Research Article
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Middle School Mathematics Teachers’ Opinions on Estimation

Year 2017, Volume: 11 Issue: 1, 48 - 80, 30.06.2017
https://doi.org/10.17522/balikesirnef.354985

Abstract

The purpose of the study is to investigate 5-8th
grades mathematics teachers’ opinions on estimation. The phenomenological
research design is used. The semi-structured interviews were conducted with
seven teachers who have been experienced in various mathematics curricula.
According to analysis, definition of estimation, types of estimation,
strategies of estimation, instructional activities in/out of the class,
difficulties during teaching of estimation and importance of estimation are
seven themes of the study. The results are revealed that most of the teachers
could not define estimation and identify types and strategies of estimation.
Even though they thought that estimation is an important skill for daily life
but they do not provide appropriate teaching environments. The most important
reason is that teachers do not believe the necessity of learning estimation,
they think that estimations is not going to be asked in the national exams and
they do not have enough competency about estimation. 

References

  • Adams, L., Onslow, B., Edmunds, G., Chapple, N., & Waters, J. (2005). Children’s development of range based estimation skills: far more than guess work. In Proceedings of the third international conference on education, Honolulu, HA.
  • Alajmi, A. H. (2009). Addressing computational estimation in the Kuwaiti curriculum. Teachers’ views. Journal of Mathematics Teacher Education, 12(4), 263-283.
  • Alajmi, A., & Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(1), 77-94.
  • Balcı, A. (2006). Sosyal bilimlerde araştırma, yöntem, teknik ve ilkeler (6th ed.), Ankara: Pegem Yayıncılık.
  • Bestgen, B. J., Reys, R. E., Rybolt, J. F., & Wyatt, J. W. (1980). Effectiveness of Systematic Instruction on Attitudes and Computational Estimation Skills of Preservice Elementary Teachers. Journal for Research in Mathematics Education, 11(2), 124-136.
  • Boz, B. (2004). Investigation of estimation ability of high school students (Unpublished Master’s Thesis). Middle East Technical University, Institute of Science, Ankara.
  • Carroll, W. (1996). Mental computation of students in a reform-based mathematics curriculum. School Science and Mathematics, 96(6), 305-311.
  • Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407.
  • Cresswell, J. W. (2008). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. Upper Saddle River, NJ: Pearson Prentice Hall.
  • Creswell, J. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). USA: SAGE Publications.
  • Çilingir, D., & Türnüklü, E. (2009). İlköğretim 6-8. sınıf öğrencilerinin matematiksel tahmin becerileri ve tahmin stratejileri. İlköğretim Online, 8(3), 637-650.
  • Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45-55.
  • Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38(1), 47-64.
  • Ford, M. I. (1994). The teachers beliefs about mathematical problem solving in the elementary school. School Science and Mathematics, 94(6), 314-322.
  • Gliner, G. S. (1991). Factors contributing to success in mathematical estimation in pre-service teachers: Types of problems and previous mathematical experience. Educational Studies in Mathematics, 22(6), 595-606.
  • Goodman, T. (1991). Computational estimation skills of preservice elementary teachers. International Journal of Mathematical Education in Science and Technology, 22(2), 259-272.
  • Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM Mathematics Education, 43(5), 709-722.
  • Hanson, S., & Hogan, T. (2000). Computational estimation skill of college students. Journal for Research in Mathematics Education, 31(4), 483-499.
  • Kagan, D. M. (1992). Implication of research on teacher belief. Educational Psychologist, 27(10), 65-70.
  • Kılıç, Ç., & Olkun, S. (2013). İlköğretim öğrencilerinin gerçek yaşam durumlarındaki ölçüsel tahmin performansları ve kullandıkları stratejiler. İlköğretim Online, 12(1), 295‐307.
  • Lemaire, P., & Lecacheur, M. (2002). Children’s strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281-304.
  • Lemaire, P., Lecacheur, M., & Farioli, F. (2000). Children’s strategies in computational estimation. Canadian Journal of Experimental Psychology, 54(2), 141-148.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly, & R. Lesh (Eds.), Research design in mathematics and science education (pp. 591-646). Mahwah, New Jersey: Lawrence Erlbaum Associates.
  • Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 13(5), 350-359.
  • Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM, The International Journal on Mathematics Education, 38(2), 96-112.
  • Liu, F. (2009). Multiplication estimation by third and fifth-grade Chinese students. School Science and Mathematics, 107(9), 325-337.
  • MEB [Milli Eğitim Bakanlığı]. (1948). İlkokul programı. İstanbul: Milli Eğitim Basımevi.
  • MEB. (1968). İlkokul programı. Ankara: Ayyıldız Matbaası.
  • MEB. (1998). İlköğretim okulu matematik dersi öğretim programı: 1-2-3. sınıflar. Ankara: Milli Eğitim Basımevi.
  • MEB. (2006). İlköğretim İngilizce Dersi (4,5,6,7 ve 8.sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009a). İlköğretim matematik dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009b). İlköğretim matematik dersi (6.-8. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009c). İlköğretim fen ve teknoloji dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009d). İlköğretim Türkçe dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2015). İlkokul matematik dersi (1, 2, 3 ve 4. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEGSB (Milli Eğitim Gençlik ve Spor Bakanlığı). (1983). İlkokul matematik programı. İstanbul: Milli Eğitim Basımevi.
  • Micklo, S. J. (1999). Estimation: It’s more than a guess. Childhood Education, 75(3), 142-145.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (3rd ed.). Newbury Park, CA: Sage Publications.
  • Mohamed, M., & Johnny, J. (2010). Investigating number sense among students. Procedia Social and Behavioral Sciences, 8, 317-324.
  • NCTM [National Council of Teachers of Mathematics]. (1989). Curriculum and evaluation standards for school mathematics. Commission on Standards for School Mathematics. Reston VA: National Council of Teachers of Mathematics.
  • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Osborne, J. (2005). The role of argument in science education. In K. Boersma (Ed.), Research and the Quality of Science Education (pp. 367-380). The Netherlands: Springer.
  • Patkin, D., & Gazit, A. (2013). On roots and squares – estimation, intuition and creativity. International Journal of Mathematical Education in Science and Technology, 44(8), 1191-1200.
  • Posamentier, A. S., & Krulik, S. (1998). Problem-Solving strategies for efficient and elegant solutions. A Research for the Mathematics Teacher. California: Corwin Press.
  • Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.
  • Reys, B. J. (1986). Teaching Computational Estimation: Concepts and Strategies. In H. L. Schoen & M. J. Zweng (Eds.), Estimation and mental computation: 1986 yearbook (pp. 31-45). Reston, VA: National Council of Teachers of Mathematics.
  • Reys, R., Reys, B., Nohda, N., Ishida, J., Yoshikawa, S., & Shimizu, K. (1991). Computational estimation performance and strategies used by fifth- and eighth-grade Japanese students. Journal for Research in Mathematics Education, 22(1), 39-58.
  • Reys, R. E., Rybolt, J. F., Bestgen, B. J,. & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183-201.
  • Rubenstein, R. (1985). Computational estimation and related mathematical skills. Journal for Research in Mathematics Education, 16(2), 106-119.
  • Segovia, I., & Castro, E. (2009). Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psychology, 7(1), 499-536.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Siegel, A. W., Goldsmith, L. T., & Madson, C. R. (1982). Skill in estimation problems of extent and numerosity. Journal for Research in Mathematics Education, 13(3), 211-232.
  • Siegler, R. S., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). New York: Psychology Press.
  • Smart, J. R. (1982). Estimation skills in mathematics. School Science and Mathematics, 82(8), 642-649.
  • Sullivan, J. L., Juhasz, B. J., Slattery, T. J., & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin & Review, 18(3), 557-563.
  • Tirosh, D., & Graeber, A. O. (1989). Preservice elementary teachers’ explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96.
  • Thompson, A. G. (1979). Estimating and Approximating. School Science and Mathematics, 79(7), 575-586.
  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
  • Toluk-Uçar, Z., & Aytekin, C. (2014). Investigation of middle school students’ estimation ability with fractions. İlköğretim Online, 13(2), 546-563.
  • Tsao, Y. L., & Pan, T. R. (2013). The computational estimation and instructional perspectives of elementary school teachers. Journal of Instructional Pedagogies, 11, 1-15.
  • Van de Walle J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn & Bacon.
  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Charlotte, NC: Information Age.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. (6. baskı)
  • Ankara: Seçkin Yayıncılık.

