Students' Understanding of The Equal Sign Based on Their Learning Experience in Arithmetic

Abstract

The equal sign is an important concept in learning mathematics karena it is used in almost all branches of mathematics, but not many studies in Indonesia have made the equal sign the focus of research. This study aims to explore how students from elementary school to college students understand the equal sign in the context of arithmetic and algebra at school. A qualitative comparative analysis can be used to analyze several cases in complex situations so that it fits the purpose of this study. Participants consisted of 6 elementary school students, 14 junior high school students, 7 high school students and 3 college students in Bandung. The results of the study indicate that the equal sign is still interpreted narrowly as "result" or a sign to put the Menjawab, and has dependence on computational methods in solving problems and drawing conclusions. Thus, it can be concluded that students' understanding of the equal sign is still at the basic level. The results of this study show evidence that the operational meaning of the equal sign that students have when learning arithmetic will not change by itself without the stimulus provided by the teacher, and even tends to cause obstacles when students learn equations in algebra.

Tanda sama dengan merupakan konsep penting dalam pembelajaran matematika karena digunakan pada hampir seluruh cabang matematika, namun belum banyak penelitian di Indonesia yang menjadikan tanda sama dengan sebagai fokus penelitian. Penelitian ini bertujuan untuk mengeksplorasi bagaimana para siswa dari mulai sekolah dasar hingga mahasiswa memahami tanda sama dengan dalam konteks aritmatika dan aljabar di sekolah. A qualitative comparative analysis dapat digunakan untuk menganalisis beberapa kasus dalam situasi yang kompleks sehingga sesuai dengan tujuan penelitian ini. Partisipan terdiri dari 6 siswa SD, 14 siswa SMP, 7 siswa SMA dan 3 Mahasiswa di Bandung. Hasil penelitian menunjukkan bahwa tanda sama dengan masih dimaknai secara sempit yaitu sebagai “menghasilkan” atau tanda untuk meletakkan jawaban, serta memiliki kebergantungan terhadap metode komputasi dalam menyelesaikan masalah dan mengambil kesimpulan. Dengan demikian, dapat disimpulkan bahwa pemahaman siswa tentang tanda sama dengan masih berada di tingkat dasar.

Keywords

algebra; arithmetic; the equal sign; qualitative comparative analysis

PDF

References

Alibali, M.W., et al. (2007). A longitudinal examination of middle school students' understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9(3), 221-247. https://doi.org/10.1080/10986060701360902

Baiduri. (2015). Mathematics education students’ understanding of equal sign and equivalent equation. Asian Social Science, 11(25), 15-24. https://www.researchgate.net/publication/283695347

Banerjee, R. (2011). Is arithmetic useful for the teaching and learning algebra?. Contemporary Education Dialogue,8(2) 137-159. DOI: 10.1177/097318491100800202

Barlow, A.T & Harmon, S.E. (2012). Problem contexts for thinking about equality: an additional resource. Childhood Education, 88(2), 96-101. http://dx.doi.org/10.1080/00094056.2012.662121

Darr, C. (2003). The meaning of “equals”. Professional Development, 2, 4-7.

Elo, S., et.al. (2014). Qualitative content analysis: A focus on trustworthiness. SAGE open, 4(1), 1-10. DOI: 2158244014522633.

Fuchs, L.S. et al. (2014). Does calculation or word-problem instruction provide a stronger route to pre-algebraic knowledge?. Journal of Educational Psychology, 106(4), 990-1006. http://dx.doi.org/10.1037/a0036793

Gunnarsson, R., Sonnerhed, W.W., & Hernell, B. (2015). Does it help to use mathematically superfluous brackets when teaching the rules for the order of operations?. Educational Studies in Mathematics, 92 (1), 91-105. DOI 10.1007/s10649-015-9667-2

Kindrat, A.N., & Osana, H.P. (2018). The relationship between mental computation and relational thinking in the seventh grade. Fields Mathematics Education Journal, 3(6), 1-22. https://doi.org/10.1186/s40928-018-0011-4

Kiziltoprak, A & Kose, N.Y. (2017). Relational thinking: the bridge between arithmetic and algebra. International Electronic Journal of Elementary Education, 10(1), 131-145. DOI: 10.26822/iejee.2017131893

Knuth, E., Stephens, A., McNeil, N., & Alibali, M. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 36, 297-312. http://www.jstor.org/stable/30034852

Knuth, E., Alibali, M., Hattikudur, S, McNeil, N., & Stephens, A (2008). The importance of equal sign understanding in the middle grades. Mathematics Teaching in the Middle School, 13(9), 514–519. http://www.jstor.org/stable/41182605

Leavy, A., Hourigan, M., & McMahon, A. (2013). Early understanding of equality. Teaching Children Mathematics, 20(4), 246-252. http://www.jstor.org/stable/10.5951/teacchilmath.20.4.0246

Machaba, F. M., (2017). Grade 9 learners’ structural and operational conceptions of the equal sign: a case study of a Secondary School in Soshanguve. EURASIA Journal of Mathematics, 3 (11), 7243-7255. DOI: 10.12973/ejmste/78017

Mattews, P.G., et al. (2010). Understanding the equal sign as a gateway to algebraic thinking. SREE, 1-6. https://www.researchgate.net/publication/259749642

McNeil, N.M., & Alibali, M.W. (2005). Why won’t you change your mind? knowledge of operational patterns hinders learning and performance on equations. Child Development, 76 (4), 883 – 899.

McNeil, N.M., et al. (2017). Consequences of individual differences in children’s formal understanding of mathematical equivalence. Child Development, 1-17. DOI: 10.1111/cdev.12948

Mirin, A. (2019). The relational meaning of the equal sign: a philosophical perspective. Paper presented at the meeting of the 22nd Annual Conference of the Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education, Oklahoma City, USA.

Molina, M., & Ambrose, R. (2006). Fostering relational thinking while negotiating the meaning of the equal sign. Teaching Children Mathematics, 13(2), 111-117.

Stephens, M., et.al. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. The Journal of Mathematical Behavior, 32(2013) 173–182. http://dx.doi.org/10.1016/j.jmathb.2013.02.001

Vermeulen, C., & Meyer, B. (2017). The equal sign: teachers’ knowledge and students’ misconceptions. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 136–147. http://dx.doi.org/10.1080/18117295.2017.1321343

Refbacks

• There are currently no refbacks.