Preservice Mathematics Teachers’
Experiences about Function and
Equation Concepts

Yüksel Dede; Danyal Soybaş

doi:10.12973/ejmste/75183

Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts

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Yüksel Dede ¹ ^* , Danyal Soybaş ²

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¹ Cumhuriyet Üniversitesi, Sivas, TURKEY² Erciyes Üniversitesi, Kayseri, TURKEY^* Corresponding Author

Abstract

The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers’ understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were collected by a questionnaire and semi-structured interviews and analyzed using existential- phenomenology. The results show that the experiences of preservice math teachers related to these concepts can be summarized under six different titles, namely, confusion of the definition of function with one-to-one and onto properties, relating it with daily life (exampling), failure to take the functioning conditions into account, the relation between the values which make the function zero and roots of the equation, multiple representations of functions and taking the defining set of functions and equations into account.

Keywords

function
equation
conception
preservice mathematics teachers

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2011, Volume 7, Issue 2, 89-102

https://doi.org/10.12973/ejmste/75183

Publication date: 21 Jun 2011

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Article Downloads: 1015

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References

Akkoç, H. (2006).Concept Images Evoked By Multiple Representations of Functions. Hacettepe Universitesi Eğitim Fakültesi Dergisi-Hacettepe University Journal of Education 30, 1-10.
Attorps, I. (2003, February).Teachers’ Image of the “Equation Concept”. CERME 3: Third Conference of the European Society for Research in Mathematics Education. Bellaria, Italy.
Attorps, I. (2006). Mathematics Teachers’ Conceptions About Equations. Department of Applied Sciences of Education.University of Helsinki.Research Report 266. Finland. Doctoral Dissertation.
Attorps, I.,& Tossavainen, T. (2007, February).Is there equality in equation? Paper presented at and to be published in the proceedings of CERME 2007, Fifth Congress of the European Society for Research in Mathematics Education, 17-21, Larnaca, Cyprus.
Attorps, I.,&Tossavainen, T. (2008, January). On the equivalence relation in students' concept image of equation. Perspectives on Mathematical Knowledge, The Sixth Swedish Mathematics Education Research Seminar, 29- 30, Stockholm, Sweden.
Attorps, I.,&Tossavainen, T. (2009). Is there always truth in equation? C. Winsløw (ed.), Nordic Research in Mathematics Education: Proceedings from NORMA08 in Copenhagen, April 21-April 25, 2008, 143–150.
Bayazit, İ. (2008). Fonksiyonlar Konusunun Öğreniminde Karşılaşılan Zorluklar ve Çözüm Önerileri. M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel Kavram Yanılgıları ve Çözüm Önerileri (s. 91- 120). Pegem Yayınları, Ankara.
Beckmann, C., Thompson, D. and Senk, S. (1999).Assessing Students' Understanding of Functions in a Graphing Calculator Environment. School Science and Mathematics. December, 99, 8; ERIC, 451
Bergman, A.&Norlander, T. (2005). “Hay Sacks Anonymous”: Living in the Shadow of the Unidentified.Psychological Aspects of Physical Inactivity from a Phenomenological Perspective. The Qualitative Report, 10(4), 795-816.
Breidenbach, D., Dubinsky, Ed., Hawks, J. & Nichols, D.(1992).Development of the Process Conception of Function. Educational Studies in Mathematics, 23(3), 247- 285.
Caldwell, F.(1994, November).Effect of Graphics Calculators on College Students Learning of Mathematical Functions and Graphs. Paper Presented at the Annual Conference of the American Mathematics Association of Two Year Colleges, 20nd, Tulsa.
Cooney, T. (1999).Developing a Topic across the Curriculum: Functions. (Ed., Peake, L.) Mathematics,Pedagogy and Secondary Teacher Education. 361 Hannover Street, USA. 27-96.
Creswell, J. W. (1998). Qualitative inquiry and research design: Choosing among five traditions. Thousand Oaks, CA: Sage Publications.
Cruz, M.& Armando, M. (1995, October). Graph, Equation and Unique Correspondence: Three Models of Students’ Thinking about Functions in a TechnologyEnhanced Precalculus Class. Paper Presented at the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. 17th, Columbus.
