6th, 7th and 8th Grade Students’ Misconceptions about the Order of Operations

Abstract

The aim of this research is to determine the misconceptions among 6th, 7th and 8th grade students about the order of operations in line with arithmetic expressions and posing and solving problems related to arithmetic expressions. The research has a mixed-method research design with concurrent-triangulation design. The study group for the research comprised a total of 240 students with 78 from 6th grade, 80 from 7th grade and 82 from 8th grade chosen with the simple random sampling method from schools located in a city in the Eastern Black Sea Region in Turkey. The research used a two-tier diagnostic test developed by the researcher to determine the misconceptions of students. According to the results of the research, it was determined that 6th, 7th  and 8th grade students performed arithmetic expressions from left to right without paying attention to order of operations, stated that only operations in brackets need to be performed first in terms of order of operations, did not pay attention to order of operation when writing or solving an arithmetic expression equal to a given number, and that students had difficulty posing a problem sentence involving arithmetic expressions and requiring order of operations.

Keywords

• Misconceptions,mathematics education,order of operations.

Kaynakça

1. Blando, J. A., Kelly, A. E., Schneider, B. R., & Sleeman, D. (1989). Analyzing and modeling arithmetic errors. Journal of Research in Mathematics Education, 20(3), 301- 308.
2. Creswell, J. W. (2003). Research design: Qualitative, quantitative, and mixed methods approaches (2nd ed.). Thousand Oaks, CA: Sage.
3. Gardella, F. (2009). Order of operations: A natural beginning. New York State Mathematics Teachers’ Journal, 59, 15-20.
4. Glidden, P. L. (2008). Prospective elementary teachers' understanding of order of operations. School Science And Mathematics, 108(4), 130-136.
5. Joseph, K. N. (2014). College students’ misconceptions of the order of operations. Fredonia, NY: Department of Mathematical Sciences, State University of New York
6. Lee, M. A. (2000). Analysis of concatenations and order of operations in written mathematics. School Science & Mathematics, 100(4), 173.
7. Linchevski, L., & Livneh, D. (1999). Structure sense: the relationship between algebraic and numerical contexts. Educational Studies in Mathematics, 40(2), 173–196.
8. Ministry of National Education [MNE]. (2005). Elementary education mathematics curriculum (1st – 5th grade). Board of Education and Discipline, Ankara, Turkey.

9. Ministry of National Education [MNE]. (2013). Middle school education mathematics curriculum (5th – 8th grade). Board of Education and Discipline, Ankara, Turkey.
10. Ministry of National Education [MNE]. (2018). Mathematics curriculum (1st – 8th grade). Board of Education and Discipline, Ankara, Turkey.
11. Pappanastos, E., Hall, M. A., & Honan, A. S. (2002). Order of operations: Do business students understand the correct order? Journal of Education for Business, 78(2), 81-84.
12. Peterson, D. (2000). History of the order of operations. Retrieved May 20, 2017 from http://mathforum.org/library/drmath/view/52582.html
13. Ocal, M , Ipek, A , Ozdemir, E., & Kar, T . (2018). Investigation of elementary school students’ problem posing abilities for arithmetic expressions in the context of order of operations. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(2), 170-191. https://doi.org/10.16949/turkbilmat.333037
14. Oksuz, C. (2009). Teaching the order of operations. Elementary Education Online, 8(2), 306-312.
15. Uca, S. (2010). A new approach when comprehending the order of operations in mathematics instruction: Mnemoni (Unpublished master’s thesis). Adnan Menderes University, Institute of Social Sciences, Aydin, Turkey.
16. Vanderbeek, G. (2007). Order of operations and RPN. Retrieved February 13, 2017 from https://digitalcommons.unl.edu/cgi/viewcontent.cgi?referer=https://www.google.com.tr/ &httpsredir=1&article=1045&context=mathmidexppap
17. Wu, H. (2007). “Order of operations” and other oddities in school mathematics. Retrieved March 15, 2018 from https://math.berkeley.edu/~wu/order5.pdf
18. Yenilmez, K. & Coksoyler, A. (2018). Difficulties encountered by sixth grade students in order of operations. Journal of Research in Education and Teaching, 7(2), 155-166.