STUDENTS’ COGNITIVE PROCESSES IN SOLVING PROBLEM RELATED TO THE CONCEPT OF AREA CONSERVATION

Rooselyna Ekawati, Ahmad Wachidul Kohar, Elly Matul Imah, Siti Maghfirotun Amin, Shofan Fiangga

Abstract


This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area conservation test. Results indicate that both samples performed more cyclic processes on formulating solution planning, regulating solution part and detecting and correcting error during the problem-solving. However, it was found that the high achiever student performed some processes than those of low achiever. Also, while the high achiever student did not predict any outcomes of his formulated strategies, the low achiever did not carry out the thought process after detecting errors of the initial solution gained. About the concept of area conservation, the finding also reveals that within the samples’ cognitive processes, the use of area formula come first before students decided to look for another strategy such as doing ‘cut-rotate-paste’ for the curved planes, which do not have any direct formula. The possible causes of the results were discussed to derive some recommendation for future studies.

Keywords


Students’ cognitive processes; Area conservation; Problem-solving

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References


Battista, M. T. (2007). The development of geometric and spatial thinking. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843–908). Charlotte, NC: Information Age Publishing Inc.

Bischoff, P. J., & Anderson, O. R. (1998). A case study analysis of the development of knowledge schema, ideational network, and higher cognitive operations among high school students who studied ecology. School Science and Mathematics, 98(5), 228-237.

Cramer, K., Post, T., & Currier, S. (1993). Learning and Teaching Ratio and Proportion: Research Implications. In D. Owens (Ed.), Research Ideas For the Classroom (pp. 159-178). NY: Macmillan Publishing Company

Freudenthal, H. (1986). Didactical phenomenology of mathematical structures (Vol. 1). Springer Science & Business Media. John P. Smith III, Marja van den Heuvel-Panhuizen, Anne R. Teppo. (2011). Learning, teaching, and using measurement: introduction to the issue. ZDM Mathematics Education (2011) 43:617–620 DOI 10.1007/s11858-011-0369-7 FIZ Karlsruhe

Hiebert, J. (1981). Units of measure: Results and implications from national assessment. The Arithmetic Teacher, 28(6), 38-43.

Jones, V. O. (2006). Cognitive processes during problem solving of middle school students with different levels of mathematics anxiety and self-esteem: case studies. A Published dissertation of Florida State University

Kordaki, M., & Balomenou, A. (2006). Challenging students to view the concept of area in triangles in a broad context: Exploiting the features of Cabri-II. International Journal of Computers for Mathematical Learning, 11(1), 99-135.

Kospentaris, G., Spyrou, P., & Lappas, D. (2011). Exploring students’ strategies in area conservation geometrical tasks. Educational Studies in Mathematics, 77(1), 105-127.

Kordaki, M., & Potari, D. (2002). The effect of tools of area measurement on students strategies: The case of a computer micro world. International Journal of Computers for Mathematical Learning, 7(1), 65-100.

Mason, J., Burton, L., & Stacey, K. (1985). Thinking mathematically (Rev. Ed.). Wokingham, UK: Addison-Wesley

Mason, J. (2015). On being stuck on a mathematical problem: What does it mean to have something come-to-mind?. LUMAT (2013-2015 Issues), 3(1), 101-121.

Miles & Huberman. (1994). Qualitative Data Analysis: An Exposed Sourcebook 2nd. London: SAGE Publication Ltd.

Montague, M. (2002). Mathematical problem solving instruction: Components, procedures, and materials. In M. Montague, & C. Warger (Eds.), Afterschool extensions: Including students with disabilities in afterschool programs. Reston, Va.: Exceptional Innovations.

Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106(2), 469.

Montague, M., Warger, C., & Morgan, T. H. (2000). Solve it! Strategy instruction to improve mathematical problem solving. Learning Disabilities Research & Practice, 15(2), 110-116.

Papadopoulous, I. (2010). Irregular Plane Figures: From the Eighteenth Century to the Modern Classroom. International Journal of Science and Mathematics Education, 8, 869-890.

Sisman, G. T., & Aksu, M. (2016). A study on sixth grade students’ misconceptions and errors in spatial measurement: length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293-1319.

Stillman, G. (1996). Mathematical Prospective and Cognitive Demand in Problem Solving. Mathematics Education Research Journal, 8(2), 174-197.

Stylianou, D. A., Kenney, P. A., Silver, E.A., & Alacaci, C. (2000). Gaining Insight into Students’ Thinking through Assessment Tasks. Mathematics Teaching in the Middle School, 6(2), 136-144

Tsai, C.-C. (1998). An analysis of Taiwanese eighth graders’ science achievement, scientific epistemological beliefs and cognitive structure outcomes after learning basic atomic theory. International Journal of Science Education, 20, 413-425

Tsai, C.-C. (1999). Content analysis of Taiwanese 14 year olds’ information processing operations shown in cognitive structures following physics instruction, with relations to science attainment and scientific epistemological beliefs. Research in Science & Technological Education, 17, 125– 138

Tsai, C.-C., & Huang, C.-M. (2001). Development of cognitive structures and information processing strategies of elementary school students learning about biological reproduction. Journal of Biological Education, 36, 21-26.

Tumová, V., & Vondrová, N. (2017). Links between Success in Non-Measurement and Calculation Tasks in Area and Volume Measurement and Pupils' Problems. Scientia in Education, 8(2), 100-129.

Yeo, J. B., & Yeap, B. H. (2010). Characterizing the cognitive processes in mathematical investigation. Accessed from http://www.cimt.plymouth.ac.uk/%20journal/jbwyeo.pdf, 10 October 2018.




DOI: https://doi.org/10.22342/jme.10.1.6339.21-36

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Journal on Mathematics Education
Doctoral Program on Mathematics Education
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