets & Zeitlinger, Lisse.
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