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Pre-Service Middle School Mathematics Teachers' Understanding of Students' Knowledge: Location of Decimal Numbers on a Number Line
ARTICLE

## Dilek Girit, Didem Akyuz

IJEMST Volume 4, Number 2,

## Abstract

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the pre-service teachers' anticipation of students' misconceptions and difficulties for the given task. To conduct our analysis, we conducted interviews with three 5th and three 6th grade students, and eight pre-service teachers. During the interviews we asked them to solve the question and explain their solution strategies. The findings of the study indicate that students and pre-service teachers approach this problem in different ways. However, both groups have a tendency to think of decimals successively and indicate precise answers rather than specifying a range of possible values. We also observed the pre-service teachers could only partially anticipate the misconceptions and difficulties faced by the students.

## Citation

Girit, D. & Akyuz, D. (2016). Pre-Service Middle School Mathematics Teachers' Understanding of Students' Knowledge: Location of Decimal Numbers on a Number Line. International Journal of Education in Mathematics, Science and Technology, 4(2), 84-100. Retrieved November 19, 2019 from https://www.learntechlib.org/p/175795/.

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### Keywords

- Arithmetic
- case studies
- Comparative Analysis
- Data Analysis
- Foreign Countries
- Grade 5
- Grade 6
- Interviews
- Knowledge Level
- Mathematics Skills
- Mathematics Teachers
- Middle School Students
- Middle School Teachers
- Misconceptions
- Number Concepts
- Numeracy
- preservice teachers
- problem solving
- Qualitative Research
- Student Teacher Attitudes
- Teacher Expectations of Students