Ortaokul Matematik Öğretmenlerinin Tahmin Hakkındaki Görüşleri

Year 2017, Volume: 11 Issue: 1, 48 - 80, 30.06.2017
https://doi.org/10.17522/balikesirnef.354985

Abstract

Bu araştırmada
5-8. sınıflar matematik öğretmenlerinin tahmin becerisi hakkındaki görüşleri
incelenmiştir. Çalışmada nitel araştırma desenlerinden olgu bilim
kullanılmıştır. Farklı ilköğretim matematik dersi öğretim programlarında
çeşitli deneyimlere sahip yedi öğretmen ile yarı-yapılandırılmış görüşmeler
yapılmıştır. Yapılan analizler sonucunda tahmin tanımı, tahmin becerisinin
çeşitleri, tahmin becerisi için kullanılan stratejiler, sınıf içi/dışı
uygulamalar, tahmin öğretiminde karşılaşılan zorluklar ve tahmin becerisinin
öğretim programındaki yeri olmak üzere yedi tema oluşturulmuştur. Elde edilen
sonuçlara göre matematik öğretmenleri tahmin becerisinin tanımını tam olarak
yapamamakla birlikte, çeşitlerini ve stratejilerini de tam olarak ortaya koyamamaktadır.
Öğretmenler bu becerinin günlük yaşamda önemli bir beceri olduğunu
söylemelerine rağmen matematik derslerinde bu becerinin öğretimine dair
herhangi bir işleniş yapmadıklarını dile getirmektedirler. Bunun altında yatan
en önemli sebepler; öğretmenlerin bu becerinin öğretilmesi gerekliliğine
inanmadıkları, ülke çapındaki sınavlarda soru olarak öğrencilerin karşısına
çıkmayacağını düşünmeleri ve kendilerinin de bu konuda yeterli donanıma sahip
olmadıklarını düşünmeleri olarak sıralanabilir.

