### An investigation of preservice mathematics teachers' teaching processes about "procedural and conceptual knowledge" related to division with fractions

#### Abstract

#### Keywords

#### Full Text:

PDF#### References

Abrosse, R., Clement, L., Philipp, R., & Chauvot, J. (2004). Assessing Preservice elementary school teachers’ beliefs about mathematics and mathematics learning: Rationale and Development of a Constructed-Response-Format Belief Survey. School Science and Mathematics Journal, 104(2), 56–69.

Akın, A. & Kabael, T. (2016). Bir matematik eğitimi araştırmasına dayalı öğretim deneyi deneyimi. Eğitimde Nitel Araştırmalar Dergisi [Journal of Qualitative Study in Education], 4(3), 7-27.

Armstrong, B. E.,& Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. Sowder & B. P. Schappelle (Eds.). Providing a foundation for teaching mathematics in the middle grades, 85–120. New York: SUNY.

Australian National Curriculum Board (2009). The shape of the Australian Curriculum. National Curriculum Board. [Çevrim-içi: http://www.acara.edu.au/verve/_resources/The_Shape_of_the_Australian_Curriculum_May_2009_file.pdf, Erişim tarihi: 15.12.2015.]

Aytekin, C. & Toluk Uçar, Z. (2014).Ortaokul öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi. İlköğretim Online, 13(2), 546‐563.

Aytekin, C. (2012). İlköğretim ikinci kademe öğrencilerinin kesirlerde tahmin becerilerinin incelenmesi. Yayımlanmamış Yüksek Lisans Tezi. Abant İzzet Baysal Üniversitesi Eğitim Bilimleri Enstitüsü, Bolu.

Ball, D. L. (1990). Preservice elementary and secondary teachers' understanding of division. Journal for Study in Mathematics Education, 21(2), 132-144.

Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Study in Mathematics Education, 23(3), 194-222.

Byrnes, J. P. & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27, 777-786.

Carpenter, T. P. (1986). Conceptual Knowledge as a Foundation for Procedural Knowledge. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge: The Case of Mathematics, 113-132. Hillsdale, NJ: Erlbaum.

Chen, L., Van Dooren, W., Chen, Q., & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919–948.

Chiu, M. (2009). Approaches to the teaching of creative and non-creative mathematical problems. International Journal of Science and Mathematics Education, 7(1), 55–79.

Cobb, P. & Steffe, L.P. (1983). The constructivist Researcher as Teacher and Model Builder. Journal for Study in Mathematics Education, 14(2), 83-94.

Davis, B. (1997). Listening for differences: An evolving conception of mathematics teaching. Journal for Study in Mathematics Education, 28 (3), 355–376.

Dubinsky, E.,& Harel, G. (1992). The Nature of the Process Conception of Function. In G.Harel, & Dubinsky, E. (Ed.), The concept of function: Aspects of epistemology and pedagogy, (Vol. 25). Washington: Mathematical Association of America.

Entwistle, N.,& Tait, H. (1990). Approaches to learning, evaluations of teaching, and preferences for contrasting academic environments. Higher Education, 19(2), 169‑194.

Glencoe Math (2013). Grade 6-8. McGraw Hill Education. Bothell, Washington.

Glencoe Math (2014). Grade 6-8. McGraw Hill Education. Bothell, Washington.

Gray, E.,& Tall, D. (1993). Success and Failure in Mathematics: The Flexible Meaning of Symbols as Process and Concept. Mathematics Teaching,14(2), 6-10.

Gray, E.,& Tall, D. (1994). Duality, ambiguity, and flexibility: a "proceptual" view of simple arithmetic. Journal of Study in Mathematics Education, 25(2), 116-140.

Haapasalo, L. (1993). Systematic constructivism in mathematical concept building. In p. Kupari & l. Haapasalo (Eds.), constructivist and curricular issues in the school mathematics education. Mathematics education study in Finland, Yearbook 1992-1993. 9-22. University of Jyväskylä: Institute for Educational Study.

Haapasalo, L.,& Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal für mathematik didaktik, 21(2), 139‑157.

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, 1–27. Hillsdale, NJ: Erlbaum.

