Evaluation of the Probability Teaching-Learning Process Based on Mathematics Teachers' Views
Year 2022,
, 1621 - 1641, 29.12.2022
Selçuk Fırat
,
Ramazan Gürbüz
Abstract
In this study, it is aimed to evaluate the probability teaching-learning process based on the views of mathematics teachers. In the research case study which is one of the qualitative research methods was used. The participants of the study consisted of eight middle and eight high school mathematics teachers and 66 students of these teachers were determined by purposive sampling. The data of the research were collected in three stages by using semi-structured interview forms and probability problems. The data obtained from the study were analyzed by open coding and axial coding methods. According to the results obtained from the first and second stages of the research, most of the teachers stated that the time allocated for the probability teaching is not enough to perform conceptual learning. High school teachers also point out that different outcomes at different levels are causing problems in the teaching of probability. While middle school teachers stressed the need to begin at an earlier age to probability teaching, high school teachers often said that they had to start with the high school level. Teachers stated that they used routine question types in the probability teaching process. In line with their views, it was determined that they reached correct solutions more than non-routine ones. Moreover, teachers made more realistic predictions about their students’ solutions to routine problems than non-routine problems.
References
- Andrew, L. (2009). Experimental probability in elementary school. Teaching Statistics, 31 (2), 34–36.
- Arican, M., & Kuzu, O. (2020). Diagnosing preservice teachers’ understanding of statistics and probability: Developing a test for cognitive assessment. International Journal of Science and Mathematics Education, 18(4), 771-790.
- Bagehot, W. (1956). Probability. In J. R. Newman (Ed.), The world of mathematics (pp. 421–455). New York, NY; Simon and Schuster.
- Bakeman, R. and Gottman, J. M. (1997). Observing interaction: An introduction to sequential analysis. Cambridge university press.
- Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.
- Batanero, C. (2020). Probability Teaching and Learning. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Second Edi, pp. 682–686). https://doi.org/10.1007/978-94- 007-4978-8_47
- Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S. & Sánchez, E. (2016). Research on teaching and learning probability. In Research on teaching and learning probability (pp. 1-33). Springer International Publishing.
- Batanero, C. and Díaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13.
- Batanero, C., Godino, J. D. & Roa, R. (2004). Training teachers to teach probability. Journal of Statistics Education, 12(1), 1-19.
- Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558-567.
- Ben-Hur, M. (2006). Concept-rich mathematics instruction: Building a strong foundation for reasoning and problem solving. Alexandria, VA: Association for Supervision and Curriculum Development.
- Borovcnik, M. G., & Kapadia, R. (2010, April). Research and developments in probability education internationally. In Proceedings of the British Congress for Mathematics Education (Vol. 30, No. 1).
- Bryant, P. and Nunes, T. (2012). Children's understanding of probability: A literature review (full Report). Nuffield Foundation.
- Bulut, S. (1994). The effects of different teaching methods and gender on probability achievement and attitudes toward probability. Doctoral Dissertation, Middle East Technical University, Ankara, Turkey.
- Bulut, S. (2001). Investigation of performances of prospective mathematics teachers on probability. Hacettepe University Journal of Education, 20, 33-39.
- Chong, J. S. Y., Chong, M. S. F., Shahrill, M. and Abdullah, N. A. (2017). Implementıng Inquıry-Based Learning and Examining the Effects In Junior College Probability Lessons. Journal on Mathematics Education, 8(2), 157-164.
- Corbin, J. and Strauss, A. (1990). Grounded theory research: Procedures, canons and evaluative criteria. Zeitschrift für Soziologie, 19(6), 418-427.
- Creswell, J. W. (2002). Educational research: Planning, conducting, and evaluating qualitative and qualitative research. Upper Saddle River, N.J.: Merrill.
- Creswell, J. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications Inc.
- Çakmak, Z. T. & Durmuş, S. (2015). Determining the concepts and subjects in the area of learning statistics and probability that 6-8th grade math students have difficulties. Abant İzzet Baysal University Journal of Faculty of Education, 15(2), 27-58. Doi: 10.17240/aibuefd.2015.15.2-5000161312
- Fırat, S. (2018). Olasılık öğretme-öğrenme sürecinin matematik öğretmenlerinin görüşlerine dayalı olarak değerlendirilmesi [Doktora Tezi]. İnönü Üniversitesi, Malatya.
- Fischbein, H. (1975). The intuitive sources of probabilistic thinking in children (Vol. 85). Springer Science & Business Media.
- Fischbein, E. & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? . Educational Studies in Mathematics, 15(1), 1-24.
- Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal of Research in Science Teaching, 28, 96-105.
- Garfield, J. (2001). Evaluating the impact of educational reform in statistics: A survey of introductory statistics courses. Final report for NSF Grant REC-9732404, 9, 13.
- Garfield, J. & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for research in Mathematics Education, 44-63.
- Gürbüz, R. (2006). Olasılık kavramlarıyla ilgili geliştirilen öğretim materyallerinin öğrencilerin kavramsal gelişimine etkisi. Buca Eğitim Fakültesi Dergisi, 20(1), 59-68.
