Relationship between Computational Estimation and Problem Solving

Despina Desli; Anastasia Lioliou

doi:10.29333/iejme/8435

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Despina Desli ¹ ^* , Anastasia Lioliou ¹

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¹ Aristotle University of Thessaloniki Faculty of Education, School of Primary Education, GREECE^* Corresponding Author

Abstract

The present study attempted to explore the relationship between computational estimation and problem solving in a sample of Year 6 children and adults (N=72). For this purpose, participants were presented with two tasks which asked them to estimate the computational result in eight arithmetic operations (Computational Estimation Task) as well as to provide solution to eight mathematical word problems, all coming from four different areas of mathematics (Problem Solving Task). The analysis of the results showed that adult participants accomplished more successful estimations compared to children, mostly with the use of rounding and algorithm strategies in both age groups. Age differences were also found in the Problem Solving Task with geometry and arithmetic problems being the most difficult for children and adults, respectively. Last, a significant positive correlation was revealed between estimation computational ability and problem solving ability: participants who had great success in computational estimation tended to indicate high success rates in problem solving. Educational implications are further discussed in terms of the role of computational estimation and problem solving in mathematics learning.

Keywords

computational estimation
problem solving
primary school mathematics

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2020, Volume 15, Issue 3, Article No: em0602

https://doi.org/10.29333/iejme/8435

Publication date: 30 Jul 2020

Article Views: 1974

Article Downloads: 1342

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References

Anestakis, P., & Desli, P. (2014). Computational estimation in the Greek primary school: Tasks proposed for its teaching. MENON: Journal of Educational Research, 1^st Thematic Issue, 75-89.
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016-1031. https://doi.org/10.1111/j.1467-8624.2008.01173.x
Cai, J. (2010). Helping elementary school students become successful mathematical problem solvers. In D.V. Lambdin, & F.K. Lester (Eds.), Teaching and learning mathematics: Translating research for elementary school teachers (pp. 9-14). Reston, VA: NCTM.
Department for Education (2013). The National curriculum in England: Key stages 1 and 2 framework document. Retrieved from https://www.gov.uk/government/collections/national-curriculum
Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in the Netherlands. ZDM Mathematics Education, 39(5-6), 405-418. https://doi.org/10.1007/s11858-007-0043-2
Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. In A.J. Baroody, & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1-33). Mahwah, NJ: Lawrence Erlbaum Associates.
Frederiksen, N. (1984). Implications of cognitive theory for instruction in problem solving. Review of Educational Research, 54(3), 363-407. https://doi.org/10.3102/00346543054003363
Ganor-Stern, D. (2015). When you don’t have to be exact: investigating computation estimation skills with a comparison task. Acta Psychologica, 154, 1-9. https://doi.org/10.1016/j.actpsy.2014.10.010
Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201
Gurbuz, R., & Erdem, E. (2016). Relationship between mental computation and mathematical reasoning. Cogent Education, 3(1), 1-18. https://doi.org/10.1080/2331186X.2016.1212683
Hogan, T., & Brezinski, K. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259-281. https://doi.org/10.1207/S15327833MTL0504_02
Holth, P. (2008). What is a problem? Theoretical conceptions and methodological approaches to the study of problem solving. European Journal of Behavior Analysis, 9(2), 157-172. https://doi.org/10.1080/15021149.2008.11434302
Jitendra, A.H., & Star, J.R. (2012). An exploratory study contrasting high- and low- achieving students’ percent word problem solving. Learning and Individual Differences, 22(1), 151-158. https://doi.org/10.1016/j.lindif.2011.11.003
Kasmer, L., & Kim, O.K. (2011). Using prediction to promote mathematical understanding and reasoning. School Science and Mathematics, 111, 20-33. https://doi.org/10.1111/j.1949-8594.2010.00056.x
Kindrat, A.N., & Osana, H.P. (2018). The relationship between mental computation and relational thinking in the seventh grade. Fields Mathematics Education Journal, 3, 6. https://doi.org/10.1186/s40928-018-0011-4
LeFevre, J. A., Greenham, S. L., & Naheed, N. (1993). The development of procedural and conceptual knowledge in computational estimation. Cognition and Instruction, 11(2), 95-132. https://doi.org/10.1207/s1532690xci1102_1
