#
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 March 27, 2023 from https://www.learntechlib.org/p/175795/.

ERIC is sponsored by the Institute of Education Sciences (IES) of the U.S. Department of Education.

Copyright for this record is held by the content creator. For more details see ERIC's copyright policy.

### 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.

These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.

Suggest Corrections to References