American Journal of Educational Research
ISSN (Print): 2327-6126 ISSN (Online): 2327-6150 Website: https://www.sciepub.com/journal/education Editor-in-chief: Ratko Pavlović
Open Access
Journal Browser
Go
American Journal of Educational Research. 2018, 6(12), 1719-1725
DOI: 10.12691/education-6-12-20
Open AccessArticle

Error Patterns in Turkish Pre-Service Elementary Teachers’ Arithmetic Operations in Power Numbers

Sevim Sevgi1,

1Mathematics and Science Education Department, Faculty of Education, Erciyes University, Kayseri, Turkey

Pub. Date: December 28, 2018

Cite this paper:
Sevim Sevgi. Error Patterns in Turkish Pre-Service Elementary Teachers’ Arithmetic Operations in Power Numbers. American Journal of Educational Research. 2018; 6(12):1719-1725. doi: 10.12691/education-6-12-20

Abstract

This study investigated the pre-service elementary teachers understanding of exponent and how they solve the exponents equations and their different solving techniques and errors. Advanced mathematics automatically develops an understanding of basics of mathematics which is enough to explain and justify the reasonings of basic of arithmetic operations. The sample of the study is seventy-nine first year pre-service elementary teachers at the university of Turkey. Two items solved in detail. Content analysis of these two item solutions were analyzed for pre-service elementary teachers understanding of mathematics and their error patterns. Majority of them solved the items by well know strategies at the books but some of them made basic computation errors. They could not apply the basic exponents rules to solutions. Elementary teachers should learn the basic of rules without computation errors since they were teaching basics of operations. Elementary teaching programs should cover more mathematics courses with ambitious mathematics teaching with basic operations and logic.

Keywords:
pre-service elementary teachers power numbers algebraic operations error patterns error analysis

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Piaget, J, To understand is to invent: The future of education. Penguin Books, 1973.
 
[2]  Piaget, J, Piaget’s theory. Springer, Berlin, Heidelberg, 1976.
 
[3]  Weber, K, Students' understanding of exponential and logarithmic functions (at the undergraduate level). In D. Quinney (Ed.), Proceedings of the 2nd International Conference on the Teaching of Mathematics (pp. 1-7). Crete, Greece: John Wiley & Sons, 2002.
 
[4]  Pitta-Pantazi, D., Christou, C., & Zachariades, T. “Secondary school students’ levels of understanding in computing exponents”, The Journal of Mathematical Behavior, 26(4), 301-311, 2007.
 
[5]  Bottoms, G, Getting students ready for Algebra I: What middle grades students need to know and be able to do. Atlanta, GA: Southern Regional Education Board, 2003.
 
[6]  Thorpe, J. A, Algebra: What should we teach and how should we teach it? In S. Wagner, & C. Kieran (Eds.), Research issues in the learning and teaching of algebra (pp. 11-24). Hillsdale, NJ: Lawrence Erlbaum Associates, 1989.
 
[7]  Pinchback, C. L, “Types of errors exhibited in a remedial mathematics course”, Focus on Learning Problems in Mathematics, 13(2), 53-62, 1991.
 
[8]  Bush, S. B., Karp, K. S, “Prerequisite algebra skills and associated misconceptions of middle grade students: A review”, Journal of Mathematical Behavior, 32, 613-632, 2013.
 
[9]  Ashlock, R. B, Errors patterns in computation: Using error patterns to help each student learn (10th ed.). Boston, MA: Allyn & Bacon, 2010.
 
[10]  Watson, S.M.R, Lopes, J., Oliveira, C., Judge, S, “Error patterns in Portuguese students’ addition and subtraction calculation tasks: implications for teaching”, Journal for Multicultural Education, 2017.
 
[11]  Dubinsky, E, Reflective abstraction in mathematical thinking, in D. Tall (ed.) Advanced Mathematical Thinking, Dordrecht: Kluwer, 1991.
 
[12]  Breidenbach, D., Dubinsky, E., Hawks, J., Nichols, D, “Development of the process conception of function”, Educational Studies in Mathematics, 23, 247-285, 1992.
 
[13]  Engelhardt, J. M, “Analysis of children’s computational errors: A qualitative approach”, British Journal of Educational Psychology, 47, 149-154. 1977.
 
[14]  Traff, U., & Samuelson, J, “Analysis of errors in multi-digit arithmetic and arithmetic word problem solving in children with mathematics learning difficulties”, Special Education, 1, 121-132, 2013.
 
[15]  Strauss, A., & Corbin, J, Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, CA: Sage, 1990.
 
[16]  Stacey, K., & MacGregor, M “Building foundations for algebra. Mathematics Teaching in the Middle School, 2(4), 252-260, 1997.
 
[17]  Mason, J, Expressing generality and the roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 65-86). The Netherlands: Kluwer Academic Publishers, 1996.
 
[18]  Busi, R., & Jacobbe, T, “Examining student work in the preparation of preservice elementary school teachers”, The Mathematics Educator, 23, 23-29, 2014.
 
[19]  Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M, “Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification”, American Educational Research Journal, 46, 501-531. 2009.
 
[20]  Thanheiser, E, “Preservice elementary school teachers’ conceptions of multidigit whole numbers”, Journal for Research in Mathematics Education, 40, 251-281. 2009.
 
[21]  Luneta, K., & Makonye, P. J, “Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa”, Acta Didactica Napocensia, 3, 35-47, 2010.
 
[22]  Sfard, A, “The development of algebra: Confronting historical and psychological perspectives”, Journal of Mathematical Behavior, 14(1), 15-39., 1995.
 
[23]  Horn, I. S., Kane, B. D., &, Wilson, J, “Making sense of student performance data: Data use logic and mathematics teachers’ learning opportunities”, Amerian Educational Research Journal, 52, 208-242. 2015.
 
[24]  Ball, D. L, “Bridging practices: Intertwining content and pedagogy in teaching and learning to teach”, Journal of Teacher Education, 51, 241-247. 2000.
 
[25]  Ball, D. L., Thames, M. H., & Phelps, G, “Content knowledge for teaching: What makes it special?”, Journal of Teacher Education, 59, 398-407. 2008.
 
[26]  Ball, D. L., Hill, H. C., & Bass, H, “Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide?”, American Educator, 14, 16-17, 20-22, 43-46, 2005.