Hiebert, J.,& Wearne, D. (1986). Procedures over concepts: The acquisition of decimal number knowledge. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics, 199–223. Hillsdale, NJ: Erlbaum.

Hofer, B. K.,& Pintrich, P. R. (1997). The development of epistemological theories: Beliefs about knowledge and knowing and their relation to learning. Review of Educational Study, 67(1), 88-140.

Hunting, R.P (1983). Emerging methodologies for understanding internal processes governing children's mathematical behaviour. The Australian Journal of Education, 27(1), 45-61.

Järvelä, J.,& Haapasalo, L. (2005). Three Types of Orientations by Learning Basic Routines in ICT. Paper presented at the Learning and Instruction on Multiple Context and Settings III. Proceedings of the Fifth Joensuu Symposium on Learning and Instruction, Joensuu.

Kadijevich, D.,& Haapasalo, L. (2001). Linking procedural and conceptual mathematical knowledge through CAL. Journal of Computer Assisted Learning, 17(2), 156-165.

Kaput, J. (1982). Differential effects of the symbol systems of arithmetic and geometry on the interpretation of algebraic symbols. Paper presented at the Annual Meeting of the American Educational Study Association, NY.

Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.

Kline, M. (1980). Mathematics: The Loss of Certainty. New York: Oxford University Press.

Lauritzen, Pal (2012). Conceptual and Procedural Knowledge of Mathematical Functions. Publications of the University of Eastern Finland.

Lesh, R., Kelly, A., (2000) Multitiered Teaching Experiments. In A. Kelly, R. Lesh (Eds.), Study Design in Mathematics and Science Education. 197-230. Lawrence Erlbaum Associates, Mahwah, New Jersey.

Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546–552.

Li, Y.,& Kulm, G. (2008). Knowledge and conﬁdence of Preservice mathematics teachers: The case of fraction division. ZDM–The International Journal on Mathematics Education, 40, 833–843.

Lo, J.J. ve Luo, F. (2012). Preservice elementary teachers’ knowledge of fraction division. J Math Teacher Educ, 15:481–500.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

MacGregor, D. (2013). Developing Mathematical Proficiency. Eps literacy and intervention. [Çevrim-içi: http://eps.schoolspecialty.com/downloads/study_papers/series/AcademyMATH_study.pdf, Erişim tarihi: 15.12.2015 ]

Macievejewski, W., Mgombelo, J. ve Savard, A. (2011). Meaningful Procedural Kknowledge in Mathematics Learning. CMESG/GCEDM Proceedings. [Çevrim-içi:http://www.math.ubc.ca/~wes/writing/meaningfulproceeduralknowledgeinmathematicslearning.pdf, Erişim Tarihi: 15.12.2015]

Marton, F.,& Säljö, R. (1976). On qualitative differences in learning: I. Outcome and process. British Journal of Educational Psychology, 46(1), 4-11.

Math Connects (2012). Grade 6-8. McGraw Hill Education.

MEB (2009). 6-8.Sınıflar Öğretim Programı. Ankara

MEB (2013). Ortaokul matematik dersi öğretim programı. Ankara

Milgram, R. James (2005). The mathematics preservice teachers need to know. Stanford University Department of Mathematics [Çevrim-içi: http://math.stanford.edu/pub/papers/milgram/FIE-book.pdf, Erişim Tarihi: 15.12.2015]

NCTM (2013). Proficiency teaching children mathematics. [Çevrim-içi: http://cliu21cng.wikispaces.com/file/view/Making%20Shifts%20Toward%20Proficiency.pdf/462127488/Making%20Shifts%20Toward%20Proficiency.pdf, Erişim Tarihi: 15.12.2015]

Nesher, P. (1986). Are mathematical understanding and algorithmic performance related. For the Learning of Mathematics, 6(3), 2‑9.

Pajares, M. F. (1992). Teacher's beliefs and educational study: Cleaning up a messy construct. Review of Educational Study, 62(3), 307-332.

Picker, S. H. & Berry, J.S. (2000). Investigating pupils’ images of mathematicians. Educational Studies in Mathematics, 43(1), 65–94.