Çetiner, Z., Kavcar, M.,&Yıldız,Y.(2003). Lise Matematik 1 Ders Kitabı. Devlet Kitapları, İstanbul, Turkey.
Dede, Y. (2004).Identifying Students’ Solution Strategies in Writing an Equation for Algebraic Word Problems. Eğitim Bilimleri ve Uygulama, 3 (6), 175-192.
Dede, Y. (2004). The Concept of Variable and Identification its Learning Difficulties. Kuram ve Uygulamada Eğitim Bilimleri, 4 (1), 25-56.
DeMarois, P.&Tall,D. (1996). Facets and Layers of the Function Concept. Proceedings of PME 20, Valencia, 2, 297–304.
Dennis, D.&Confrey, J. (1995). Functions of a curve: Leibniz's ... functions and its meaning for the parabola. The College Mathematics Journal, 26(2), 124-131.
Denzin, N.K. (1988) Triangulation. In: J.P. Keeves (Ed.), Educational Research, Methodology, and Measurement: An International Handbook (p. 511-513). Oxford: Pergamon Press.
Dubinsky, Ed.&Harel, G. (1992). The Nature of the Process Conception of Function.in G. Harel & Ed. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 85-107.
Dooren, W., Verschaffel, L.& Ongehena, P. (2003). Preservice teachers’ preferred strategies for solving arithmetic and algebra word problems. Journal of Mathematics Teacher Education 6, 27-52.
Dossey, J. (1999). Modeling with Functions.(Ed., L., Peake) Mathematics, Pedagogy and Secondary Teacher Education. 361 Hannover Street, USA. 221-280.
Dreyfus, T. & Eisenberg, T.(1982). Intuitive functional concepts: A baseline study on. intuitions. Journal for Research in Mathematics, 13(5), 360–380.
Eisenberg, T.(1991). Functions and Associated Learning Difficulties. Advanced Mathematical Thinking (Ed. D.Tall). Kluwer Academic Publishers, Dordrecht, Boston, London..140-152.
Even, R. (1988, July). Pre-Service Teachers Conceptions of the Relationships Between Functions and Equations. PME XII., Hungary.
Fujii, T. (2003). Probing students understanding of variables through cognitive conflict problems: Is the concept of a variable so difficult for students to understand? Proceedings of the 2003 Joint Meeting of PME and PMENA, vol. 1, Honolulu, HI, USA, pp. 49–65.
Gaea, L., Orit, Z.,&Kay. S.(1990). Functions, Graphs, and Graphing: Tasks, Learning, and Teaching. Review of Educational Research. 60(1), 1-64.
Giorgi, A.(1985).Sketch of a psychological phenomenological method. In A Giorgi (ed) Phenomenology and Psychological Research. Pittsburgh, PA: Duquesne University Press.
Graham, A.,&Thomas, J. (2000). Building versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics 41, 265-282.
Gray, E. & Tall, D. (1994). Duality, Ambiguity and Flexibility: A Proceptual view of Simple Arithmetic. Journal of Research in Mathematics Education, 25(2), 115-141.
Hauge, S.(1993). Functions and Relations: Some Applications from Database Management for the Teaching of Classroom Mathematics. Eric Document Reprodoction Service, ED 365519.
Herscovics, N.,&Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher, 73(8), 572- 580.
Hitt, F. (1998). Difficulties in the Articulation of Different Representations Linked to the Concept of Function. Journal of Mathematical Behavior, 17 (1), 123-134.
Hull, R. (2003). Describing Non-Institutionalized Male Rape. Unpublished Master’s Dissertation. Rand Afrikaans University.
Hull, S. & Seabold,D. (1995). Mathematics Leadership, CAMT, 2005. Functions & Equations. Functions & Equations. Retrieved from http://www.utdanacenter.org /mathtoolkit /instruction/activities/alg1.php (July 24, 2008)
Hunting, R. P. (1997). Clinical Interview Methods in Mathematics Education Research and Practice. Journal of Mathematical Behavior, 16(2), 145-165.
Jones, M. (2006). Demystifying functions: The historical and pedagogical difficulties of the concept of the function. Undergraduate Math Journal, 7 (2), 1-20.
Ketterlin-Geller, L., Jungjohann, K., Chard, D.,& Baker, S. (2007). From Arithmetic to Algebra. Educational Leadership, 65(3), 66-71.
Kieran, C. (1992). The Learning and Teaching of School Algebra. Handbook of Research on Mathematics Teaching and Learning.(Ed D.,Grouws). Macmillan Library Reference, New York, 390-419.
Kleiner, I. (1989). Evolution of the Function Concept: A Brief Survey. The College Mathematics Journal, 20 (4), 282- 300.
Knuth, E. (2000).Understanding Connections between Equations and Graphs. The Mathematics Teacher, 93 (1), 48-53.
