Investigating volume estimation performance and strategies of 6th-Grade children and adults

References

• Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., & Alibali, M. W. (2020). The future of embodied design for mathematics teaching and learning. Frontiers in Education, 5, 147. https://doi.org/10.3389/feduc.2020.00147
   Google Scholar
• Andrews, P., Xenofontos, C., & Sayers, J. (2021). Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential; competence. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2020.1868591
   Web of Science ®Google Scholar
• Battista, M. T. (2003). Understanding students’ thinking about area and volume measurement. In D. H. Clements & G. Bright (Eds.), Learning and teaching measurement (pp. 122–142). NCTM.
   Google Scholar
• Battista, M. T., & Clements, D. H. (1996). Students’ understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258–292. https://doi.org/10.2307/749365
   Web of Science ®Google Scholar
• Boulton-Lewis, G., Wilss, L., & Mutch, S. (1996). An analysis of young children’s strategies and use of devices for length measurement. Journal of Mathematical Behavior, 15(3), 329–347. https://doi.org/10.1016/S0732-3123(96)90009-7
   Google Scholar
• Campbell, K. J., Watson, J. M., & Collis, K. F. (1992). Volume measurement and intellectual development. Journal of Structural Learning, 11(3), 279–298.
   Google Scholar
• Casey, B. M., Dearing, E., Vasilyeva, M., Ganley, C. M., & Tine, M. (2011). Spatial and numerical predictors of measurement performance: The moderating effects of community income and gender. Journal of Educational Psychology, 103(2), 296–311. https://doi.org/10.1037/a0022516
   Web of Science ®Google Scholar
• Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach (2nd ed.). Routledge.
   Google Scholar
• Crites, T. (1992). Skilled and less skilled estimators' strategies for estimating discrete quantities. The Elementary School Journal, 92(5), 601–619. https://www.jstor.org/stable/1001741
   Google Scholar
• Curry, M., Mitchelmore, M., & Outhred, L. (2006). Development of children’s learning of length, area, and volume measurement principles. In H. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 377–384). PME.
   Google Scholar
• Desli, D., & Giakoumi, M. (2017). Children’s length estimation performance and strategies in standard and non-standard units of measurement. International Journal for Research in Mathematics Education, 7(3), 61–84. http://sbem.iuri0094.hospedagemdesites.ws/revista/index.php/ripem/article/view/1381/pdf
   Google Scholar
• Desli, D., & Lioliou, A. (2020). Relationship between computational estimation and problem solving. International Electronic Journal of Mathematics Education, 15(3). https://doi.org/10.29333/iejme/8435
   Google Scholar
• Deslis, D., & Desli, D. (2022). Does this answer make sense? Primary school students and adults judge the reasonableness of computational results in context-based and context–free mathematical tasks. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-022-10250-0
   Web of Science ®Google Scholar
• Dorko, A., & Speer, N. (2015). Calculus students’ understanding of area and volume units. Investigations in Mathematics Learning, 8(1), 23–46. https://doi.org/10.1080/24727466.2015.11790346
   Google Scholar
• Dowker, A. (1997). Young children’s addition estimates. Mathematical Cognition, 3(2), 141–154. https://doi.org/10.1080/135467997387452
   Google Scholar
• Erdogan, F., & Erben, T. (2020). An investigation of the measurement estimation strategies used by gifted students. Journal of Computer and Education Research, 8(15), 201–223. https://doi.org/10.18009/jcer.680284
   Google Scholar
• Foster, C. (2011). Productive ambiguity in the learning of mathematics. For the Learning of Mathematics, 31(2), 3–7.
   Google Scholar
• Fyfe, E. R., & Rittle-Johnson, B. (2016). Feedback both helps and hinders learning: The causal role of prior knowledge. Journal of Educational Psychology, 108(1), 82–97. https://doi.org/10.1037/edu0000053
   Web of Science ®Google Scholar
• Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM Mathematics Education, 43(5), 709–722. https://doi.org/10.1007/s11858-011-0338-1
   Google Scholar
• Ho, A., & McMaster, H. (2019). Is ‘capacity’ volume? Understandings of 11 to 12-year-old children. In G. Hine, S. Blackley, & A. Cooke (Eds.), Mathematics education research: Impacting practice, Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 356–363). MERGA.
