Ortaokul Matematik Öğretmenlerinin Temsil Kullanımına İlişkin Öğrenci ve Öğretim Stratejileri Bilgileri

Deniz Eroğlu; Dilek Tanışlı; Dilek Tanışlı

doi:10.17522/nefefmed.53039

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Year 2015, Volume: 9 Issue: 1, 275 - 307, 24.06.2015

Deniz Eroğlu , Dilek Tanışlı Dilek Tanışlı

https://doi.org/10.17522/nefefmed.53039

Cited By: 7

Abstract

– Knowledge of students and knowledge of teaching strategies could be regarded as the main components of teachers’ knowledge. The purpose of this study was to investigate how elementary mathematics teachers interpret the students’ answers including erroneous representation, which strategies these teachers offer to overcome students’ errors and how their interpretations and offered strategies differ in terms of their experience years. Basic qualitative research approach was used. For the purpose of the study, clinical interviews were conducted with 5 elementary mathematics teachers, and 3 of teachers’ professional experience is less than ten years and 2 of teachers’ professional experience is more than thirty years. Results of the study revealed that teachers poorly interpret the students’ errors and correspondingly they offer only limited strategies in order to overcome students’ errors. Furthermore, results showed that -contrary to expectations- less-experienced and highly experienced teachers showed similar results in terms of their interpretations of students’ answers and offered strategies in order to overcome students’ errors

Keywords

Mathematics teachers, representation, knowledge of students, knowledge of teaching strategies

