Abstract
This chapter reports two studies that examined the early algebraic thinking of Korean students. Firstly, it deals with students’ understanding of the equal sign , expressions , and equations as they progress through elementary school. Secondly, it investigates how third graders respond to diverse assessment items related to early algebraic thinking . The overall results show high percentages of correct answers. Whereas a majority of students showed a tendency to use computation, a detailed analysis of strategies used by students indicated some were capable of employing a structural approach. This chapter closes with discussions of the development of early algebraic thinking through the mathematics curriculum and the relationship between computational proficiency and algebraic thinking.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
An ANOVA test tells you whether you have an overall difference between your groups, but it does not tell you which specific groups differed—post hoc tests do.
References
Blanton, M., Levi, L., Crites, T., & Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3–5. In B. J. Dougherty & R. M. Zbiek (Eds.), Essential understandings series. Reston, VA: National Council of Teachers of Mathematics.
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87.
Britt, M. S., & Irwin, K. C. (2011). Algebraic thinking with and without algebraic representation: A pathway for learning. In J. Cai & E. Knuth (Eds.), Early algebraization (pp. 137–159). New York: Springer.
Brizuela, B. M., Blanton, M., Sawrey, K., Newman-Owens, A., & Gardiner, A. M. (2015). Children’s use of variables and variable notation to represent their algebraic ideas. Mathematical Thinking and Learning, 17(1), 34–63.
Byrd, C. E., McNeil, N. M., Chesney, D. L., & Matthews, P. G. (2015). A specific misconception of the equal sign acts as a barrier to children’s learning of early algebra. Learning and Individual Differences, 38, 61–67.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In Frank K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669–705). Charlotte, NC: Information Age.
Fujii, T., & Stephens, M. (2008). Using number sentences to introduce the idea of variable. In C. E. Greenes, & R. Rubenstein (Eds.), Algebra and algebraic thinking in school mathematics (70th Yearbook of the National Council of Teachers of Mathematics, pp. 127–140). Reston, VA: NCTM.
Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York: Routledge.
Ki, J. S., & Cheong, Y. O. (2008). The analysis of elementary school students’ understanding of the concept of equality sign in contexts and the effects of its teaching methods [in Korean with English abstract]. School Mathematics, 10(4), 539–557.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12(3), 317–326.
Kieran, C. (2014). What does research tell us about fostering algebraic thinking in arithmetic? Research brief for National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/Research-and-Advocacy/Research-Brief-and-Clips/Algebraic-Thinking-in-Arithmetic/.
Kieran, C., Pang, J., Schifter, D., & Ng, S. F. (2016). Early algebra: Research into its nature, its learning, its teaching (ICME 13 Topical surveys). New York: Springer.
Kim, J., Choi, J., & Pang, J. (2016). How do elementary school students understand ‘=’? Performance on various item types [in Korean with English abstract]. Journal of Educational Research in Mathematics, 26(1), 79–101.
Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.
Matthews, P., Rittle-Johnson, B., McEldoon, K., & Taylor, R. (2012). Measure for measure: What combining diverse measures reveals about children’s understanding of the equal sign as an indicator of mathematical equality. Journal for Research in Mathematics Education, 43(3), 316–350.
McNeil, N. M., Fyfe, E. R., & Dunwiddie, A. E. (2015). Arithmetic practice can be modified to promote understanding of mathematical equivalence. Journal of Educational Psychology, 107(2), 423–436.
Molina, M., & Ambrose, R. (2008). From an operational to a relational conception of the equal sign: Third graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61–80.
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Author. Retrieved from http://www.corestandards.org/Math/.
New Zealand Ministry of Education. (2009). The New Zealand curriculum: Mathematics standards for years 1–8. Retrieved from http://nzcurriculum.tki.org.nz/National-Standards/Mathematics-standards/The-standards/.
Ontario Ministry of Education. (2005). The Ontario curriculum, grades 1–8, mathematics (revised). Retrieved from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf.
Pang, J., & Choi, I. (2016). An analysis of algebraic thinking by third graders [in Korean with English abstract]. Education of primary school mathematics, 19(3), 223–247.
Pang, J., Cho, S., & Kim, J. (2017). An analysis of variable concept in the elementary mathematics textbooks and workbooks [in Korean with English abstract]. The Mathematical Education, 56(1), 81–100.
Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26, 257–277.
Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, I., Gardiner, A. M., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. Journal of Mathematical Behavior, 32(2), 173–182.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford & A. P. Schulte (Eds.), The ideas of algebra K-12 (1988 Yearbook, pp. 8–19). Reston, VA: National Council of Teachers of Mathematics.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Pang, J., Kim, J. (2018). Characteristics of Korean Students’ Early Algebraic Thinking: A Generalized Arithmetic Perspective. In: Kieran, C. (eds) Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68351-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-68351-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68350-8
Online ISBN: 978-3-319-68351-5
eBook Packages: EducationEducation (R0)