   Google Scholar
• 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
   Google Scholar
• Huang, H.-M. E. (2020). Effects of grade level and objects size on students’ measurement estimation performance. Eurasia Journal of Mathematics, Science and Technology Education, 16(12). https://doi.org/10.29333/ejmste/9342
   Google Scholar
• Huang, H.-M. E., & Wu, H.-Y. (2019). Supporting children’s understanding of volume measurement and ability to solve volume problems: Teaching and learning. Eurasia Journal of Mathematics, Science and Technology Education, 15(12). https://doi.org/10.29333/ejmste/109531
   Google Scholar
• Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students’ accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171–178. https://doi.org/10.1111/j.1949-8594.2011.00130.x
   Google Scholar
• Joram, E., Gabriele, A. J., Bertheau, M., Gelman, R., & Subrahmanyam, K. (2005). Children’s use of the reference point strategy for measurement estimation. Journal for Research in Mathematics Education, 36(1), 4–23. https://doi.org/10.2307/30034918
   Web of Science ®Google Scholar
• Joram, E., Subrahmanyam, K., & Gelman, R. (1998). Measurement estimation: Learning to map the route from number to quantity and back. Review of Educational Research, 68(4), 413–449. https://doi.org/10.3102/00346543068004413
   Web of Science ®Google Scholar
• Luwel, K., & Verschaffel, L. (2008). Estimation of ‘real’ numerosities in elementary school children. European Journal of Psychology of Education, 3(3), 319–338. https://doi.org/10.1007/BF03173002
   Google Scholar
• 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.
   Google Scholar
• Möhring, W., Frick, A., & Newcombe, N. S. (2018). Spatial scaling, proportional thinking, and numerical understanding in 5- to 7-year-old children. Cognitive Development, 45, 57–67. https://doi.org/10.1016/j.cogdev.2017.12.001
   Web of Science ®Google Scholar
• Park, D.-Y., Park, M.-H., & Bates, A. B. (2018). Exploring young children’s understanding about the concept of volume through engineering design in a STEM activity: A case study. International Journal of Science and Mathematics Education, 16(2), 275–294. https://doi.org/10.1007/s10763-016-9776-0
   Web of Science ®Google Scholar
• Pike, C. D., & Forrester, M. A. (1997). The influence of number-sense on children’s ability to estimate measures. Educational Psychology, 17(4), 483–500. https://doi.org/10.1080/0144341970170408
   Google Scholar
• Pizarro, N., Gorgorio, N., & Albarracin, L. (2015). Primary teachers’ approach to measurement estimation activities. In Proceedings of the 9th Congress of the European Society for Research in Mathematics Education (pp. 3227–3233). CERME.
   Google Scholar
• Reece, C. S., & Kamii, C. (2001). The measurement of volume: Why do young children measure volume inaccurately? School Science and Mathematics, 101(7), 356–361. https://doi.org/10.1111/j.1949-8594.2001.tb17969.x
   Google Scholar
• Ruwisch, S., Heid, M., & Weiher, D. F. (2015). Measurement estimation in primary school: Which answer is adequate? In K. Beswick, T. Muir, & J. Wells (Eds.), Proceedings of 39th Psychology of Mathematics Education Conference (Vol. 4, pp. 113–120). PME.
   Google Scholar
• Saiz, M., & Figueras, O. (2009). A research-based workshop designed for volume tasks. In B. Clarke, B. Grevholm, & R. Millman (Eds.), Tasks in primary mathematics teacher education (pp. 147–160). Springer. https://doi.org/10.1007/978-0-387-09669-8_11
   Google Scholar
• Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
   Google Scholar
• Sayers, J., Petersson, R., Rosenqvist, E., & Andrews, P. (2020). Estimation: An inadequately operationalised national curriculum competence. In R. Marks (Ed.), Proceedings of the British Society for research into learning mathematics (1st ed., Vol. 40, pp. Article 14). https://bsrlm.org.uk/wpcontent/uploads/2020/05/BSRLM-CP-40-1-14.pdf
   Google Scholar
• 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(1), 499–539. https://doi.org/10.25115/ejrep.v7i17.1359
   Google Scholar
• 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), 1–14. https://doi.org/10.1016/j.edurev.2019.01.002
   Google Scholar
• 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). Psychology Press.
   Google Scholar
• 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. https://doi.org/10.1007/s10763-015-9642-5
   Web of Science ®Google Scholar
• Smith, J. P. (2007). Tracing the origins of weak learning of spatial measurement. Retrieved December 11, 2020, from https://www.msu.edu/~stemproj/presentations/STEM_MSUColloquium_2007.pdf
   Google Scholar
• Sowder, J. (1992). Estimation and number sense. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). Macmillan Publishing Company.
   Google Scholar
• Tran, C., Smith, B., & Buschkuehl, M. (2017). Support of mathematical thinking through embodied cognition: Nondigital and digital approaches. Cognitive Research: Principles and Implications, 2(1), 16. https://doi.org/10.1186/s41235-017-0053-8
   PubMedGoogle Scholar
• Yang, D. C. (2017). Performance of fourth graders when judging the reasonableness of a computational result. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-017-9862-y
   Web of Science ®Google Scholar