## 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.

### Similar content being viewed by others

## 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)