Krathwohl, D. R. (1993). Methods of educational & social science research (2nd ed.). New York: Longman.
Laughbaum, E. (2003). Developmental Algebra with Function as the Underlying Theme. Mathematics and Computer Education 37(1), 63-71.
Lincoln, Y. S.,& Guba, E. G. (1985). Naturalistic Inquiry. Newburry Park, CA: Sage Publications.
MacGowen, M., DeMories, P. & Tall,D. (2000). Using the Function Machine as a Cognitive Root for Building a Rich Concept Image of the Function Concept. (Ed. F. Maria) Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology Mathematics Education, 22nd, Tucson, Arizona.
MacGregor, M. (1998). How Students Interpret Equations: Intuition versus Taught Procedures. Language and Communication in the Mathematics Classroom. (Ed. H. Steinbring& M. Bartolini). NCTM, Reston, Virginia, USA. 262-270.
MacGregor, M.& Stacey, K. (1997). Students’ understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33, 1-19.
MacGregor, M.&Stacey, K. (1996, July). Learning to formulate equations for problems. PME 20, Valencia, Spain, 3, 289-303.
Maharaj, A. (2008).Some insights from research literature for teaching and learning mathematics. South African Journal of Education, 28(3), 401-414.
Malcolm J.S. (2008).The function concept in middle-years mathematics. The Australian Mathematics Teacher, 64(2), 36-40.
Milli Eğitim Bakanlığı (National Education Ministry) .(2005). İlköğretim Matematik Dersi 6-8. Sınıflar Öğretim Programı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
Milli Eğitim Bakanlığı (National Education Ministry) .(2005). Orta Öğretim Matematik (9, 10, 11 ve 12. Sınıflar) Dersi Öğretim Programı, Talim ve Terbiye Kurulu Başkanlığı, Ankara.
Milli Eğitim Bakanlığı (National Education Ministry). (2000). İlköğretim Okulu Matematik Programı 6-7-8. Sınıf. Talim ve Terbiye Kurulu Başkanlığı.Milli Eğitim Basımevi, Istanbul.
Milli Eğitim Bakanlığı (National Education Ministry).(1992).Ortaöğretim Matematik Dersi Programları. Talim ve Terbiye Kurulu Başkanlığı. Milli Eğitim Basımevi, Istanbul.
National Council of Teachers of Mathematics (NCTM).(1989). Curriculum and evaluation standards for school mathematics. Reston, VA.
National Council of Teachers of Mathematics (NCTM).(2000). Principles and Standards for School Mathematics. Reston, VA.
Odman, P. J. (1988). Hermeneutics. In J. P. Keeves (Ed.), Educational research, methodology and measurement: An international handbook. Oxford: Pergamon Press.
Özer, H. (2000). İlköğretim Matematik 7 Ders Kitabı. Özer Yay. İstanbul.
Patton, M.(1990). Qualitative evaluation and research methods. Beverly Hills, CA: Sage.
Philipp, R. (1992).The Many Uses of Algebraic Variables. The Mathematics Teacher. 85(7), 557-561.
Pope, L. (1994).Teaching Algebra. Mathematics Education: A Handbook for Teachers, Welsington College of Education: New Zealand, 1, 88-99.
Real L., F.(1996). Secondary pupils’ translation of algebraic relationships into everyday language: a hong kong study. (Eds. Luis, P.&Angel, G.) PME 20, Valencia, Spain 3, 280-287.
Reconceptualising school algebra, algebra rationale.(1997). Retrieved from http://www.sun.ac.za/MATHED/HED/ Rational.pdf > (September 20, 2001).
Rojano, T. (1988, November).Teaching Equation Solving: A Teaching Experiment with a Concrete Syntactic Approach. North American Chapter of the International Group for the Psychology of Mathematics Education, 10th, Dekalb, Illinois.
Schroeder, T. L.; Schoeffer, C. M.; Reish, C. P.; Donovan, J. E. (2002, April). Preservice Teachers’ Understanding of Functions: A Performance Assessment Based on NonRoutine Problems Analyzed in Terms of Versatility and Adaptability. Interim Report. Paper presented at the Annual Meeting of the American Educational Research Association. New Orleans, LA.
Sfard, A. (1991). On the Dual Nature of Mathematical Conceptions: Reflections on processes and objects as different sides of the same coins, Educational Studies in Mathematics, 22, 1-36.
Sfard,A.(1992).Operational Origins of Mathematical Objects and the Quandary of Reification-The Case of Function, in Harel & Ed. Dubinsky (Eds.), The Concept of Function Aspects of Epistemology and Pedagogy, United States of America: Mathematical Association of America, pp. 59- 85.
Smith, J., Eisenmann, B., Jansen, A.& Star, J. (2000, April). Studying mathematical transitions: how do students navigate fundamental changes in curriculum and pedagogy? Paper presented at the Annual Meeting of the American Educational Research Association Meeting, 24-28, New Orleans, LA.
