Content analysis of elementary mathematics textbooks in situations based on approximation and estimation

Raei, Fatemeh; Kazemi, Mohammad Bagher

doi:10.48310/pma.2025.14345.4138

Content analysis of elementary mathematics textbooks in situations based on approximation and estimation

Document Type : Research Paper

Authors

¹ Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran

² Department of Mathematics, University of Zanjan, Zanjan, Iran

10.48310/pma.2025.14345.4138

Abstract

The purpose of this research is to analyze elementary mathematics textbooks in situations based on approximation and estimation. The present research method is quantitative-qualitative content analysis.
The content analysis was done by the Krippendorff method and with the statistical population of the first to sixth grade math textbooks published in 1401. The contents of the books have been categorized according to the components of estimation (measurement, quantity, calculations and number line). Based on the findings of this research, by comparing the number of situations related to estimation in elementary math textbooks, the authors have paid the necessary attention to this topic, which is one of the goals of the curriculum in the field of mathematics learning.
The mentioned positions are about the estimation of calculations and number line, and they are less focused on measurement and quantity. Among different grades, the number of estimation positions in the first and third grades is less. The estimation of some concepts such as length, area, … has been mentioned, but the estimation of concepts such as temperature, angle and coordinate axes has not been discussed. Considering their importance in mathematics and daily life, teaching these items is also recommended.

Keywords

References

Andrews, P., Xenofontos, C., & Sayers, J. (2022). 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, 53(8), 2199–2225. https://doi.org/10.1080/0020739X.2020.1868591

Booth, J., Newton, K., & Twiss-Garrity, L. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110–118. https://doi.org/10.1016/j.jecp.2013.09.001

Cai, D., Zhang, L., Li, Y., Wei, W., & Georgiou, G. K. (2018). The role of approximate number system in different mathematics skills across grades. Frontiers in Psychology, 9, Article 1733. https://doi.org/10.3389/fpsyg.2018.01733

Chaman-Ara, S. (2018). Approximate numbers and estimation. Growth of Elementary Education, 22(4), 8-11. [In Persian]

Chaman-Ara, S. (2018). Approximate numbers and estimation. Growth of Elementary Education, 22(5), 8-10. [In Persian]

Cohen, D. J., & Sarnecka, B. W. (2014). Children’s number-line estimation shows development of measurement skills (not number representations). Developmental Psychology, 50(6), 1640–1652. https://doi.org/10.1037/a0035901

Crites, T. (1992). Skilled and less skilled estimators’ strategies for estimating discrete quantities. The Elementary School Journal, 92(5), 601-619. https://doi.org/10.1086/461709

Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45–55.

https://doi.org/10.2307/749163

Dowker, A. (2003). Young children’s estimates for addition: The zone of partial knowledge and understanding. In A. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructive adaptive expertise (pp. 243–266). Lawrence Erlbaum Associates.

Ganor-Stern, D. (2016). Solving math problems approximately: A developmental perspective. PLOS ONE, 11(5), e0155515. https://doi.org/10.1371/journal.pone.0155515

Ganor-Stern, D. (2018). Do exact calculation and computation estimation reflect the same skills? Developmental and individual differences perspectives. Frontiers in Psychology, 9, Article 1316. https://doi.org/10.3389/fpsyg.2018.01316

Hoth, J., Heinze, A., Weiher, D., Ruwisch, S., & Huang, H. (2019). Primary school students’ length estimation competence—A cross-country comparison between Taiwan and Germany. In J. Novotná & H. Moraová (Eds.), Opportunities in learning and teaching elementary mathematics (pp. 201–211). Charles University.

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

Kenedi, A. K., Helsa, Y., Ariani, Y., Zainil, M., & Hendri, S. (2019). Mathematical connection of elementary school students to solve mathematical problems. Journal on Mathematics Education, 10(1), 69-80. https://doi.org/10.22342/jme.10.1.5416.69-80

Kilpatrick, J., & Swafford, J. (2007). Helping children learn mathematics. National Academies Press. (M. Behzad & Z. Goya, Trans.; 2008) [In Persian]. Fatemi Cultural Institute.

Krippendorff, K. (2018). Content analysis: An introduction to its methodology (4th ed.). SAGE Publications. (H. Naebi, Trans.; 2019) [In Persian]. Nashr-e Ney.

Lemaire, P., Lecacheur, M., & Farioli, F. (2000). Children’s strategy use in computational estimation. Canadian Journal of Experimental Psychology, 54 (2), 141–148.

https://doi.org/10.1037/h0087336

McIntosh, A. (2004). Where we are today. In A. McIntosh & L. Sparrow (Eds.), Beyond written computation (pp. 3–14). MASTEC.

Mildenhall, P. (2016). Estimation in the primary school: developing a key mathematical skill for life. Australian Primary Mathematics Classroom, 21(1), 18-22.

Ministry of Education of Iran. (2012). National curriculum of the Islamic Republic of Iran. [In Persian]

Reys, L. H. (1984). Affective Variables and Mathematics Education. Elementary School Journal, 84(5), 547–557. https://doi.org/10.1086/461384

Russo, J. (2018). Dynamic estimation: A guided approach to refining student estimates. Australian Primary Mathematics Classroom, 23(3), 4-7.

Sayers, J., Petersson, J., Rosenqvist, E., & Andrews, P. (2020a). Estimation: An inadequately operationalised national curriculum competence. In R. Marks (Ed.), Proceedings of the British Society for Research into Learning Mathematics, 40(2).

Sayers, J., Petersson, J., Rosenqvist, E., & Andrews, P. (2020b). Opportunities to learn foundational number sense in three Swedish year one textbooks: Implications for the importation of overseas-authored materials. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2019.1688406

Schneider, M., Grabner, R. H., & Paetsch, J. (2009). Mental number line, number line estimation, and mathematical achievement: Their interrelations in grades 5 and 6. Journal of Educational Psychology, 101(2), 359–372. https://doi.org/10.1037/a0013840

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., Thompson, C., & Opfer, J. E. (2009). The Logarithmic-to-Linear Shift: One Learning Sequence, Many Tasks, Many Time Scales. Mind, Brain, and Education, 3(3), 143-150. https://doi.org/10.1111/j.1751-228X.2009.01064.x

Smets, K., Sasanguie, D., Szücs, D., & Reynvoet, B. (2015). The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison. Journal of Cognitive Psychology, 27(3), 310–325. https://doi.org/10.1080/20445911.2014.996568

Sowder, J. (1992). Estimation and number sense. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 371–389). National Council of Teachers of Mathematics.

Xenofontos, C., Alkan, S. H., & Andrews, P. (2023). Estimation in the Primary Mathematics Curricula of Cyprus, Greece and Turkey: A Privileged or Prevented Competence? Athens Journal of Education, 10(1), 117-138. https://doi.org/10.30958/aje.10-1-7

Yaftian, N., & Abbasi, F. (2022). A comparative analysis of the concepts presented in the mathematics textbooks of the elementary level in Iran and Japan. Curriculum Planning Research, 12(2), 122-152. [In Persian]

Zhu, M., Cai, D., & Leung, A. (2017). Number Line Estimation Predicts Mathematical Skills: Difference in Grades 2 and 4. Frontiers in Psychology, 8, 1576.

https://doi.org/10.3389/fpsyg.2017.01576