International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education Indexed in ESCI
Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties
APA
In-text citation: (Bingolbali et al., 2011)
Reference: Bingolbali, E., Akkoç, H., Ozmantar, M. F., & Demir, S. (2011). Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. International Electronic Journal of Mathematics Education, 6(1), 40-59. https://doi.org/10.29333/iejme/260
AMA
In-text citation: (1), (2), (3), etc.
Reference: Bingolbali E, Akkoç H, Ozmantar MF, Demir S. Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. INT ELECT J MATH ED. 2011;6(1), 40-59. https://doi.org/10.29333/iejme/260
Chicago
In-text citation: (Bingolbali et al., 2011)
Reference: Bingolbali, Erhan, Hatice Akkoç, Mehmet Fatih Ozmantar, and Servet Demir. "Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties". International Electronic Journal of Mathematics Education 2011 6 no. 1 (2011): 40-59. https://doi.org/10.29333/iejme/260
Harvard
In-text citation: (Bingolbali et al., 2011)
Reference: Bingolbali, E., Akkoç, H., Ozmantar, M. F., and Demir, S. (2011). Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. International Electronic Journal of Mathematics Education, 6(1), pp. 40-59. https://doi.org/10.29333/iejme/260
MLA
In-text citation: (Bingolbali et al., 2011)
Reference: Bingolbali, Erhan et al. "Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties". International Electronic Journal of Mathematics Education, vol. 6, no. 1, 2011, pp. 40-59. https://doi.org/10.29333/iejme/260
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Bingolbali E, Akkoç H, Ozmantar MF, Demir S. Pre-Service and In-Service Teachers’ Views of the Sources of Students’ Mathematical Difficulties. INT ELECT J MATH ED. 2011;6(1):40-59. https://doi.org/10.29333/iejme/260

Abstract

This paper examines the views of pre-service and in-service teachers with regard to the sources of students' mathematical difficulties. A group of 40 pre-service mathematics, 15 in-service mathematics and 15 in-service elementary teachers participated in this study. Questionnaires are used as data collection tools to see what the participants think about the sources of student difficulties. The notion of "obstacles to learning" is used as a framework to analyze the collected data. The analysis is carried out on the basis of three main categories to which participant teachers attribute students' difficulties: epistemological causes, psychological causes and pedagogical causes. The data analysis reveals that both pre-service and in-service teachers tend to attribute students' difficulties to student-related factors, namely psychological causes. We discuss the findings in terms of these three sources of learning difficulties, educational implications and note the usefulness of the employing the “obstacles to learning framework” in examining not only students' learning difficulties but also teachers' views of the sources for student difficulties.

