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http://dx.doi.org/10.7468/jksmec.2020.23.1.45

Some Remarks on the Sameness and the Meaning of the Equal Sign in Elementary School Mathematics Textbooks  

Paek, Dae Hyun (Busan National University of Education)
Publication Information
Education of Primary School Mathematics / v.23, no.1, 2020 , pp. 45-61 More about this Journal
Abstract
The concept of equality is given as a way of reading the equal sign without dealing it explicitly in elementary school mathematics. The meaning of the equal sign can be largely categorized as operational and relational views. However, most elementary school students understand the equal sign as an operational symbol for just writing the required answers. It is essential for them to understand a relational concept of the equal sign because algebraic thinking in middle school mathematics is based on students' understanding of a relational view of the equal sign. Recently, the relational meaning of the equal sign is emphasized in arithmetic. Hence it is necessary for elementary school students to have some activities so that they experience a relational meaning of the equal sign. In this study, we investigate the meaning of the equal sign and contexts of the equal sign in elementary school mathematics to discuss explicit ways to emphasize the concept of equality and relational views of the equal sign.
Keywords
sameness; the equal sign; the meaning of the equal sign; elementary school mathematics textbooks;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Ko, J. S., Choi, J. H., Lee., S. E. & Park, K. S. (2016). An analysis on aspects of equalities with monomial left-hand side presented in Korean elementary school mathematics textbooks. Journal of Elementary Mathematics Education in Korea, 20(4), 583-599.
2 Ministry of Education (2018a). Elementary school mathematics 1-2. Chunjae Education(Inc.).
3 Ministry of Education (2018b). Elementary school mathematics 2-2. Chunjae Education(Inc.).
4 Ministry of Education (2018c). Elementary school mathematics 3-2. Chunjae Education(Inc.).
5 Ministry of Education (2018d). Elementary school mathematics 4-2. Chunjae Education(Inc.).
6 Ministry of Education (2019a). Elementary school mathematics 1-1. Chunjae Education(Inc.).
7 Ministry of Education (2019b). Elementary school mathematics 2-1. Chunjae Education(Inc.).
8 Ministry of Education (2019c). Elementary school mathematics 3-1. Chunjae Education(Inc.).
9 Ministry of Education (2019d). Elementary school mathematics 4-1. Chunjae Education(Inc.).
10 Ministry of Education (2019e). Elementary school mathematics 5-1. Chunjae Education(Inc.).
11 Ministry of Education (2019f). Elementary school mathematics 5-2. Chunjae Education(Inc.).
12 Ministry of Education (2019g). Elementary school mathematics 6-1. Chunjae Education(Inc.).
13 Ministry of Education (2019h). Elementary school mathematics 6-2. Chunjae Education(Inc.).
14 Ministry of Education (2019i). Teacher's guide for elementary school mathematics 5-2. Chunjae Education (Inc.).
15 Ki, J. & Chong, Y. O. (2008). The analysis of elementary students' understanding of the concept of equality sign in contexts and the effects of its teaching methods. School Mathematics, 10(4), 537-555.
16 Kim, J., Pang, J. & Choi, J. (2016). An analysis of elementary students' understanding of the equal sign by using rasch model, J. of Korean Soc. Math. Ed. Ser. A: The Mathematics Education, 55(1), 1-19.
17 Kim, J., Choi, J. & Pang, J. (2016). How do elementary school students understand '='? -Performance on various item types-, Journal of Educational Research in Mathematics, 26(1), 79-101.
18 Paek, D. H. (2017). A note on the use of properties of operations and the equal sign in elementary school mathematics, Journal of Elementary Mathematics Education in Korea, 21(4), 643-662.
19 Lee, C. H. & Kim, S. H. (2003). The analysis of the concept of equal symbol and the investigation of the students' understanding of it, Journal of Educational Research in Mathematics, 13(3), 287-307.
20 Lee, J. (2018). A critical consideration on the use of equal sign in $19{\div}5=3{\cdots}4$, School Mathematics, 20(1), 209-225.   DOI
21 Yim, J. (2013). Discrepancy between reading and writing equality number sentences in Korean language. Journal of Elementary Mathematics Education in Korea, 17(2), 207-223.
22 Altieri, M. B., Balka, D. S. Day, R., Gonsalves, P. D., Grace, E. C., Krulik, S. et al. (2009a). Math connects. Grade K-1, Macmillan/ McGraw-Hill.
23 Bloch, E. D.(2000). Proofs and Fundamentals A first course in abstract mathematics. Birkhauser.
24 Altieri, M. B., Balka, D. S. Day, R., Gonsalves, P. D., Grace, E. C., Krulik, S. et al. (2009b). Math connects. Grade 1-1, Macmillan/ McGraw-Hill.
25 Altieri, M. B., Balka, D. S. Day, R., Gonsalves, P. D., Grace, E. C., Krulik, S. et al. (2009c). Math connects. Grade 1-2, Macmillan/ McGraw-Hill.
26 Altieri, M. B., Balka, D. S. Day, R., Gonsalves, P. D., Grace, E. C., Krulik, S. et al. (2009d). Math connects. Grade 2-1, Macmillan/ McGraw-Hill.
27 Carpenter, T. P., Franke, M. L. & Levi, S. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.
28 Falkner, K. P., Levi, L., & Carpenter, T. P. (1999). Children's understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6(4), 232-236.   DOI
29 Jones, I., Inglis, M., Gilmore, C., & Evans, R. (2013). Teaching the substitutive conception of the equals sign. Research in Mathematics Education 15(1), 34-49.   DOI
30 McNeil, N. M. (2004). You'll see what you mean: Students encode equations based on their knowledge of arithmetic. Cognitive Science, 283 (3), 451-466.
31 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.
32 Norwood, K. S., Roby, T., Mendoza Epperson, J. A. Dixon, J. K., Scheer, J. K., Wright, D. G. et al. (2009). HSP math grade 1. Harcourt School Publishers.
33 Reys, R., Lindquist, M., Lambdin, D., & Smith, N. (2015). Helping children learn mathematics. Wiley.
34 Yim, J. (2019). Meaning of the expression a : b = c : d and implications for teaching, Journal of Elementary Mathematics Education in Korea, 23(3), 273-288.
35 Rittle-Johnson, B., Matthews, P. G., Taylor, R. S., & McEldoon, K. L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103, 85-104.   DOI
36 Saenz-Ludlow, A. & Walgamuth, C. (1998). Third graders' interpretations of equality and the equal symbol, Educational Studies in Mathematics 35, 153-187.   DOI
37 Stephens, A. C., Knuth, E. J., Blanton, M. L., Isler, L., Gardiner, A. M., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students' understanding. The Journal of Mathematical Behavior, 32(2), 173-182.   DOI