References

  • Adams, L., Onslow, B., Edmunds, G., Chapple, N., & Waters, J. (2005). Children’s development of range based estimation skills: far more than guess work. In Proceedings of the third international conference on education, Honolulu, HA.
  • Alajmi, A. H. (2009). Addressing computational estimation in the Kuwaiti curriculum. Teachers’ views. Journal of Mathematics Teacher Education, 12(4), 263-283.
  • Alajmi, A., & Reys, R. (2007). Reasonable and reasonableness of answers: Kuwaiti middle school teachers’ perspectives. Educational Studies in Mathematics, 65(1), 77-94.
  • Balcı, A. (2006). Sosyal bilimlerde araştırma, yöntem, teknik ve ilkeler (6th ed.), Ankara: Pegem Yayıncılık.
  • Bestgen, B. J., Reys, R. E., Rybolt, J. F., & Wyatt, J. W. (1980). Effectiveness of Systematic Instruction on Attitudes and Computational Estimation Skills of Preservice Elementary Teachers. Journal for Research in Mathematics Education, 11(2), 124-136.
  • Boz, B. (2004). Investigation of estimation ability of high school students (Unpublished Master’s Thesis). Middle East Technical University, Institute of Science, Ankara.
  • Carroll, W. (1996). Mental computation of students in a reform-based mathematics curriculum. School Science and Mathematics, 96(6), 305-311.
  • Cramer, K., & Post, T. (1993). Connecting research to teaching proportional reasoning. Mathematics Teacher, 86(5), 404-407.
  • Cresswell, J. W. (2008). Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. Upper Saddle River, NJ: Pearson Prentice Hall.
  • Creswell, J. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). USA: SAGE Publications.
  • Çilingir, D., & Türnüklü, E. (2009). İlköğretim 6-8. sınıf öğrencilerinin matematiksel tahmin becerileri ve tahmin stratejileri. İlköğretim Online, 8(3), 637-650.
  • Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45-55.
  • Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38(1), 47-64.
  • Ford, M. I. (1994). The teachers beliefs about mathematical problem solving in the elementary school. School Science and Mathematics, 94(6), 314-322.
  • Gliner, G. S. (1991). Factors contributing to success in mathematical estimation in pre-service teachers: Types of problems and previous mathematical experience. Educational Studies in Mathematics, 22(6), 595-606.
  • Goodman, T. (1991). Computational estimation skills of preservice elementary teachers. International Journal of Mathematical Education in Science and Technology, 22(2), 259-272.
  • Gooya, Z., Khosroshahi, L. G., & Teppo, A. R. (2011). Iranian students’ measurement estimation performance involving linear and area attributes of real-world objects. ZDM Mathematics Education, 43(5), 709-722.
  • Hanson, S., & Hogan, T. (2000). Computational estimation skill of college students. Journal for Research in Mathematics Education, 31(4), 483-499.
  • Kagan, D. M. (1992). Implication of research on teacher belief. Educational Psychologist, 27(10), 65-70.
  • Kılıç, Ç., & Olkun, S. (2013). İlköğretim öğrencilerinin gerçek yaşam durumlarındaki ölçüsel tahmin performansları ve kullandıkları stratejiler. İlköğretim Online, 12(1), 295‐307.
  • Lemaire, P., & Lecacheur, M. (2002). Children’s strategies in computational estimation. Journal of Experimental Child Psychology, 82(4), 281-304.
  • Lemaire, P., Lecacheur, M., & Farioli, F. (2000). Children’s strategies in computational estimation. Canadian Journal of Experimental Psychology, 54(2), 141-148.
  • Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for Developing Thought-Revealing Activities for Students and Teachers. In A. Kelly, & R. Lesh (Eds.), Research design in mathematics and science education (pp. 591-646). Mahwah, New Jersey: Lawrence Erlbaum Associates.
  • Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 13(5), 350-359.
  • Lingefjärd, T. (2006). Faces of mathematical modeling. ZDM, The International Journal on Mathematics Education, 38(2), 96-112.
  • Liu, F. (2009). Multiplication estimation by third and fifth-grade Chinese students. School Science and Mathematics, 107(9), 325-337.
  • MEB [Milli Eğitim Bakanlığı]. (1948). İlkokul programı. İstanbul: Milli Eğitim Basımevi.
  • MEB. (1968). İlkokul programı. Ankara: Ayyıldız Matbaası.
  • MEB. (1998). İlköğretim okulu matematik dersi öğretim programı: 1-2-3. sınıflar. Ankara: Milli Eğitim Basımevi.
  • MEB. (2006). İlköğretim İngilizce Dersi (4,5,6,7 ve 8.sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009a). İlköğretim matematik dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009b). İlköğretim matematik dersi (6.-8. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009c). İlköğretim fen ve teknoloji dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2009d). İlköğretim Türkçe dersi (1.-5. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEB. (2015). İlkokul matematik dersi (1, 2, 3 ve 4. sınıflar) öğretim programı. Retrieved from http://ttkb.meb.gov.tr.
