Discussions about teaching area measurement in primary school have been ongoing over some decades. However, investigations that thoroughly examine the current research on conceptual understanding in area measuring in elementary schools are still lacking. The objective of this paper is to review whether conceptual knowledge in area measurement may support students to obtain better results in primary schools. This study is to gain insight into how conceptual knowledge in area measurement has been portrayed for primary school students, and reveal possible omissions and gaps in the synthesized literature on the subject. To gather information, two databases were used: Scopus and Web of Science. Primary searches pulled up many studies on the subject of investigation. After analyzing abstracts and eliminating duplicates, our systematic review indicates that there seems a direct link between conceptual understanding and area measurement in primary school mathematics. Hence, teaching children the principle of area measurement rather than a procedure for solving problems seems to be the most effective way of improving problem-solving skills and conceptual understanding for primary students.
Citation: Hafiz Idrus, Suzieleez Syrene Abdul Rahim, Hutkemri Zulnaidi. Conceptual knowledge in area measurement for primary school students: A systematic review[J]. STEM Education, 2022, 2(1): 47-58. doi: 10.3934/steme.2022003
Discussions about teaching area measurement in primary school have been ongoing over some decades. However, investigations that thoroughly examine the current research on conceptual understanding in area measuring in elementary schools are still lacking. The objective of this paper is to review whether conceptual knowledge in area measurement may support students to obtain better results in primary schools. This study is to gain insight into how conceptual knowledge in area measurement has been portrayed for primary school students, and reveal possible omissions and gaps in the synthesized literature on the subject. To gather information, two databases were used: Scopus and Web of Science. Primary searches pulled up many studies on the subject of investigation. After analyzing abstracts and eliminating duplicates, our systematic review indicates that there seems a direct link between conceptual understanding and area measurement in primary school mathematics. Hence, teaching children the principle of area measurement rather than a procedure for solving problems seems to be the most effective way of improving problem-solving skills and conceptual understanding for primary students.
[1] |
Battista, M.T., Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. Mathematical Thinking and Learning, 2004, 6(2): 185–204. https://doi.org/10.1207/s15327833mtl0602_6 doi: 10.1207/s15327833mtl0602_6 |
[2] |
Byrnes, J.P. and Wasik, B.A., Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 1991, 27(5): 777–786. https://doi.org/10.1037//0012-1649.27.5.777 doi: 10.1037//0012-1649.27.5.777 |
[3] |
Castle, K. and Needham, J., (2007). First graders' understanding of measurement. Early Childhood Education Journal, 2007, 35(3): 215‒221. https://doi.org/10.1007/s10643-007-0210-7 |
[4] |
Clements, D.H., et al., Sarama, J., Van Dine, D.W., Barrett, J.E., Cullen, C.J., Hudyma, A., Dolgin, R., Cullen, A. L., & Eames, C. L. (2018b). Evaluation of three interventions teaching area measurement as spatial structuring to young children. Journal of Mathematical Behavior, 2018, 50: 23–41. https://doi.org/10.1016/j.jmathb.2017.12.004 |
[5] |
Common Core State Standards Initiative, Common Core State Standards for Mathematics, 2010. In Development. http://www.corestandards.org/ |
[6] |
Crooks, N.M. and Alibali, M.W., Defining and Measuring Conceptual Knowledge in Mathematics. Developmental Review, 2014, 34(4): 344–377. https://doi.org/10.1016/j.dr.2014.10.001 doi: 10.1016/j.dr.2014.10.001 |
[7] |
Cross, C.T. and Woods, T.A., Mathematics Learning in Early Childhood Paths Toward Excellence and Equity (H. Schweingruber (ed.)), The National Academic Press, 2009. |
[8] |
Grewal, A., Kataria, H. and Dhawan, I., Literature search for research planning and identification of research problem. Indian Journal of Anaesthesia, 2016, 60(9): 635–639. https://doi.org/10.4103/0019-5049.190618 doi: 10.4103/0019-5049.190618 |
[9] |
Hiebert, J., Why Do Some Children Have Trouble Learning Measurement Concepts? The Arithmetic Teacher, 1984, 31(7): 19–24. https://doi.org/10.5951/at.31.7.0019 doi: 10.5951/at.31.7.0019 |
[10] |
Hiebert, J., Conceptual and procedural knowledge: The case of mathematics. In Conceptual and Procedural Knowledge: The Case of Mathematics. Lawrence Erlbaum Associates, 1986. https://doi.org/10.4324/9780203063538 |
[11] |
Hord, C. and Xin, Y.P., Teaching Area and Volume to Students with Mild Intellectual Disability. Journal of Special Education, 2015, 49(2): 118‒128. https://doi.org/10.1177/0022466914527826 doi: 10.1177/0022466914527826 |
