Research Article
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Year 2018, , 513 - 528, 15.07.2018
https://doi.org/10.12973/eu-jer.7.3.513

Abstract

References

  • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal of Research in Mathematics Education, 21, 132-144.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389- 407.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, California: Sage Publications, Inc.
  • Engelbrecht, J., Harding, A., & Potgieter, M. (2005). Undergraduate students’ performance and confidence in procedural and conceptual mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 701-712.
  • Even, R. (1993). Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
  • Hiebert, J., & Lefevre P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics, (pp.1- 27). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Isiksal, M. (2006). A study on pre-service elementary mathematics teachers‟ subject matter knowledge and pedagogical content knowledge regarding the multiplication and division of fractions. Unpublished doctoral dissertation, Middle East Technical University, Turkey.
  • Lucus, C. A. (2006). Is subject matter knowledge affected by experience? The case of composition of functions. In J. Novotna, H. Moraova, M. Kraka & N. Stehlikova (Eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 97-104). Prague: PME
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.
  • National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Nilsson, P., & Lindstrom, T. (2012, July). Connecting Swedish compulsory school teachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts. Paper presented at the 12th International Congress on Mathematical Education, Seoul, Korea.
  • Philipp, R., Schappelle, B., Siegfried, J., Jacobs, V., & Lamb, L. (2008). The effects of professional development on the mathematical content knowledge of K-3 teachers. In annual meeting of the American Educational Research Association, New York.
  • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The Knowledge Quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
  • Siegfried, J. M., Gordon, J. M., & Garcia, J. R. (2007). Barely in STEP: How professional development affects teachers’ perspectives on and analysis of student work. In T. Lambert & L. R. Wiest (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. University of Nevada: Reno.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-22.
  • Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, California: Sage Publications, Inc.
  • Thanheiser, E. (2009). Preservice elementary school teachers' conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251-281.

An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey

Year 2018, , 513 - 528, 15.07.2018
https://doi.org/10.12973/eu-jer.7.3.513

Abstract

The
aim of this qualitative case study is to investigate prospective mathematics
teachers’ subject matter knowledge of the underlying concepts of standard and
nonstandard algorithms used to solve the problems with whole numbers. Twenty
three prospective mathematics teachers enrolled in the Elementary Mathematics
Education Program of one of the most successful universities in Turkey were the
participants of the study. The data was collected through four tasks containing
basic algorithms. More specifically, the Ones Task assessed participants’
understanding of the underlying place value concepts of standard algorithms.
The Andrew Task and the Doubling Task required participants to conceptualize
and interpret nonstandard strategies. In the Division Task, participants were
expected to provide in-depth explanation for the difference between
multiplication and division and between partitive division and measurement
division. The content analysis method was used to analyze the data. The results
of the study revealed that more than half of the prospective mathematics
teachers had knowledge about the place value of 1 in addition and subtraction,
and also multiplication. However, most of the prospective teachers could not
explain the underlying principle and the meaning of the nonstandard algorithm
in subtraction. Similar to their knowledge on subtraction, prospective
teachers’ knowledge on division was limited.

References

  • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal of Research in Mathematics Education, 21, 132-144.
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389- 407.
  • Creswell, J. W. (2007). Qualitative inquiry and research design: Choosing among five approaches (2nd ed.). Thousand Oaks, California: Sage Publications, Inc.
  • Engelbrecht, J., Harding, A., & Potgieter, M. (2005). Undergraduate students’ performance and confidence in procedural and conceptual mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 701-712.
  • Even, R. (1993). Subject matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94-116.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press, Teachers College, Columbia University.
  • Hiebert, J., & Lefevre P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics, (pp.1- 27). Hillsdale, NJ: Lawrence Erlbaum Associates.
  • Isiksal, M. (2006). A study on pre-service elementary mathematics teachers‟ subject matter knowledge and pedagogical content knowledge regarding the multiplication and division of fractions. Unpublished doctoral dissertation, Middle East Technical University, Turkey.
  • Lucus, C. A. (2006). Is subject matter knowledge affected by experience? The case of composition of functions. In J. Novotna, H. Moraova, M. Kraka & N. Stehlikova (Eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 97-104). Prague: PME
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.
  • National Research Council. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
  • Nilsson, P., & Lindstrom, T. (2012, July). Connecting Swedish compulsory school teachers' content knowledge of probability to their level of education, teaching years and self-assessments of probability concepts. Paper presented at the 12th International Congress on Mathematical Education, Seoul, Korea.
  • Philipp, R., Schappelle, B., Siegfried, J., Jacobs, V., & Lamb, L. (2008). The effects of professional development on the mathematical content knowledge of K-3 teachers. In annual meeting of the American Educational Research Association, New York.
  • Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346.
  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The Knowledge Quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281.
  • Siegfried, J. M., Gordon, J. M., & Garcia, J. R. (2007). Barely in STEP: How professional development affects teachers’ perspectives on and analysis of student work. In T. Lambert & L. R. Wiest (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. University of Nevada: Reno.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harward Educational Review, 57(1), 1-22.
  • Strauss, A., & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park, California: Sage Publications, Inc.
  • Thanheiser, E. (2009). Preservice elementary school teachers' conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251-281.
There are 21 citations in total.

Details

Primary Language English
Subjects Studies on Education
Journal Section Research Article
Authors

Reyhan Tekin Sitrava

Publication Date July 15, 2018
Published in Issue Year 2018

Cite

APA Tekin Sitrava, R. (2018). An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey. European Journal of Educational Research, 7(3), 513-528. https://doi.org/10.12973/eu-jer.7.3.513
AMA Tekin Sitrava R. An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey. eujer. July 2018;7(3):513-528. doi:10.12973/eu-jer.7.3.513
Chicago Tekin Sitrava, Reyhan. “An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms With Whole Numbers: A Case of Turkey”. European Journal of Educational Research 7, no. 3 (July 2018): 513-28. https://doi.org/10.12973/eu-jer.7.3.513.
EndNote Tekin Sitrava R (July 1, 2018) An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey. European Journal of Educational Research 7 3 513–528.
IEEE R. Tekin Sitrava, “An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey”, eujer, vol. 7, no. 3, pp. 513–528, 2018, doi: 10.12973/eu-jer.7.3.513.
ISNAD Tekin Sitrava, Reyhan. “An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms With Whole Numbers: A Case of Turkey”. European Journal of Educational Research 7/3 (July 2018), 513-528. https://doi.org/10.12973/eu-jer.7.3.513.
JAMA Tekin Sitrava R. An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey. eujer. 2018;7:513–528.
MLA Tekin Sitrava, Reyhan. “An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms With Whole Numbers: A Case of Turkey”. European Journal of Educational Research, vol. 7, no. 3, 2018, pp. 513-28, doi:10.12973/eu-jer.7.3.513.
Vancouver Tekin Sitrava R. An Investigation of Prospective Mathematics Teachers’ Knowledge of Basic Algorithms with Whole Numbers: A Case of Turkey. eujer. 2018;7(3):513-28.