Stacey, K.&MacGregor, M. (2000).Learning the algebraic method of solving problems. Journal of Mathematical Behavior, 18 (2), 149-167.
Stallings, L.(2000). A Brief History of Algebraic Notation. School Science and Mathematics, 100 (5), 230-235.
Stephens, A. C.(2001).A study of students' translations from equations to word problems. In R. Speiser, C. A. Mahar, & C. N. Walter (Eds.).Proceedings of the twenty-third annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 133-134). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
Swadener, M.& R. Soedjadi. (1988). Values, Mathematics Education And The Task Of Developing Pupils’ Personalities: An Indonesian Perspective. Educational Studies in Mathematics. 19(2),193-208.
Tall, D.(1992).The Transition to Advanced Mathematical Thinking: Functions, Limits, Infinity, and Proof. (Ed. D.Grouws). Handbook of Research on Mathematics Teaching And Learning. Macmillan Library Reference, New York, 495-510.
Tall, D.&Vinner, S.(1981).Concept Image and Concept Definition in Mathematics with particular reference to Limits and Continuity. Educational Studies in Mathematics, 12, 151-169.
Tall, D., MacGowen, M.&DeMories, P. (2000, October). The Function Machine as a Cognitive Root for the Function Concept. (Ed. F. Maria). Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology Mathematics Education, 22nd, Tucson, Arizona, Volume 1-2., 251-257.
Thompson, P. W. (1994). Students, Functions, and the Undergraduate Curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in Collegiate Mathematics Education, 1 (Issues in Mathematics Education, vol. 4, pp. 21-44). Providence, RI: American Mathematical Society.
Thompson, P. W.& Sfard, A. (1994). Problems of Reification: Representations and Mathematical Objects. In D. Kirshner (Ed.) Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education-North America, Plenary Sessions, Vol. 1 (pp. 1- 32). Baton Rouge, LA: Lousiana State University.
Ursini, S.&Trigerous, M. (2001). A model for the uses of variable in elementary algebra. In Van den Heuvel & M. Panhuizen. (Eds.), Proceedings of the XXV PME International Conference (Vol. 4, pp. 327-334). Utrecht, Netherlands.
Van Ameron, B. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics 54, 63-75.
Van Someren, M. W.,Barnard, Y. F., & Sandberg, J. A. C. (1994). The think-aloud method: A practical guide to modeling cognitive processes. San Diego, CA: Academic Press Ltd.
Vinner, S.& Dreyfus, T. (1989). Images and definitions for the concept of. function. Journal For Research In Mathematics Education. 20(4), 356-366.
Vinner, S.(1983). Concept definition, concept image and the notion of function. The International Journal of Mathematical Education in Science and Technology, 14(3), 293- 305.
Wheatley, G. (1995). Thinking in variables. Retrieved from <http://www.simcalc.umassd.edu/NewWebsite/EAdownloads /Wheatley.pdf.> (September 29,2001).
Williams, C.(1998). Using Concept Maps to Assess Conceptual Knowledge of Function. Journal for Research in Mathematics Education, 29(4), 414-421.

How to cite this article

APA

Dede, Y., & Soybaş, D. (2011). Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts. Eurasia Journal of Mathematics, Science and Technology Education, 7(2), 89-102. https://doi.org/10.12973/ejmste/75183

Vancouver

Dede Y, Soybaş D. Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts. EURASIA J Math Sci Tech Ed. 2011;7(2):89-102. https://doi.org/10.12973/ejmste/75183

AMA

Dede Y, Soybaş D. Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts. EURASIA J Math Sci Tech Ed. 2011;7(2), 89-102. https://doi.org/10.12973/ejmste/75183

Chicago

Dede, Yüksel, and Danyal Soybaş. "Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts". Eurasia Journal of Mathematics, Science and Technology Education 2011 7 no. 2 (2011): 89-102. https://doi.org/10.12973/ejmste/75183

Harvard

Dede, Y., and Soybaş, D. (2011). Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts. Eurasia Journal of Mathematics, Science and Technology Education, 7(2), pp. 89-102. https://doi.org/10.12973/ejmste/75183

MLA

Dede, Yüksel et al. "Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts". Eurasia Journal of Mathematics, Science and Technology Education, vol. 7, no. 2, 2011, pp. 89-102. https://doi.org/10.12973/ejmste/75183