Lemaire, P., & Lecacheur, M. (2002). Children’s strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281-304. https://doi.org/10.1016/S0022-0965(02)00107-8
Lemaire, P., & Lecacheur, M. (2011). Age-related changes in children’s executive functions and strategy selection: A study in computational estimation. Cognitive Development, 26(3), 282-294. https://doi.org/10.1016/j.cogdev.2011.01.002
Lester, F. K. Jr. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1). Retrieved from https://scholarworks.umt.edu/tme/vol10/iss1/12
Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Springer Open. https://doi.org/10.1007/978-3-319-40730-2_1
McIntosh, A. J. (2005). Developing computation. Hobart: Department of Education, Tasmania.
Mcintosh, A. J., Reys, B. J., & Reys, R. E. (1992). A proposed framework for examining number sense. For the Learning of Mathematics 12(3), 2-8.
NCTM (2000). Principles and standards for school Mathematics. Reston, VA: NCTM.
Polya, G. (1973). How to solve it. Princeton, New Jersey: Princeton University Press.
Reys, R. E. (1984). Mental computation and estimation: Past, present and future. The Elementary School Journal, 84(5), 546-557. https://doi.org/10.1086/461383
Reys, R., Bestgen, B., Ryblot, J., & Wyatt, J. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183-201. https://doi.org/10.2307/748555
Schoenfeld, A. (1992). Learning to think mathematically: Problem-solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York: MacMillan.
Segovia, I., & Castro, E. (2009). Computational and measurement estimation: curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psychology, 17(7), 1696-2095.
Sekeris, E., Verschaffel, L., & Luwel, K. (2019). Measurement, development, and stimulation of computational estimation abilities in kindergarten and primary education: A systematic literature review. Educational Research Review, 27, 1-14. https://doi.org/10.1016/j.edurev.2019.01.002
Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: a review. In J.I.D., Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). New York: Psychology Press.
Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.2307/749846
Sowder, J. T. (1992). Estimation and number sense. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371-389). New York, NY: Macmillan.
Stein, M. K., Boaler, J., & Silver, E. A. (2003). Teaching mathematics through problem solving: Research perspectives. In H. L. Schoen, & R. I. Charles (Eds.), Teaching mathematics through problem solving: Grades 6-12 (pp. 245-256). Reston, VA: NCTM.
Tsao, Y. L. (2009). Teaching computational estimation. In C.H. Yang (Ed.), Educational consulting book: Effective teaching methods (pp.45-54). Taiwan, Taipei: National Taipei University of Education.
Usiskin, Z. (1986). Reasons for estimating. In H. L. Schoen, & M. J. Zweng (Eds.), Estimation and mental computation. NCTM. Reston, VA.
van de Walle, J. A., & Lovin, L. H. (2006). Teaching student-centered mathematics: Grades K-3. New York: Pearson.
van den Heuvel-Panhuizen, M. (2001). Children learn mathematics. Utrecht, The Netherlands: Freudenthal Institute, Utrecht University.
Verschaffel, L., & De Corte, E. (1997). Word problems: a vehicle for promoting authentic mathematical understanding and problem solving in the primary school. In T. Nunes, & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 69-97). UK: Psychology Press Ltd.
Yang, D. C. (2019). Performance of fourth graders when judging the reasonableness of a computational result. International Journal of Science and Mathematics Education, 17(1), 197-215. https://doi.org/10.1007/s10763-017-9862-y

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APA

Desli, D., & Lioliou, A. (2020). Relationship between Computational Estimation and Problem Solving. International Electronic Journal of Mathematics Education, 15(3), em0602. https://doi.org/10.29333/iejme/8435

Vancouver

Desli D, Lioliou A. Relationship between Computational Estimation and Problem Solving. INT ELECT J MATH ED. 2020;15(3):em0602. https://doi.org/10.29333/iejme/8435

AMA

Desli D, Lioliou A. Relationship between Computational Estimation and Problem Solving. INT ELECT J MATH ED. 2020;15(3), em0602. https://doi.org/10.29333/iejme/8435

Chicago

Desli, Despina, and Anastasia Lioliou. "Relationship between Computational Estimation and Problem Solving". International Electronic Journal of Mathematics Education 2020 15 no. 3 (2020): em0602. https://doi.org/10.29333/iejme/8435

Harvard

Desli, D., and Lioliou, A. (2020). Relationship between Computational Estimation and Problem Solving. International Electronic Journal of Mathematics Education, 15(3), em0602. https://doi.org/10.29333/iejme/8435

MLA

Desli, Despina et al. "Relationship between Computational Estimation and Problem Solving". International Electronic Journal of Mathematics Education, vol. 15, no. 3, 2020, em0602. https://doi.org/10.29333/iejme/8435