References

Armstrong, D., Gosling, A., Weinman, J., & Marteau, T. (1997). The place of inter-rater reliability in qualitative research: an empirical study. Sociology, 31(3), 597-606.
Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing.
Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Ball, D. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T. P. Carpenter and E. Fennema (Eds.), Learning, Teaching, and Assessing Rational Number Concepts (pp.157-195). Hillsdale, NJ: Lawrence Erlbaum Associates.
Ball, D. B, Thames M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59, 389-407.
Baştürk, S. (2009). Ortaöğretim matematik öğretmen adaylarına göre fen edebiyat fakültelerindeki alan eğitimi. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 10(3), 137- 160.
Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics 2. 34-42.
Billings, E. M. H., & Klanderman, D. (2000). Graphical representations of speed: Obstacles preservice K-8 teachers experience. School Science and Mathematics, 100 (8), 440- 451.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3 (2), 77-101.
Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students’ solving processconstrained and process-open problems. Mathematical Thinking and Learning, 2, 309–340.
Cai, J. (2005). U.S. and Chinese teachers’ constructing, knowing, and representations to teach mathematics. Mathematical Thinking and Learning, 7(2), 135–169.
Cai, J., & Lester Jr., F. (2005). Solution representations and pedagogical representations in Chinese and U.S. classrooms. Journal of Mathematical Behavior, 24, 221–237.
Cai, J., & Wang, T. (2006). U.S. and Chinese teachers’ conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Mathematics and Science Education, 4, 145-186.
Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174.
Charalambos, Y. C., Hill, H.,C. & Ball, D. L.(2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441-463.
Clement, J. (2000) Analysis of clinical interviews: Foundations and model viability. In Lesh, R. and Kelly, A., Handbook of research methodologies for science and mathematics education (pp. 341-385). Hillsdale, NJ: Lawrence Erlbaum.
Cramer, K., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifthgrade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–44.
Çelik, D., & Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
DeLoache, J. S. (1991). Symbolic functioning in very young children: Understanding of pictures and models. Child Development, 62, 736-752.
DeWindt-King, A. M., & Goldin, G. A. (2003). Children’s visual imagery: Aspects of cognitive representation in solving problems with fractions. Mediterranean Journal for Research in Mathematics Education, 2, 1-42.
Diezmann, Carmel M (1999) Assessing diagram quality: Making a difference to representation. In Proceedings of the 22nd Annual Conference of Mathematics Education Research Group of Australasia, pages 185-191, Adelaide.
Dole, S., Cooper, T.J., Baturo, A.R., & Conoplia, Z. (1997). Year 8, 9 and 10 students’ understanding and access of percent knowledge. In F. E. Biddulph & K, Carr (Eds.), People in mathematics education. Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia, Rotorua, July 7-11, 1997 (pp.147-154). New Zealand : University of Waikato Printery.
Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as source of teacher presentation of the subject matter. Educational Studies in Mathematic, 29, 1-19.
Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students' mathematical thinking and knowledge. In L. English (Ed.), Second handbook of international research in mathematics education (pp. 202-222). NY: Routedge.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed), Handbook of research on mathematics teaching and learning. NewYork: National Council of Teachers of Mathematics.
Gfeller, M. K., Niess, M.L., & Lederman, N. G. (1999). Preservice teachers’ use of multiple representations in solving arithmetic mean problems. School Science and Mathematics, 99(5), 250-257.
Grossman, P.L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Hill, H.C., Rowan, B., & Ball, D.L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371- 406.
Huang, R., & Cai, J. (2007). Constructing pedagogical representations to teach linear relations in Chinese and U.S. classrooms. In Woo, J. H., Lew, H. C., Park, K. S. & Seo, D. Y. (Eds.). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 65-72. Seoul: PME.
Hunting, R. P. (1997). Clinical interview methods in mathematics education research and practice. Journal of Mathematical Behavior, 16(2), 145-165.
Hwang, W. Y., Chen, N.S., Dung,J.J., & Yang, L.Y. (2007). Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. Educational Technology and Society, 10 (2), 191-212.
İpek, A.S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 11(3), 681-700.
Lapp, D. A., & Cyrus, V. F. (2000). Using data-collection devices to enhance students’ understanding. Mathematics Teachers, 93(6), 504-510.
Liamputtong, P. (2009). Qualitative data analysis: Conceptual and practical considerations. Health Promotion Journal of Australia, 20(2), 133-139.
Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, Sources and Development of Pedagogical Content Knowledge for Science teaching. In J. Gess-Newsome & N. G. Lederman (Eds.), Examining Pedagogical Content Knowledge: The Construct and Its Implications for Science Education (pp. 95-132). Dordrecht, The Netherlands: Kluwer Academic.
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.
Monoyiou, A., Papageorgiou, P., & Gagatsis, A. (2007, February). Students’ and teachers’ representations in problem solving. Paper presented at Congress of the European Society for Research in Mathematics Education, Larnaca, Cyprus.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Niemi, H. 2002. Active learning – A cultural change needed in teacher education and schools. Teaching and Teacher Education. 18 (8), 763–780.
Niemi, D. (1996). Assessing conceptual understanding in mathematics. Journal of Educational Research, 89(6), 351-363.
Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge: Pedagogical content knowledge as a conceptual tool to understand teachers as professionals. Research in Science Education, 38, 261–284.
Patterson, N.D., & Norwood, K.S. (2004). A case study of teacher beliefs on students’ belief about multiple representations. International Journal of Science and Mathematics Education, 2(1), 5-23.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.
Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn & Bacon.
Wu, Z. (2004). The study of middle school teachers’ understanding and use of mathematical representation in relation to teachers’ zone of proximal development in teaching fractions and algebraic functions. Unpublished Doctoral Dissertation, Department of Teaching, Learning and Culture. Texas A&M University, College Station.
Yıldırım, A., & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8. Baskı), Ankara: Seçkin Yayınevi.

Ortaokul Matematik Öğretmenlerinin Temsil Kullanımına İlişkin Öğrenci ve Öğretim Stratejileri Bilgileri

Year 2015, Volume: 9 Issue: 1, 275 - 307, 24.06.2015

Deniz Eroğlu , Dilek Tanışlı Dilek Tanışlı

https://doi.org/10.17522/nefefmed.53039

Cited By: 7

Abstract

Öğrenci bilgisi ve öğretim stratejileri bilgisi öğretmenin sahip olması gereken bilginin temel bileşenleri olarak görülebilir. Bu çalışmada ortaokul matematik öğretmenlerinin öğrencilerin hatalı temsil içeren yanıtlarını nasıl yorumladıklarını, bu hatalı yanıtlar için hangi öğretim stratejilerini önerdikleri, bu yorum ve stratejilerin mesleki deneyim yılına göre nasıl değiştiğini belirlemek amaçlanmıştır. Araştırmada temel nitel araştırma yaklaşımı benimsenmiştir. Araştırmanın amacı doğrultusunda mesleki deneyimi on yılın altında olan 3 ve mesleki deneyimi otuz yılın üzerinde olan 2 toplamda 5 ortaokul matematik öğretmeni ile klinik görüşmeler gerçekleştirilmiştir. Verilerin analizi sonucunda öğretmenlerin öğrenci hatalarını yorumlamada yetersiz kaldıkları ve buna bağlı olarak da önerdikleri stratejilerin çeşitliliğinin az olduğu ortaya çıkmıştır. Sonuçlar mesleki deneyim yıllarına göre incelendiğinde ise deneyimli ve deneyimi az olan öğretmenlerin öğrenci yorumlarının ve önerdikleri stratejilerin benzer olduğu görülmüştür.