  • MEGSB (Milli Eğitim Gençlik ve Spor Bakanlığı). (1983). İlkokul matematik programı. İstanbul: Milli Eğitim Basımevi.
  • Micklo, S. J. (1999). Estimation: It’s more than a guess. Childhood Education, 75(3), 142-145.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (3rd ed.). Newbury Park, CA: Sage Publications.
  • Mohamed, M., & Johnny, J. (2010). Investigating number sense among students. Procedia Social and Behavioral Sciences, 8, 317-324.
  • NCTM [National Council of Teachers of Mathematics]. (1989). Curriculum and evaluation standards for school mathematics. Commission on Standards for School Mathematics. Reston VA: National Council of Teachers of Mathematics.
  • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Osborne, J. (2005). The role of argument in science education. In K. Boersma (Ed.), Research and the Quality of Science Education (pp. 367-380). The Netherlands: Springer.
  • Patkin, D., & Gazit, A. (2013). On roots and squares – estimation, intuition and creativity. International Journal of Mathematical Education in Science and Technology, 44(8), 1191-1200.
  • Posamentier, A. S., & Krulik, S. (1998). Problem-Solving strategies for efficient and elegant solutions. A Research for the Mathematics Teacher. California: Corwin Press.
  • Raymond, A. M. (1997). Inconsistency between a beginning elementary school teacher’s mathematics beliefs and teaching practice. Journal for Research in Mathematics Education, 28(5), 550-576.
  • Reys, B. J. (1986). Teaching Computational Estimation: Concepts and Strategies. In H. L. Schoen & M. J. Zweng (Eds.), Estimation and mental computation: 1986 yearbook (pp. 31-45). Reston, VA: National Council of Teachers of Mathematics.
  • Reys, R., Reys, B., Nohda, N., Ishida, J., Yoshikawa, S., & Shimizu, K. (1991). Computational estimation performance and strategies used by fifth- and eighth-grade Japanese students. Journal for Research in Mathematics Education, 22(1), 39-58.
  • Reys, R. E., Rybolt, J. F., Bestgen, B. J,. & Wyatt, J. W. (1982). Processes used by good computational estimators. Journal for Research in Mathematics Education, 13(3), 183-201.
  • Rubenstein, R. (1985). Computational estimation and related mathematical skills. Journal for Research in Mathematics Education, 16(2), 106-119.
  • Segovia, I., & Castro, E. (2009). Computational and measurement estimation; curriculum foundations and research carried out at the University of Granada. Electronic Journal of Research in Educational Psychology, 7(1), 499-536.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Siegel, A. W., Goldsmith, L. T., & Madson, C. R. (1982). Skill in estimation problems of extent and numerosity. Journal for Research in Mathematics Education, 13(3), 211-232.
  • Siegler, R. S., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75(2), 428-444.
  • Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation: A review. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 197-212). New York: Psychology Press.
  • Smart, J. R. (1982). Estimation skills in mathematics. School Science and Mathematics, 82(8), 642-649.
  • Sullivan, J. L., Juhasz, B. J., Slattery, T. J., & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin & Review, 18(3), 557-563.
  • Tirosh, D., & Graeber, A. O. (1989). Preservice elementary teachers’ explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96.
  • Thompson, A. G. (1979). Estimating and Approximating. School Science and Mathematics, 79(7), 575-586.
  • Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127-146). New York: Macmillan.
  • Toluk-Uçar, Z., & Aytekin, C. (2014). Investigation of middle school students’ estimation ability with fractions. İlköğretim Online, 13(2), 546-563.
  • Tsao, Y. L., & Pan, T. R. (2013). The computational estimation and instructional perspectives of elementary school teachers. Journal of Instructional Pedagogies, 11, 1-15.
  • Van de Walle J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Allyn & Bacon.
  • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Charlotte, NC: Information Age.
  • Yıldırım, A., & Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. (6. baskı)
  • Ankara: Seçkin Yayıncılık.
There are 66 citations in total.

Details

Journal Section Makaleler
Authors

Burçak Boz-yaman

Safure Bulut

Publication Date June 30, 2017
Submission Date June 9, 2016
Published in Issue Year 2017 Volume: 11 Issue: 1

Cite

APA Boz-yaman, B., & Bulut, S. (2017). Middle School Mathematics Teachers’ Opinions on Estimation. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(1), 48-80. https://doi.org/10.17522/balikesirnef.354985

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