PISA (2012). Ulusal ön raporu. Yenilik ve eğitim teknolojileri genel müdürlüğü. [Çevrim-içi:http://yegitek.meb.gov.tr/meb_iys_dosyalar/2013_12/13053601_pisa2012_ulusal_n_raporu.pdf, Erişim Tarihi: 15.12.2015]

Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Study in Mathematics Education, 28, 550–576.

Resnick, L.,& Omanson, S. F. (1987). Learning to understand arithmetic. In G. R. (Ed.), Advances in Instructional Psychology, 3. Hillsdale, NJ: Erlbaum.

Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Study in Mathematics Education, 20(4), 338–355.

Schoenfeld, A. H. (2007). Method. In F. K. Lester (Ed.), Second handbook of study on mathematics teaching and learning, 69–110. Greenwich, CT: information Age Publishing.

Sfard, A. (1991). On the dual nature of mathematical conceptions: theoretical reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1‑36.

Sinincrop, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions,153–161. Reston: NCTM.

Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education, 177-194. Boston, MA: Kluwer Academic Press.

Steffe, L.P. & Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly ve R.A. Lesh (Eds.), Handbook of Study design in mathematics and science education (pp. 267-306), Mahwah, NJ: Lawrence Erlbaum Associates, Publishers.

Steffe, L.P. (1984). The teaching experiment methodology in a constructivist study program. In M. Zweng. (ed.). Proceeding of the fourth International Congress on Mathematical Education, 469-471.

Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15(2), 105–127.

Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the study. In D. A. Grouws (Ed.), Handbook of Study on Mathematics Teaching and Learning, 127–146. New York: Macmillan.

Tirosh, D. (2000). Enhancing pre-service teachers' knowledge of children's conceptions: the case of division of fractions. Journal for Study in Mathematics Education, 31(1), 5-25.

Toluk Uçar, Z., Pişkin, M., Akdoğan ,E. N., ve Taşçı,D. (2010). İlköğretim öğrencilerinin matematik, matematik öğretmenleri ve matematikçiler hakkındaki inançları. Eğitim ve Bilim, 35(155), 131-144.

Utley, J. ve Redmond, A. (2008). Preservice elementary teacher attitudes towards and knowledge of the division of fractions. Paper presented at the annual meeting of the Study Council on Mathematics Learning, Oklahoma City, OK.

Vergnaud, G. (1990). Epistemology and psychology of mathematics education. In P. K. Nesher, J. (Ed.), Mathematics and cognition: a study synthesis by the international group for the psychology of mathematics education. Cambridge: Cambridge University Press, 14-30.

Zucker, B. (1984). The relation between understanding and algorithmic knowledge in decimals. Unpublished Master Thesis. University of Haifa.

Gökkurt, B., Şahin Ö. & Soylu, Y. (2012). Matematik Öğretmenlerinin Matematiksel Alan Bilgileri ile Pedagojik Alan Bilgileri Arasındaki ilişkinin incelenmesi. The Journal of Academic Social Science Studies, 5(8), 997-1012.

Gökkurt, B., Şahin, Ö., Soylu, Y. & Soylu, C. (2013). Examining Pre-Service Teachers’ Pedagogical Content Knowledge on Fractions in Terms of Students’ Errors. International Online Journal of Educational Sciences, 5(3), 719-735.

Işıksal, M. (2006). İlköğretim matematik öğretmen adaylarının kesirlerde çarpma ve bölmeye ilişkin alan ve pedagojik içerik bilgileri üzerine bir çalışma. (Yayımlanmamış doktora tezi). Orta Doğu Teknik Üniversitesi, Ankara.

Kahan, J., Cooper, D., & Bethea, K. (2003). The role of mathematics teachers’ content knowledge in their teaching: a framework for study applied to a study of student teachers. Journal of Mathematics Teacher Education, 6, 223-252.

Yeşildere, S. (2008, Ağustos). İlköğretim matematik öğretmen adaylarının sayı örüntüleri ile ilgili pedagojik alan bilgilerinin incelenmesi. VIII Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi. Bolu: Abant İzzet Baysal Üniversitesi.

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

**ISSN: 1305-3515**