References

  • Akbulut, K. & Işık, A. (2005). Limit kavramının anlaşılmasında etkileşimli öğretim stratejisinin etkinliğinin incelenmesi ve bu süreçte karşılaşılan kavram yanılgıları [The effect of interactive teaching strategies on the comprehension of the limit concept and the misconceptions met during this process]. Kastamonu Eğitim Fakültesi Dergisi [Kastamonu Journal of School of Education], 13(2), 497-512.
  • Akkoç, H., Bingolbali, E., & Ozmantar, F. (2008). Investigating the technological pedagogical content knowledge: A case of derivative at a point. In O. Figueras, & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XXX North American Chapter (Vol. 2, pp.17-24). Morelia: PME.
  • An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle-school, mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education 7, 145–172.
  • Askew, M., Brown, M., Rhodes, V., William, D., & Johnson, D. (1997). Effective teachers of numeracy in UK primary schools: Teachers‟ beliefs, practices, and pupils‟ learning. In E. Pehkonen (Ed.), Proceedings of the 21st International Group for the Psychology of Mathematics Education Conference (Vol. 2, pp. 31-42). Lahti: PME
  • Ausubel, D. P. (1968). Educational psychology: A cognitive view. New York: Holt, Rinehart and Winston.
  • Bachelard, G. (2002). The formation of the scientific mind: A contribution to a psykoanalysis of objective knowledge. Manchester: Clinamen Press. (Original work published in French in 1938)
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching : What makes it special? Journal of Teacher Education, 59, 389-407.
  • Bingolbali, E., Ozmantar, F. M., & Akkoç, H. (2008). Curriculum reform in primary mathematics education: Teacher difficulties and dilemmas. In O. Figueras & A. Sepúlveda (Eds.), Proceedings of the Joint Meeting of the 32nd Conference of the International Group for the Psychology of Mathematics Education, and the XXX North American Chapter (Vol. 2, pp. 169-176). Morelia: PME.
  • Booth, L. R. (1988). Children‟s difficulties in beginning algebra. In A. Coxford (Ed.), The Ideas of Algebra, K-12 (pp. 20-32). Reston, VA: National Council of Teachers of Mathematics.
  • Brousseau, G. (1997). Theory of didactical situations in mathematics (N. Balacheff, M. Cooper, R. Southland, & V. Warfield (Eds. & Trans.)). Dordrecht, Boston: Kluwer Academic Publishers.
  • Brown, M., Askew, M., Rhodes, V., William, D., & Johnson, D. (1997). Effective teachers of numeracy in UK primary schools: Teachers‟ content knowledge and pupils‟ learning. In E. Pehkonen (Ed.), Proceedings of the 21st International Group for the Psychology of Mathematics Education Conference (Vol. 2, pp. 121-128). Lahti: PME.
  • Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced Mathematical Thinking (pp. 153-166). Boston: Kluwer.
  • Dorier, J. L., Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level, An ICMI Study (pp. 255-274). Dordrecht, The Netherlands: Kluwer Academic Publishers.
  • Floden, R. (1996). What teachers need to know about learning. In M. Kennedy (Ed.), Teaching Academic Subjects to Diverse Learners (pp. 181–202). New York: Teachers College Press.
  • Goulding, M., Rowland, T., & Barber, P. (2002). Does it matter? Primary teacher trainees‟ subject knowledge in mathematics. British Educational Research Journal, 28(5), 689- 704. doi: 10.1080/0141192022000015543a
  • Graeber, A. O. (1993). Misconceptions about multiplication and division. In D. L. Chambers (Ed.), Putting Research into Practice in the Elementary Grades (pp. 97-100). Reston, VA: National Council of Teachers of Mathematics.
  • Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
  • Hart, K. M., Brown, M., Kerslake, D., Kuchemann, D., Johnson, D., Ruddock, G., & McCartney, M. (1980). Secondary school children’s understanding of mathematics. London: Chelsea College of Science and Technology.
  • Lamb, J., & Booker, G. (2004). The impact of developing teacher conceptual knowledge on students‟ knowledge of division. In M. J. Hoines, & A. B. Fuglestad (Eds), Proceedings of the 28th International Group for the Psychology of Mathematics Education Conference (Vol. 3, pp. 177-182). Bergen: PME.
  • Linchevski, L., & Vinner, S. (1988). The naive concept of sets in elementary teachers. In A. Borbas, A. (Ed.), Proceedings of the12th International Conference of the International Group for the Psychology of Mathematics Education (PME), (Vol. 2, pp. 471-478). Veszprém (Hungary): Hungarian National Centre for Educational Technology.
  • Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, sources and development of pedagogical content knowledge for science teaching. In Gess-Newsome, & Lederman (Eds.), Examining Pedagogical Content Knowledge: The Construct and Its Implications for Science Education (pp. 95-144). Dordrecht: Kluwer Academic Publishers.
  • McClain, K., & Bowers, J. (2000). Supporting pre-service teachers‟ understanding of place value and multi-digit addition and subtraction. In T. Nakahara, & M. Koyama (Eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 279–286). Hiroshima: PME.
  • Mishra, P. & Koehler, M.J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054. doi: 10.1111/j.1467-9620.2006.00684.x
  • Niess, M. L., Ronau, R. N., Shafer, K. G., Driskell, S. O., Harper S. R., Johnston, C., Browning, C., Özgün-Koca, S. A., & Kersaint, G. (2009). Mathematics teacher TPACK standards and development model. Contemporary Issues in Technology and Teacher Education, 9, 4-24.
  • Ozmantar, M. F., Akkoç, H., Bingolbali, E., Demir, S., & Ergene, B. (2010). Pre-service mathematics teachers‟ use of multiple representations in technology-rich environments. Eurasia Journal of Mathematics, Science & Technology Education, 6(1), 19-36.
  • Ozmantar, M. F., & Bingolbali, E. (2009). Sınıf öğretmenleri ve matematiksel zorlukları [Primary teachers and their mathematical difficulties], Gaziantep Üniversitesi Sosyal Bilimler Dergisi [Gaziantep Journal of Social Science], 8(2), 401-427.
  • Penso, S. (2002). Pedagogical content knowledge: How do student teachers identify and describe the causes of their pupils‟ learning difficulties? Asia–Pacific Journal of Teacher Education, 30, 25-37. doi: 10.1080/13598660120114959
  • Philippou, G. N., & Christou, C. (1998). The effects of a preparatory mathematics program in changing prospective teachers‟ attitudes towards mathematics. Educational Studies in Mathematics, 35, 189-206. doi: 10.1023/A:1003030211453
  • Pimm, D. (1987). Speaking mathematically: Communication in mathematics classrooms. London: Routledge & Kegan Paul.
  • Resnick, L. (1983). Mathematics and science learning: A new conception. Science, 220, 477- 478. doi:10.1126/science.220.4596.477
  • Selden, A., & Selden, J. (2001). Tertiary mathematics education research and its future. In D. A. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICMI Study (pp. 237-254). Hingham, MA: Kluwer Academic Publishers.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14. doi: 10.3102/0013189X015002004
  • Sierpinska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18, 371–397.
  • Stipek, D., Givvin, K., Salmon, J., & MacGyvers, V. (2001). Teachers‟ beliefs and practices related to mathematics instruction. Teaching and Teacher Education. 17(2), 213-226. doi: 10.1016/S0742-051X(00)00052-4
  • Tall, D. O. (Ed.) (1991). Advanced mathematical thinking. Kluwer, Boston.
  • Tall, D. O., & Vinner, S. (1981). Concept image and concept definition in mathematics, with particular reference to limits and continuity. Educational Studies in Mathematics, 12, 151–169. doi: 10.1007/BF00305619
  • Tanner, H. (2000). Becoming a successful teacher of mathematics. London, UK: Routledge Falmer.
  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51–64. doi: 10.1023/A:1003011913153
  • Verschaffel, L., Greer, B., & Torbeyns, J. (2006). Numerical thinking. In A. Gutierrez, & P. Boero (Eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (pp. 51-82). Rotterdam/Taipei: Sense Publishers.
  • Williams, S. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22(3), 219-236. doi:10.2307/749075

License

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.