Keywords

Matematik öğretmeni, temsil, öğrenci bilgisi, öğretim stratejisi bilgisi

References

Armstrong, D., Gosling, A., Weinman, J., & Marteau, T. (1997). The place of inter-rater reliability in qualitative research: an empirical study. Sociology, 31(3), 597-606.
Ball, D. L. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Unpublished doctoral dissertation, Michigan State University, East Lansing.
Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Ball, D. (1993). Halves, pieces, and twoths: Constructing representational contexts in teaching fractions. In T. P. Carpenter and E. Fennema (Eds.), Learning, Teaching, and Assessing Rational Number Concepts (pp.157-195). Hillsdale, NJ: Lawrence Erlbaum Associates.
Ball, D. B, Thames M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?. Journal of Teacher Education, 59, 389-407.
Baştürk, S. (2009). Ortaöğretim matematik öğretmen adaylarına göre fen edebiyat fakültelerindeki alan eğitimi. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 10(3), 137- 160.
Bell, A., & Janvier, C. (1981). The interpretation of graphs representing situations. For the Learning of Mathematics 2. 34-42.
Billings, E. M. H., & Klanderman, D. (2000). Graphical representations of speed: Obstacles preservice K-8 teachers experience. School Science and Mathematics, 100 (8), 440- 451.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3 (2), 77-101.
Cai, J. (2000). Mathematical thinking involved in U.S. and Chinese students’ solving processconstrained and process-open problems. Mathematical Thinking and Learning, 2, 309–340.
Cai, J. (2005). U.S. and Chinese teachers’ constructing, knowing, and representations to teach mathematics. Mathematical Thinking and Learning, 7(2), 135–169.
Cai, J., & Lester Jr., F. (2005). Solution representations and pedagogical representations in Chinese and U.S. classrooms. Journal of Mathematical Behavior, 24, 221–237.
Cai, J., & Wang, T. (2006). U.S. and Chinese teachers’ conceptions and constructions of representations: A case of teaching ratio concept. International Journal of Mathematics and Science Education, 4, 145-186.
Capraro, M. M., Kulm, G., & Capraro, R. M. (2005). Middle grades: Misconceptions in statistical thinking. School Science and Mathematics, 105(4), 165-174.
Charalambos, Y. C., Hill, H.,C. & Ball, D. L.(2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441-463.
Clement, J. (2000) Analysis of clinical interviews: Foundations and model viability. In Lesh, R. and Kelly, A., Handbook of research methodologies for science and mathematics education (pp. 341-385). Hillsdale, NJ: Lawrence Erlbaum.
Cramer, K., Post, T. R., & delMas, R. C. (2002). Initial fraction learning by fourth- and fifthgrade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33, 111–44.
Çelik, D., & Sağlam-Arslan, A. (2012). Öğretmen adaylarının çoklu gösterimleri kullanma becerilerinin analizi. İlköğretim Online, 11(1), 239-250.
DeLoache, J. S. (1991). Symbolic functioning in very young children: Understanding of pictures and models. Child Development, 62, 736-752.
DeWindt-King, A. M., & Goldin, G. A. (2003). Children’s visual imagery: Aspects of cognitive representation in solving problems with fractions. Mediterranean Journal for Research in Mathematics Education, 2, 1-42.
Diezmann, Carmel M (1999) Assessing diagram quality: Making a difference to representation. In Proceedings of the 22nd Annual Conference of Mathematics Education Research Group of Australasia, pages 185-191, Adelaide.
Dole, S., Cooper, T.J., Baturo, A.R., & Conoplia, Z. (1997). Year 8, 9 and 10 students’ understanding and access of percent knowledge. In F. E. Biddulph & K, Carr (Eds.), People in mathematics education. Proceedings of the 20th annual conference of the Mathematics Education Research Group of Australasia, Rotorua, July 7-11, 1997 (pp.147-154). New Zealand : University of Waikato Printery.
Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as source of teacher presentation of the subject matter. Educational Studies in Mathematic, 29, 1-19.
Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students' mathematical thinking and knowledge. In L. English (Ed.), Second handbook of international research in mathematics education (pp. 202-222). NY: Routedge.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed), Handbook of research on mathematics teaching and learning. NewYork: National Council of Teachers of Mathematics.
Gfeller, M. K., Niess, M.L., & Lederman, N. G. (1999). Preservice teachers’ use of multiple representations in solving arithmetic mean problems. School Science and Mathematics, 99(5), 250-257.
Grossman, P.L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
Hill, H.C., Rowan, B., & Ball, D.L. (2005). Effects of teachers' mathematical knowledge for teaching on student achievement. American Education Research Journal, 42(2), 371- 406.
Huang, R., & Cai, J. (2007). Constructing pedagogical representations to teach linear relations in Chinese and U.S. classrooms. In Woo, J. H., Lew, H. C., Park, K. S. & Seo, D. Y. (Eds.). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 65-72. Seoul: PME.
Hunting, R. P. (1997). Clinical interview methods in mathematics education research and practice. Journal of Mathematical Behavior, 16(2), 145-165.
Hwang, W. Y., Chen, N.S., Dung,J.J., & Yang, L.Y. (2007). Multiple representation skills and creativity effects on mathematical problem solving using a multimedia whiteboard system. Educational Technology and Society, 10 (2), 191-212.
İpek, A.S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 11(3), 681-700.
Lapp, D. A., & Cyrus, V. F. (2000). Using data-collection devices to enhance students’ understanding. Mathematics Teachers, 93(6), 504-510.
Liamputtong, P. (2009). Qualitative data analysis: Conceptual and practical considerations. Health Promotion Journal of Australia, 20(2), 133-139.
Magnusson, S., Krajcik, J., & Borko, H. (1999). Nature, Sources and Development of Pedagogical Content Knowledge for Science teaching. In J. Gess-Newsome & N. G. Lederman (Eds.), Examining Pedagogical Content Knowledge: The Construct and Its Implications for Science Education (pp. 95-132). Dordrecht, The Netherlands: Kluwer Academic.
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. San Francisco: Jossey-Bass.
Monoyiou, A., Papageorgiou, P., & Gagatsis, A. (2007, February). Students’ and teachers’ representations in problem solving. Paper presented at Congress of the European Society for Research in Mathematics Education, Larnaca, Cyprus.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.
Niemi, H. 2002. Active learning – A cultural change needed in teacher education and schools. Teaching and Teacher Education. 18 (8), 763–780.
Niemi, D. (1996). Assessing conceptual understanding in mathematics. Journal of Educational Research, 89(6), 351-363.
Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge: Pedagogical content knowledge as a conceptual tool to understand teachers as professionals. Research in Science Education, 38, 261–284.
Patterson, N.D., & Norwood, K.S. (2004). A case study of teacher beliefs on students’ belief about multiple representations. International Journal of Science and Mathematics Education, 2(1), 5-23.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57, 1-22.
Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn & Bacon.
Wu, Z. (2004). The study of middle school teachers’ understanding and use of mathematical representation in relation to teachers’ zone of proximal development in teaching fractions and algebraic functions. Unpublished Doctoral Dissertation, Department of Teaching, Learning and Culture. Texas A&M University, College Station.
Yıldırım, A., & Şimşek, H. (2011). Sosyal bilimlerde nitel araştırma yöntemleri (8. Baskı), Ankara: Seçkin Yayınevi.

There are 47 citations in total.

Details

Primary Language	Turkish
Journal Section	Makaleler
Authors	Deniz Eroğlu Dilek Tanışlı This is me Dilek Tanışlı This is me
Publication Date	June 24, 2015
Submission Date	June 24, 2015
Published in Issue	Year 2015 Volume: 9 Issue: 1

Cite

APA	Eroğlu, D., Tanışlı, D., & Tanışlı, D. (2015). Ortaokul Matematik Öğretmenlerinin Temsil Kullanımına İlişkin Öğrenci ve Öğretim Stratejileri Bilgileri. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 9(1), 275-307. https://doi.org/10.17522/nefefmed.53039