## References

View References & Citations Map- An, S., Kulm, G. & Wu, Z. (2004). The pedagogical content knowledge of middle school teachers in China and the U.S. Journal of Mathematics Teacher Education, 7, pp. 145-172.
- Anderson, J., White, P. & Sullivan, P. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem solving beliefs and practices. Mathematics Education Research Journal, 17(2), 9-38.
- Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM Mathematics Education, 44, 223-247.
- Bright, G.W., Behr, M.J., Post, T.R., & Wachsmuth, I. (1988). Identifying fractions on number lines, Journal for Research in Mathematics Education, 19(3), 215–232.
- Brousseau, G., Brousseau, N., & Warfield, V. (2007). Rationals and decimals as required in the school curriculum Part 2: From rationals to decimals. Journal of Mathematical Behavior, 26, 281-300.
- Cooney, T.J. (1999). Conceptualizing teachers’ ways of knowing. Educational Studies in Mathematics, 38(1-3), 163-187.
- Creswell, J.W. (2005). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (2nd Ed.). Upper Saddle River, NJ: Pearson Education, Inc.
- Creswell, J.W. (2007). Qualitative inquiry& Research design: Choosing among five approaches (2nd ed.). USA: Sage Publications. Depeape, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. & Van
- Dooren, W. (2015). Teachers' content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92.
- Glasgow, R., Ragan, G., Fields, W.M., Reys, R., & Wasman, D. (2000). The decimal dilemma. Teaching Children Mathematics, 7(2), 89–93.
- Fennema, E., Carpenter, T., Franke, M., Levi, L., Jacobs, V. & Empson, S. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education, 27(4), 403-434.
- Fraenkel, J.R., Wallen, N.E, & Hyun, H.H. (2012). How to design and evaluate research in education (8th ed.). Mc-Graw Hill Companies, Inc.: New York.
- Fuglestad, A.B. (1996). Teaching decimal numbers with spreadsheet as support for diagnostic teaching. In A. Buquet, J. Cabrera, E. Rodriguez& M.H. Sanchez (Eds.), ICME 8 (pp. 79-89). Spain: ICME.
- Janvier, C. (1987). Translation processes in mathematics education. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 27-32). Hillsdale, NJ: Lawrence
- McMullen, J., Hannula-Sormunen, M.M., & Lehtinen, E. (2015). Preschool spontaneous focusing on numerosity predicts rational number conceptual knowledge 6 years later. ZDM, 1-12.
- Merenluoto, K. (2003). Abstracting the density of numbers on the number line a quasi-experimental study. In N.A. Pateman, B.J. Dougherty& J. Zilliox (Eds.), Proceedings of the 2003 Joint Meeting of PME and PMENA (Vol. 3, pp. 285-292). Honolulu, HI: CRDG, College of Education, the University of
- Merriam, S.B. (1998). Qualitative research and case study applications in education. Jossey-Bass Publishers: San Francisco.
- Michaelidou, N., Gagatsis, A., & Pitta-Pantazi, D. (2004). The number line as a representation of decimal numbers: A research with sixth grade students. In M.J. Hoines, & A.B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (pp. 305–312). Bergen, Norway: PME.
- Moss, J. & Case, R. (1999). Developing children's understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122-147.
- Neumann, R. (1998). Students’ ideas on the density of fractions. In Proceedings of the Annual Meeting of the Gesellschaft fur Didaktik der Mathematik (pp. 97-104).
- Patton, M.Q. (1990). Qualitative evaluation and research methods (2nd ed.). Newbury Park, CA: Sage Publications, Inc.
- Putt, I.J. (1995). Pre-service teacher ordering of decimal numbers: When more is smaller and less is larger! Focus on Learning Problems in Mathematics, 17(3), 1-15.
- Raymond, A. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.
- Smith, C.L., Solomon, G.E.A., & Carey, S. (2005). Never getting to zero: Elementary school students’ understanding of the infinite divisibility of number and matter. Cognitive Psychology, 51, 101–140.
- Stacey, K. (2005). Travelling the road to expertise: A longitudinal study of learning. In H.L. Chick & J.L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, 1, 19-36. Melbourne: PME
- Stacey, K., Helme, S., Steinle, V., Baturo, A., Irwin, K., & Bana, J. (2001). Pre-service teachers’ knowledge of difficulties in decimal numeration. Journal of Mathematics Teacher Education, 4(3), 205-225.
- Stake, R. (1995). The art of case study research. Thousand Oaks, CA: Sage.
- Steinle, V. & Stacey, K. (1998). The incidence of misconceptions of decimal notation amongst students in grades 5 to 10. In C. Kanes, M. Goos & E. Warren (Eds.), Teaching mathematics in new times (Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australia, pp. 548-555). Brisbane: MERGA.
- Steinle, V., & Stacey, K. (2004). Persistence of decimal misconceptions and readiness to move to expertise. Proceedings of the 28th conference of the International Groups for the Psychology of Mathematics Education, 4, 225-232.
- Thipkong, S., & Davis, E.J. (1991). Preservice elementary teachers’ misconceptions in interpreting and applying decimals. School Science and Mathematics, 91, 93–99.
- Thompson, C.S., & Walker, V. (1996). Connecting Decimals and Other Mathematical Content. Teaching Children Mathematics, 2(8), 496-502.
- Tsao, Y.L. (2005). The number sense of pre-service elementary school teachers. College Student Journal, 39(4), 647-679.
- Türnüklü, E.B., & Yeşildere, S. (2007). The pedagogical content knowledge in mathematics: pre-service primary mathematics teachers' perspectives in Turkey. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-13.
- Ubuz, B. & Yayan, B. (2010). Primary teachers’ subject matter knowledge: Decimals. International Journal of Mathematical Education in Science and Technology, 41(6), 787-804.
- Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction, 14(5), 453-467.
- Vamvakoussi, X., & Vosniadou, S. (2007). How many numbers are there in a rational numbers interval? Constraints, synthetic models and the effect of the number line. Reframing the Conceptual Change Approach in Learning and Instruction.
- Vamvakoussi, X. & Vosniadou, S. (2010) How many decimals are there between two fractions? Aspects of secondary school students’ understanding of rational numbers and their notation, Cognition and 100 Girit & Akyuz
- VandeWalle J.A., Karp K.S., & Bay-William, J.M. (2013). Elementary and middle school mathematics: teaching developmentally (8th Ed.). United States of America: Pearson Education, Inc.
- Veloo, P.K. (2012). The Development of Number Sense Proficiency: An Intervention Study with Year 7 Students in Brunei Darussalam. The Mathematics Educator, 13(2), 39-54.
- Yin, R.K. (2003). Case study research: Design and method (3rd Ed.). Thousand Oaks, CA: Sage.
- Widjaja, W., Stacey, K. & Steinle, V. (2008). Misconceptions about density of decimals: Insights from Indonesian Pre-service Teachers. Journal of Science and Mathematics Education in Southeast Asia, 31(2), 117-131.

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