Supporting Children’s Understanding of Volume Measurement and Ability to Solve Volume Problems: Teaching and Learning

Hsin-Mei E. Huang; Hsin-Yueh Wu

doi:10.29333/ejmste/109531

Full Text (PDF)

Hsin-Mei E. Huang ¹ ^* , Hsin-Yueh Wu ¹

More Detail

¹ University of Taipei, Taiwan, REPUBLIC OF CHINA^* Corresponding Author

Abstract

This research examined the effects of two instructional treatments on training performance in solid volume measurement and potential effects on solving capacity and displaced volume problems by two related studies. Fifty-three fifth-graders from a public elementary school in Taipei, Taiwan, participated. In the Phase 1 study, the children (n = 27) who received a curriculum that integrated geometric knowledge with concepts of volume measurement (GKVM) showed greater competence in solving problems than did those (n = 26) who received a curriculum that emphasized measurement procedures and volume calculation (VM). In the subsequent Phase 2, the same two groups received identical instruction in capacity, and the group that received the GKVM curriculum showed better problem-solving performance than did the other group. The one-on-one interview data showed that the children’s prior knowledge of solid volume measurement had a critical influence on the solving of advanced problems involving capacity and volume displacement concepts.

Keywords

geometric knowledge
problem solving
solid volume
volume measurement
water volume

License

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

EURASIA J Math Sci Tech Ed, 2019, Volume 15, Issue 12, Article No: em1789

https://doi.org/10.29333/ejmste/109531

Publication date: 29 Aug 2019

Article Views: 3384

Article Downloads: 7069

Open Access References How to cite this article

References

Battista, M. T. (2003). Understanding students’ thinking about area and volume measurement. In D. H. Clements, & G. Bright (Eds.), Learning and teaching measurement. 2003 Year book (pp. 122-142). Reston, VA: National Council of Teachers of Mathematics.
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: A project of National Council of Teachers Mathematics (pp. 843-908). Charlotte, NC: Information Age Publishing.
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.
Battista, M. T., & Clements, D. H. (1998). Students’ understanding of three-dimensional cube arrays: Findings from a research and curriculum development project. In R. Lehrer, & D. Chazan (Eds.), Designing learning environment for developing understanding of geometry and space (pp. 227-248). Mahwah, NJ: Erlbaum.
Bell, D., Hughes, E. R., & Rogers, J. (1975). Area, weight, and volume: Monitoring and encouraging children conceptual development. London, Great Britain: Thomas Nelson & Sons.
Braithwaite, D. W., & Goldstone, R. L. (2015). Effects of variation and prior knowledge on abstract concept learning. Cognition and Instruction, 33(3), 226-256. https://doi.org/10.1080/07370008.2015.1067215.
Cabrilog Company (2009). About Cabrilog history. Retrieved from http://www.Cabrilog.com.
Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Los Angeles, CA: SAGE publications.
Dickson, L., Brown, M., & Gibson, O. (1984). Children learn mathematics: A teacher’s guide to recent research. London, Great Britain: Holt, Rinehart and Winston Ltd.
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.
Goldin, G. A. (2003). Representation in school mathematics: A unifying research perspective. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275-285). Reston, VA: National Council of Teachers of Mathematics.
Guven, B. (2012). Using dynamic geometry software to improve eight grade students’ understanding of transformation geometry. Australasian Journal of Educational Technology, 28(2), 364-382. https://doi.org/10.14742/ajet.878.
Hawes, Z., Moss, J., Caswell, B., Naqvi, S., & MacKinnon, S. (2017). Enhancing children’s spatial and numerical skills through a dynamic spatial approach to early geometry instruction: Effects of a 32-week intervention. Cognition and Instruction, 35(3), 236-264. https://doi.org/10.1080/07370008.2017.1323902.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning Journal for Research in Mathematics Education, 28(5), 524-549. https://doi.org/10.2307/749690.
Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York, NY: Macmillan.
