Lütfi İNCİKABI, Abdullah Çağrı BİBER, Müjdat TAKICAK, Semiha Betül BAYAM

An Investigation of Seventh Grade Students' Performances on Conceptual, Procedural and Graphical Problems Regarding Circles

The purpose of this study is to determine seventh grade students preferences among the procedural, conceptual and graphical questions in the subject of circles, to define their success levels in their preferences, and to compare students success levels in one question type with their performances in other question types. The methodology adopted during this research was case study. Based on criterion-based purposive sampling strategy, 98 middle school students were selected as the participants. Data were collected through an achievement test consisting of nine questions (three per question type). The results obtained from the study indicated that students mostly preferred graphical question types. Moreover, majority of students could not succeeded high levels in their preferred question types. In addition, the students performed better in graphical question types; however, the failure in procedural question types was remarkable.

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Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183-198.
Ates, S., & Stevens, J. T. (2003). Teaching line graphs to tenth grade students having different cognitive developmental levels by using two different instructional modules. Research in Science & Technological Education, 21(1), 55-66
Baker, R. S., Corbett, A. T., Koedinger, K. R. (2001). Toward a model of learning data representations. In J. D. Moore and K. Stenning (Eds), Proceedings of the 23rd Annual Conference of the Cognitive Science Society (pp. 4550). Mahwah, NJ: Erlbaum.
Baki, A. (1998). Balancing the conceptual and Procedural knowledge in teaching mathematics. Declaration presented to the Mathematics Symposium at Atatürk University 40. Anniversary of Establishment.
Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Ankara: Harf Eğitim Yayıncılığı.
Baki, A., & Kartal, T. (2004). Assessing the algebra knowledge of high-school students in terms of conceptual and Procedural knowledge. V. National Science and Mathematics Education Congress Declaration Book. Ankara: State Books Management Publishing House, 2002.
Baykul, Y. (2000). İlköğretimde matematik öğretimi: 1-5. sınıflar için. Pegem A. Yayıncılık.
Berg, C. A., & Smith, P. (1994). Assessing students' abilities to construct and interpret line graphs: Disparities between multiple‐choice and free‐response instruments. Science Education, 78(6), 527-554.
Bowen, G. M., Roth, W. M., & McGinn, M. K. (1999). Interpretations of graphs by university biology students and practicing scientists: Toward a social practice view of scientific representation practices. Journal of Research in Science Teaching, 36(9), 1020-1043.
Cifarelli, V. (1998). The development of mental representations as a problem solving activity. The Journal of Mathematical Behavior, 17(2), 238-264.
Clement, J. (1985, July). Misconceptions in graphing. Proceedings of the Ninth International Conference for the Psychology of Mathematics Education (Vol. 1, pp. 369-375). Utrecht,, The Netherlands: Utrecht University. An Investigation of Seventh Grade Students Performances on Conceptual, Procedural and Graphic... 11
Coştu, B. (2007). Comparison of students performance on procedural, conceptual and graphical chemistry gas problems. Journal of Science Education and Technology, 16(5), 379-386.
Coştu, B. (2010). Procedural, conceptual and graphical chemistry problems. Asian Journal of Chemistry, 22, 8 (11), 6013-6025.
Dreyfus, T., & Eisenberg, T. (1982). Intuitive functional concepts: A baseline study on intuitions. Journal for Research in Mathematics Education, 13(5), 360-380.
Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Portsmouth, NH: Heinemann.
Douady, R. (1986). Jeux de cadres et dialectique outil/objet. Recherches en Didactique des Mathématiques, 7(2), 5-32.
Eisenberg, T. (1991). Functions and associated learning difficulties. Advanced mathematical thinking (pp. 140-152). Springer Netherlands.
Erkan Erkoç, N., & Coştu, B. (2011, July). Comparison of chemistry teacher candidates in terms of conceptual, Procedural and graphical success at classroom level. II. National Chemistry Education Congress. Ataturk University, Erzurum.
Even, R. (1998). Factors involved in linking representations of functions. Journal of Mathematical Behavior, 17(1), 105-121.
Gagatsis, A., Michaelidou, E., & Shiakalli, M. (2000). Functions: A game of changing fields of representation. Nicosia: Erasmus IP.
Hadjidemetriou, C., & Williams, J. (2002). Children's graphical conceptions. Research in Mathematics Education, 4(1), 69-87.
