ERG SES G 04, Initial Teacher Education
Mathematics teachers content knowledge and pedagogical knowledge is a primary knowledge for improving mathematics achievement. Knowledge of content is and nature of errors provide corrective feedbacks to teachers (Ashlock, 2010). Teachers can determine their misconceptions and difficulties so they can increase their content and pedagogical knowledge. In the early ages, students make systematics and consistent errors at arithmetic operations. Teachers’ suppose these errors as careless mistakes or reflect a lack of frequency. This case is not always right, some of the errors are misconceptions. These errors may persist thought students’ academic life, and they affect the acquisition of advanced mathematics (Watson, Lopes, Oliveira, Judge, 2017). Aim of this descriptive study is to investigate the reasons of pre-service elementary teachers’ errors in algebraic operations in powers.
The researcher examined the error types in algebraic operations made by 85 Turkish pre-service elementary teachers. Each freshman pre-service elementary teacher completed a written mathematics achievement test. Pre-service elementary teachers was attending Basic Mathematics I course two hours in a week though the fall semester. Mathematics achievement test was designed as final exam of the course. A coding system was based on Engelhardt’ s (1977) and Traff and Samuelson’s (2013) work was used . was used to grade the power question. A reliability check was performed by an expert at mathematics.
Data frequency analyses revealed that most common type of error was miscalculation for addition, multiplication and division of power numbers. The second most common error type was related to common parentheses of numbers. Frequencies of the error patterns of powers numbers was given. Pre-service elementary teachers’ errors suggested that their error patterns in arithmetic operations is related to conceptual and procedural knowledge and skills. Error analysis lets instructors to ensure that all students have an opportunity to succeed in mathematics. Error analysis can yield important information about pre-service elementary teachers’ thinking, understanding, and misconceptions (Busi & Jacobbe, 2014; Silver, Mesa, Morris, Star, & Benker, 2009; Thanheiser, 2009). Misconceptions come from prior knowledge and errors are the result of their naïve concept. (Luneta & Makonye, 2010).Diagnostic assessment of student error patterns gives teachers the opportunity to deliver meaningful instruction to every student (Horn, Kane, & Wilson, 2015) and promote equality among a diverse population of students.Teachers’ knowledge of common student misconceptions and errors as one of the six constructs of mathematics teacher effectiveness to foster student learning (Ball, 2000; Ball, Thames, & Phelps, 2008; Hill & Ball, 2004) First limitation of the study is convenient sampling. Future studies would be enhanced by including pre-service elementary teachers from different universities. Second limitation is the administration of only 2 questions.
Ashlock, R. B. (2010). Errors patterns in computation: Using error patterns to help each student learn (10th ed.). Boston, MA: Allyn & Bacon. Ball, D. L. (2000). Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51, 241-247. doi: 10.1177/0022487100051003013 Ball, D. L., Hill, H. C., & Bass, H. (2005, Fall). 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. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 398-407. doi: 10.1177/0022487108324554. Busi, R., & Jacobbe, T. (2014). Examining student work in the preparation of preservice elementary school teachers. The Mathematics Educator, 23, 23-29. Horn, I. S., Kane, B. D., &, Wilson, J. (2015). Making sense of student performance data: Data use logic and mathematics teachers’ learning opportunities. American Educational Research Journal, 52, 208-242. doi: 10.3102/0002831215573773. Luneta, K., & Makonye, P. J. (2010). Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa. Acta Didactica Napocensia, 3, 35-47 Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46, 501-531. doi: 10.3102/0002831208326559. Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40, 251-281. Retrieved from http://www.jstor.org/stable/40539337 Watson, S.M.R, Lopes, J., Oliveira, C., Judge, S. (2017). Error patterns in Portuguese students’ addition and subtraction calculation tasks: implications for teaching, Journal for Multicultural Education, https://doi.org/10.1108/JME-01-2017-0002
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