Hsieh, M.-H., & Huang, H.-M. E. (2013). The influence of digital materials for teaching volume measurement on fourth-graders' learning of volume concepts. In National Academy for Educational Research (Ed.), Conference handbook of 2013 Trend of Development of Digital Textbooks for Elementary and Junior-High Schools, pp. 91-99. (In Chinese.) Taipei, Taiwan: Taipei Branch of National Academy for Educational Research.
Huang, H.-M. E. (2015a). Elementary-school teachers’ instruction in measurement: Cases of classroom teaching of spatial measure in Taiwan. In L. Fan, N.Y. Wong, J. Cai, & S.-Q. Li (Eds.), How Chinese teach mathematics: Perspectives from insiders, pp. 149-184. Singapore: World Scientific Publishing Co.
Huang, H.-M. E. (2015b). An experiment of three-dimensional spatial geometry and volume measurement integrated digital teaching materials and instruction. Chinese Journal of Science Education, 23(1), 53-82. (In Chinese.) https://doi.org/10.6173/CJSE.2015.2301.03.
Huang, H.-M. E. (2017). Curriculum interventions for area measurement instruction to enhance children’s conceptual understanding. International Journal of Science and Mathematics Education, 15(7), 1323-1341. https://doi.org/10.1007/s10763-016-9745-7.
Kerslake, D. (1976). Volume and capacity. Mathematics Teaching, 77, 14-15.
Lehrer, R. (2003). Developing understanding of measurement. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 179-192). Reston, VA: National Council of Teachers of Mathematics.
Ministry of Education (2010). Grade 1-9 curriculum guidelines. Mathematics filed. (In Chinese) Taipei, Taiwan: Author.
National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Reston, VA: Author.
Novick, L. R., & Hmelo, C. E. (1994). Transferring symbolic representations across nonisomorphic problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(6), 1296-1321. https://doi.org/10.1037/0278-7393.20.6.1296.
Resnick, L. B. (2010). 2009 Wallace Foundation distinguished lecture: nested learning systems for the thinking curriculum Educational Researcher, 39(3), 183-197. https://doi.org/10.3102/0013189X10364671.
Seufert, T. (2003). Supporting coherence formation in learning from multiple representations. Learning and Instruction, 13, 227-237. https://doi.org/10.1016/S0959-4752(02)00022-1.
Shaffer, D. W., & Kaput, J. J. (1999). Mathematics and virtual cultural: An evolutionary perspective technology and mathematics education Educational Studies in Mathematics, 37, 97-119. https://doi.org/10.1023/A:1003590914788.
Simon, M. A. (1996). Beyond inductive and deductive reasoning: The search for a sense of knowing. Educational Studies in Mathematics, 30, 197-210. https://doi.org/10.1007/BF00302630.
Tan, N.-J. (1998). A study on the students’ misconceptions of area in the elementary school. (In Chinese.) Journal of National Taipei Teachers College, XI, 573-602.
The University of Chicago School Mathematics Project (2012). Everyday mathematics: Teacher’s lesson guide (Grade 5) (3rd ed., Vol. 2). Chicago, IL: The McGraw-Hill companies.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: Teaching developmentally (8th ed.). New York, NY: Pearson.
Vasilyeva, M., Ganley, C. M., Casey, B. M., Dulaney, A., Tillinger, M., & Anderson, K. (2013). How children determine the size of 3D structures: Investigating factors influencing strategy choice. Cognition and Instruction, 31(1), 29-61. https://doi.org/10.1080/07370008.2012.742086.

How to cite this article

APA

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), em1789. https://doi.org/10.29333/ejmste/109531

Vancouver

Huang HME, Wu HY. Supporting Children’s Understanding of Volume Measurement and Ability to Solve Volume Problems: Teaching and Learning. EURASIA J Math Sci Tech Ed. 2019;15(12):em1789. https://doi.org/10.29333/ejmste/109531

AMA

Huang HME, Wu HY. Supporting Children’s Understanding of Volume Measurement and Ability to Solve Volume Problems: Teaching and Learning. EURASIA J Math Sci Tech Ed. 2019;15(12), em1789. https://doi.org/10.29333/ejmste/109531

Chicago

Huang, Hsin-Mei E., and Hsin-Yueh Wu. "Supporting Children’s Understanding of Volume Measurement and Ability to Solve Volume Problems: Teaching and Learning". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 12 (2019): em1789. https://doi.org/10.29333/ejmste/109531

Harvard

Huang, H.-M. E., and 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), em1789. https://doi.org/10.29333/ejmste/109531

MLA

Huang, Hsin-Mei E. et al. "Supporting Children’s Understanding of Volume Measurement and Ability to Solve Volume Problems: Teaching and Learning". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 12, 2019, em1789. https://doi.org/10.29333/ejmste/109531