[12] |
Huang, H.-M.E. and Witz, K.G., Children's Conceptions of Area Measurement and Their Strategies for Solving Area Measurement Problems. Journal of Curriculum and Teaching, 2013, 2(1): 10–26. https://doi.org/10.5430/jct.v2n1p10 doi: 10.5430/jct.v2n1p10 |
[13] |
Hurrell, D.P., Conceptual Knowledge OR Procedural Knowledge or Conceptual Knowledge AND Procedural Knowledge: Why the Conjunction is Important to Teachers. Australian Journal of Teacher Education, 2021, 46(2): 57–71. https://doi.org/10.14221/ajte.2021v46n2.4 doi: 10.14221/ajte.2021v46n2.4 |
[14] |
II, J.P.S., Males, L. and Gonulates, F., Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation's Challenges. Faculty Publications: Department of Teaching, Learning and Teacher Education, 2016, 18(4): 239–270. https://doi.org/10.1080/10986065.2016.1219930 doi: 10.1080/10986065.2016.1219930 |
[15] |
De Jong, T. and Ferguson-Hessler, M.G.M., (1996). Types of qualities of knowledge. Educational Psychologist, 1996, 31(2), 105–113. https://doi.org/10.1207/s15326985ep3102_2 |
[16] |
Lehrer, C., Developing Understanding of Measurement. A Research Companion to Principles and Standards for School Mathematics, 2003: 179–192. |
[17] |
Machaba, F.M., The concepts of area and perimeter: Insights and misconceptions of Grade 10 learners. Pythagoras - Journal of the Associantion for Mathematics Education of South Africa, 2016, 37(1): 1–11. https://doi.org/10.4102/pythagoras.v37i1.304 doi: 10.4102/pythagoras.v37i1.304 |
[18] |
Mendezabal, M.J.N. and Tindowen, D.J.C., Improving Students' Attitude, Conceptual Understanding and Procedural Skills in Differential Calculus Through Microsoft Mathematics. Journal of Technology and Science Education, 2018, 4(4): 385–397. https://doi.org/10.3926/jotse.356 doi: 10.3926/jotse.356 |
[19] |
Naidoo, N., Creating a Deeper Understanding of Area and Perimeter in the Primary Classroom. |
[20] |
Outhred, L.N. and Mitchelmore, M.C., Young children's intuitive understanding of rectangular area measurement. Journal for Research in Mathematics Education, 2000, 31(2): 144–167. https://doi.org/10.2307/749749 doi: 10.2307/749749 |
[21] |
Perry, O. and Perry, J., Mathematics I. In Macmillan Technician Series (1st ed.), 1981. https://doi.org/10.1007/978-1-349-05230-1 |
[22] |
Ploger, D. and Hecht, S., Enhancing children's conceptual understanding of mathematics through chartworld software. Journal of Research in Childhood Education, 2009, 23(3): 267–277. https://doi.org/10.1080/02568540909594660 doi: 10.1080/02568540909594660 |
[23] |
Rittle-Johnson, B., Iterative development of conceptual and procedural knowledge in mathematics learning and instruction. In The Cambridge Handbook of Cognition and Education, 2019: 124–147. https://doi.org/10.1017/9781108235631.007 |
[24] |
Rittle-Johnson, B. and Alibali, M.W., Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology, 1999, 91(1): 175–189. https://doi.org/10.1037/0022-0663.91.1.175 doi: 10.1037/0022-0663.91.1.175 |
[25] |
Robinson, K.M. and Dube, A.K., A microgenetic study of the multiplication and division inversion concept. Canadian Journal of Experimental Psychology, 2009, 63(3): 193–200. https://doi.org/10.1037/a0013908 doi: 10.1037/a0013908 |
[26] |
Sholihah, S.Z. and Afriansyah, E.A., Analisis Kesulitan Siswa dalam Proses Pemecahan Masalah Geometri Berdasarkan Tahapan Berpikir Van Hiele. Mosharafa: Jurnal Pendidikan Matematika, 2017, 6(2): 287–298. https://doi.org/10.31980/mosharafa.v6i2.317 doi: 10.31980/mosharafa.v6i2.317 |
[27] |
Star, J.R., Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 2005, 36(5): 404–411. |
[28] |
Stephen, M. and Clements, D.H., Linear and Area Measurement in Prekindergarten to Grade 2. Learning and Teaching Measurement, 2003, 5(1): 3‒16. |
[29] |
Tan Sisman, G. and Aksu, M., A Study on Sixth Grade Students' Misconceptions and Errors in Spatial Measurement: Length, Area, and Volume. International Journal of Science and Mathematics Education, 2015, 14(7): 1293–1319. https://doi.org/10.1007/s10763-015-9642-5 doi: 10.1007/s10763-015-9642-5 |
[30] |
Tan Şişman, G. and Aksu, M., Sixth grade students' performance on length, area, and volume measurement. Egitim ve Bilim, 2012, 37(166): 141–154. |
[31] |
Wahid, N.T.A., Talib, O., Sulaiman, T. and Puad, M.H.M., A Systematic Literature Review on the Problem-Posing Strategies for Biology Problem-Posing Multimedia Module Design. International Journal of Academic Research in Business and Social Sciences, 2018, 8(12): 1020–1032. https://doi.org/10.6007/ijarbss/v8-i12/5150 doi: 10.6007/ijarbss/v8-i12/5150 |
[32] |
Yuberta, K.R., Supporting Students' Understanding of Area Measurement Using Rme Approach. International Conference on Education 2018 Teachers in the Digital Age, 2019, 3(1): 199–206. |
Publications included and excluded from the systematic review