Harel, G. (1989). Learning and teaching linear algebra: Difficulties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11, 139-48.
Hiebert, J. (Ed.). (2013). Conceptual and procedural knowledge: The case of mathematics. Routledge.
Hiebert J., & Carpenter T. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65 97). New York: Macmillan.
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 Erlbaum.
Incikabı, L., Tuna, A., & Biber, A. Ç. (2012). İlköğretim matematik öğretmen adaylarının kümelerle ilgili kavramsal bilgilerinin analizi. Erzincan Üniversitesi Eğitim Fakültesi Dergisi, 14(2), 523-538.
Kaput, J. J. (1985). Representation and problem solving: Methodological issues related to modeling. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 381-398). Hillsdale, NJ: Lawrence Erlbaum.
Kaput, J. J. (1987). Toward a theory of symbol use in mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 159-195). Hillsdale, NJ: Lawrence Erlbaum. 12
L. İncikabı, A. Ç. Biber, M. Takıcak, S. B. Bayam Keller, B. A., & Hirsch, C. R., (1998). Student preferences for representations of functions. International Journal of Mathematical Education in Science and Technology, 29(1), 1- 17.
Kekule, M. (2008). Graphs in physics education. GIREP 2008 Conference physics curriculum design, development and validation, Nicosia, Cyprus.
Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of educational research, 60(1), 1-64.
Lenton, G., Stevens, B., & Illes, R. (2000). Numeracy in science: Pupils' understanding of graphs. School science review, 82(299), 15-23.
Lesh, R., Post, T., & Behr, M. (1987a). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33-40). Hillsdale, NJ: Lawrence Erlbaum.
Lesh, R., Behr, M., & Post, T. (1987b). Rational number relations and proportions. In C.
Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41-58). Hillsdale, NJ: Lawrence Erlbaum.
Mack, N. (1995). Confounding whole-number and fraction concept when building on informal knowledge. Journal for Research Mathematics Education, 26(5), 422-441.
McGowan, M., & Tall, D. (2001). Flexible thinking, consistency, and stability of responses:A study of divergence. [Online]: Retrieved on 7-February 2005, at URL: http://www.warwick.ac.uk/staff/David.Tall/drafts/dot2001-mcgowen-tall-draft.pdf. MoNE, (2012). İlkögretim matematik dersi (6-8 sınıflar) öğretim programı [Elementary school mathematics teaching program (grades 6-8)]. Ankara, Turkey.
Moseley, B. (2005). Students early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 3769. NES (1993), National education standards: Observe, interact, change, learn. National Academic Press, Washington, DC. NCTM, (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Owens, K. D., & Clements M. A. (1998). Representations in spatial problem solving in the classroom. The Journal of Mathematical Behavior, 17, 197-218.
Özsoy,N., & Kemankaşlı, N. (2004). Basic mistakes and conceptual errors of secondary school students about circles. Turkish Online Journal of Educational Technology, 3(4), 140-147.
Piez, C. M., & Voxman, M.H. (1997). Multiple representations-using different perspectives to form a clearer picture. Mathematics Teachers, 90(2), 164-166.
Roth, W. M., & McGinn, M. K. (1998). Inscriptions: A social practice approach to representations. Review of Educational Research, 68(1), 35-59.
Soylu, Y, & Aydın, S., (2006). Matematik derslerinde kavramsal ve işlemsel öğrenmenin dengelenmesinin önemi üzerine bir çalişma. Erzincan Eğitim Fakültesi Dergisi, 8(2), 83-95. An Investigation of Seventh Grade Students Performances on Conceptual, Procedural and Graphic... 13
Şandır, H., Ubuz, B. ve Argün, Z., (2004). Ortaöğretim 9. sınıf öğrencilerinin mutlak değer kavramındaki öğrenme hatalari ve kavram yanilgılari. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi Bildiriler Kitabı, (Cilt: II, ss: 1107-1112). Ankara: Devlet Kitapları Müdürlüğü Basımevi.
Tairab, H. H., & Khalaf Al-Naqbi, A. K. (2004). How do secondary school science students interpret and construct scientific graphs? Journal of Biological Education, 38(3), 127- 132.
Van de Walle, J. A. (1990). Elementary school mathematics, teaching developmentally. Addison-Wesley/Longman, Route 128, Reading, MA 01867.
Wang, T. W. (1989). A Course on applied linear algebra. Chemical Engineering Education, 23(4), 236-41.
Widjaja, Y. B., & Heck, A. (2003). How a realistic mathematics education approach and microcomputer-based laboratory worked in lessons on graphing at an Indonesian junior high school. Journal of science and mathematics Education in Southeast Asia, 26(2), 1- 51.
Yang, D. C., Li, M. N., & Lin, C.I. A study of the performance of 5th graders in number sense and its relationship to achievement in mathematics. International Journal of Science and Mathematics Education, 6(4), 789-807.