You are here

Home » Content

AN INVESTIGATION OF THE CONCEPT OF VARIABLE IN TURKISH ELEMENTARY MATHEMATICS TEACHERS’ GUIDEBOOKS

Journal Name:

  • Journal of Educational and Instructional Studies in the World

Publication Year:

  • 2013

Key Words:

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
This research was aimed to investigate the presentation of the concept of variable in the algebra learning domain of Turkish elementary mathematics teachers’ guide books. Furthermore, it is particularly focused on whether explicit guidance on the teaching of the concept of variable for teachers is in these books. For this purpose, mathematics teachers’ guide books for sixth, seventh, and eighth grade level were examined by using document analysis as the method of research. Results indicated that variables were situated in the books with the meanings of pattern generalizer, unknown, placeholder, parameter, varying quantity and arbitrary symbols. Furthermore, although pattern generalizer was being touched in all grade levels, parameter and arbitrary symbols were only given in eight grade levels. On the other hand, explicit guidance for teachers was not found in the books. There was limited information about students’ misconceptions and different definitions of variable in the teachers’ guide books of all grade levels.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon arastrmx_116392_3_pp_139-149.pdf
  • 1
139-149
  • English

REFERENCES

References: 

Akgün, L., & Özdemir, M. E. (2006). Students’ understanding of variables as general number and unknown: A case study. The Teaching of Mathematics, 9(1). 45-61.
Asquith, P., Stephens, A., Knuth, E., & Alibali, M. (2007). Middle school teachers’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
Ball, D. L., & D. K. Cohen (1996). Reform by the book: What is or might be the role of curriculum materials in teacher learning and instructional reform?. Educational Researcher, 25(9), 6-8.
Bednarz, N., Kieran, C., & Lee, L. (1996). Approaches to algebra: Perspectives for research and teaching. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Bloom B. S. (1956). Taxonomy of educational objectives, handbook I: The cognitive domain. New York: David McKay Co Inc.
Booth, L. R. (1984). Algebra: Children’s strategies and errors. Windsor, UK: NFER-Nelson.
Booth, L. R. (1986). Difficulties in algebra. Australian Mathematics Teacher, 42(3), 2-4.
Booth, L. R. (1988). Children’s difficulties in beginning algebra. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra, K-12 (pp. 20-32). Reston, VA: National Council of Teachers of Mathematics.
Bottoms, G. (2003). Getting students ready for algebra: What middle grades students need to know and be able to do, Atlanta, GA: Southern Regional Education Board.
Boz, N. (2007). Interactions between knowledge of variables and knowledge about teaching variables. Sosyal Bilimler Arastırmaları Dergisi, 1, 1-18.
Cai, J. (2004): Introduction to the Special Issue on developing algebraic thinking in the earlier grades from an international perspective. The Mathematics Educator, 8(1), p. 1-5.
COPYRIGHT @ JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES IN THE WORLD 146
JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES
IN THE WORLD
February, March, April 2013, Volume: 3 Issue: 1 Article: 17
ISSN: 2146-7463
Cai, J. et. al. (2005). The Development of Students' Algebraic Thinking in Earlier Grades: A Cross-Cultural Comparative Perspective. ZDM: The International Journal on Mathematics Education.
Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically. Portsmouth, NH: Hienemann.
Clement,J., Narode,R., & Rosnick, P. (1981). Intuitive misconceptions in algebra as a source of math anxiety. Focus on Learning Problems in Mathematics, 3(4), 36-45.
Davis, R. B. (1984). Learning Mathematics: The Cognitive Science Approach to Mathematics Education. Norwood, NJ: Ablex.
Davis, E.A. & Krajcik, J.S, (2005) Designing Educative Curriculum Materials to Promote Teacher Learning. Educational Researcher, 34(3), 3 -14.
Dede, Y. & Argün, Z. (2003). Değişken Kavramının Öğretimi: Harf Sembollerin Farklı Kullanımları. Burdur Eğitim Fakültesi Dergisi, 4(6), 39-5.
Dogbey, G. Y. (2010). Concepts of variable in middle-grades mathematics textbooks during four eras of mathematics education in the United States. Unpublished Doctoral Dissertation, University of South Florida, Florida.
Fujii, T., & Stephens, M. (2001). Fostering an understanding of algebraic generalization through numerical expressions. In H. Chick, K. Stacey, J. Vincent & J. Vincent (Eds.), Proceedings of the 12th conference of the International Commission on Mathematics Instruction (Vol. 1, pp. 258-264). Melbourne: ICMI.
Kaput, J., & Blanton, M. (2005) Algebraifying the elementary mathematics experience in a teacher-centered, systemic way. In T. Romberg, T. Carpenter, & F. Dremock (Eds.) Understanding Mathematics and Science Matters (pp. 99–125). Mahwah, NJ: Lawrence Erlbaum Associates.
Kieran, C. (1988). The equation-solving errors of novice and intermediate algebra students. In L. Streefland (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education (pp. 141-146). Noordwijkerhout, The Netherlands: State University of Utrecht, Research Group on Mathematics Education and Educational Computer Centre.
Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Eds.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
Kieran, C., & Chalouh, L. (1992). Pre-algebra: The transition from arithmetic to algebra. In T. D. Owens (Eds.), Research ideas for the classroom: Middle grades.
Kuchemann, D. E. (1978). Children’s understanding of numerical variables. Mathematics in School, 7(4), 23-26.
Kuchemann, D. E. (1981). Algebra. In K. M. Hart (Eds.), Children’s understanding of mathematics: 11-16, (pp. 102-119). London: John Murray.
MacGregor, M.E. (1986). A fresh look at fruit salad algebra. Australian Mathematics Teacher, 42(4), 9-11.
Macgregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33, 1-19.7
MacGregor, M. & Stacey, K. (1993). Cognitive models underlying students’ formulation of simple linear equations. Journal for Research in Mathematics Education, 24(3) 217- 232.
COPYRIGHT @ JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES IN THE WORLD 147
JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES
IN THE WORLD
February, March, April 2013, Volume: 3 Issue: 1 Article: 17
ISSN: 2146-7463
Marzano, R. J., & Kendall, J. S. (2008). Designing & assessing educational objectives: Applying the new taxonomy. Thousand Oaks, CA: Corwin Press.
Milli Eğitim Bakanlığı (MEB). (2012a). İlköğretim matematik 6. sınıf öğretmen kılavuz kitabı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
Milli Eğitim Bakanlığı (MEB). (2012b). İlköğretim matematik 7. sınıf öğretmen kılavuz kitabı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
Milli Eğitim Bakanlığı (MEB). (2012c). İlköğretim matematik 8. sınıf öğretmen kılavuz kitabı. Ankara: Devlet Kitapları Müdürlüğü Basımevi.
National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author.
Nie,B., Cai,J., & Moyer,J.C. (2009). How a standards-based mathematics curriculum differs from a traditional curriculum: With a focus on intended treatments of the ideas of variable. ZDM (International Journal on Mathematics Education), 41(6), 777–792.
Oliver, A.I. (1984). Developing basic concepts in elementary algebra. Proceedings of the Eighth International Conference for the Psychology of Mathematics Education. Sydney.
Philipp, R. A. (1992). The many uses of algebraic variables. Mathematics Teacher, 85(7), 560.
Reys, R. E., Reys, B. J., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of standards-based middle grades mathematics curriculum materials on student achievement. Journal for Research in Mathematics Education, 34(1), 74-95.
Robitaille, D. F., & Travers, K. J. (1992). International studies of achievement in mathematics. In D. A. Grouws (Ed.), Handbook of Research on mathematics. Teaching and Learning (pp. 687-709). New York: Macmillan; Reston, VA: National Council of Teachers of Mathematics.
Schoenfeld, A. H., & Arcavi, A. (1988). On the meaning of variable. Mathematics Teacher, 81, 420-427.
Sleeman, D. H. (1984). An attempt to understand students’ understanding of basic algebra. Cognitive Science, 8, 387-412.
Smith, E. (2003). Stasis and change: Integrating patterns, functions, and algebra throughout the K- 12 curriculum. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards of School Mathematics (pp. 136–150). Reston, VA: National Council of Teachers of Mathematics.
Soylu, Y. (2008). 7. sınıf öğrencilerinin cebirsel ifadeleri ve harf sembollerini (değişkenleri) yorumlamaları ve bu yorumlarda yapılan hatalar. Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 25, 237-248.
Stacey, K., Kendal, M. (2004) Algebra: A world of difference. In K. Stacey, H. Chick, M. Kendal (Eds.) The Future of the Teaching and Learning of Algebra: The 12th ICMI Study. (pp. 329 – 346) Kluwer, Dordrecht.
Ursini, S., & Trigueros, M., (2001). A model for the uses of variable in elementary algebra. In Van den Heuvel-Panhuizen, M. (Ed.), Proceedings of the 25th conference of the international group for the psychology of mathematics education, 4, 327–334. Utrecht, Netherlands: Freudenthal Institute.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford, (Eds.). The ideas of algebra, K-12. 1988 Yearbook (pp. 8-19). Reston, VA; National Council of Teachers of Mathematics.
COPYRIGHT @ JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES IN THE WORLD 148
JOURNAL OF EDUCATIONAL AND INSTRUCTIONAL STUDIES
IN THE WORLD
February, March, April 2013, Volume: 3 Issue: 1 Article: 17
ISSN: 2146-7463
Wagner, S. (1999). What are these things called variables. In B. Moses (Ed.), Algebraic thinking, Grades K-12: Readings from the NCTM’s school-based journals and other publications (pp. 316-320). Reston, VA: National Council of Teachers of Mathematics.
Watson, J. (1990). Research for teaching: Learning and teaching algebra. Australian Mathematics Teacher, 46(3), 12-14.
Welder, R. M. (2007). Pre-service elementary teachers' mathematical content knowledge of prerequisite algebra concepts. Dissertation Abstracts International, 68(2), 504.
White, P., & Mitchelmore, M. (1996). Conceptual knowledge in Introductory Calculus. Journal for Research in Mathematics Education, 27, 79-95.
Wollman, W. (1983). Determining the sources of error in a translation from sentence to equation. Journal for Research in Mathematics Education, 14, 169-181.
COPYRIGHT

Thank you for copying data from http://www.arastirmax.com