- Gürbüz, R. (2007). The effects of computer aided instruction on students’ conceptual development: A case of probability subject. Eurasion Journal of Educational Research, 28, 75-87
- Gürbüz, R. & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers & Education, 58(3), 931-941.
- Haller, S. K. (1997). Adopting probability curricula: The content and pedagogical content knowledge of middle grades teachers [Doctoral dissertation]. University of Minnesota.
- Hawkins, A. S. and Kapadia, R. (1984). Children's conceptions of probability—a psychological and pedagogical review. Educational Studies in Mathematics, 15(4), 349-377.
- HodnikČadež, T. & Škrbec, M. (2011). Understanding the concepts in probability of pre-school and early school children. Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 263-279.
- Ingram, J. (2022). Randomness and probability: Exploring student teachers’ conceptions. Mathematical Thinking and Learning, 1-19. https://doi.org/10.1080/10986065.2021.2016029
- Jacobbe, T. & Horton, R. M. (2010). Elementary school teachers' comprehension of data displays. Statistics Education Research Journal, 9(1), 27-45.
- Jendraszek, P. A. (2008). Misconceptions of probability among future teachers of mathematics. Columbia University.
- Jones, G. A. (1974). The performances of first, second, and third grade children on five concepts of probability and the effects of grade, I.Q., and embodiments on their performance [Doctoral dissertation]. Indiana University, Bloomington.
- Jones, G. A. (2005). Exploring probability in school. Challenges for teaching and learning. Springer. https://doi.org/10.1007/b105829
- Jones, G. A., Langrall, C., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909–955). Information Age Publishing, Inc. & National Council of Teachers of Mathematics.
- Kurt Birel, G. (2017). The investigation of pre-service elementary mathematics teachers' subject matter knowledge about probability. Mersin University Journal of the Faculty of Education, 13 (1), 348-362. Doi: 10.17860/mersinefd.306023
- Lee, P. Y. (Ed.). (2006). Teaching secondary school mathematics: A resource book. Singapore: McGraw-Hill.
Liu, Y. and Thompson, P. (2007). Teachers' understandings of probability. Cognition and Instruction, 25(2-3), 113-160.
- Ministry of National MoNE (1990). Primary school mathematics curriculum. Ankara: MoNE
- Ministry of National MoNE (2009). Elementary school mathematics curriculum (Grades 6-8). Ministry of National Education, Ankara.
- Ministry of National Education (MoNE) (2013a). Middle school mathematics curriculum (Grades 5–8). Ministry of National Education, Ankara.
- Ministry of National Education (MoNE) (2013b). High school mathematics curriculum (Grades 9-12). Ministry of National Education, Ankara.
- Memnun, D. S. (2008). Olasılık kavramlarının öğrenilmesinde karşılaşılan zorluklar, bu kavramların öğrenilememe nedenleri ve çözüm önerileri. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15), 89-101.
- Njenga, D. N. (2010). Seventh-grade curriculum in probability (a guide for teachers). [Master’s thesis]. Louisiana State University.
- Noddings, N., Gilbert-MacMillan, K. and Lutz, S. (1980). What does an individual gain in small group mathematical problem solving. In Meeting of the American Educational Research Association, Montreal.
- Patton, M. Q. (2002) Qualitative Research and Evaluation Methods. Thousand Oaks, CA: Sage Publications, Inc.
- Paul, M. & Hlanganipai, N. (2014). The nature of misconceptions and cognitive obstacles faced by secondary school mathematics students in understanding probability: A case study of selected Polokwane secondary schools. Mediterranean Journal of Social Sciences, 5(8), 446.
- Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. New York: Norton.
- Pijls, M., Dekker, R. & Van Hout-Wolters, B. (2007). Reconstruction of a collaborative mathematical learning process. Educational Studies in Mathematics, 65, 309-329.
- Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula, T. J. Buttery, & E. Guyton (Eds.), Handbook of research on teacher education (pp. 102–119). Macmillan
- Richardson, V., Anders, P., Tidwell, D. & Lloyd, C. (1991). The relationship between teachers’ beliefs and practices in reading comprehension instruction. American Educational Research Journal, 28(3), 559-586.
- Shaughnessy, J. M. (1992). Research on probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). Macmillan Publishing Company.
- Staub, F. C. and Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344.
- Stohl, H. (2005). Probability in teacher education and development. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345–366). Springer.
- Strauss, A. L. & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park: Sage.
- Strauss, A. & Corbin, J. (1998). Basics of qualitative research techniques. Sage publications.
- Swenson, K. A. (1997). Middle school mathematics teachers' subject matter knowledge and pedagogical content knowledge of probability: Its relationship to probability instruction [Doctoral dissertation]. Oregon State University.
- Talawat, P. (2015). Thai secondary school students’ probability misconceptions: The impact of formal instruction [Doctoral Dissertation]. University of California.
- Taylor, F. M. (2011). Why teach probability in the elementary classroom. Louisiana Association of Teachers Mathematics Journal, 2(1).
- 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). MacMillan.
- Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education 4(4), 305 – 337.
- Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. Baskı). Ankara: Seçkin Yayıncılık.
- Yin, R.K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.
Olasılık Öğretme-Öğrenme Sürecinin Matematik Öğretmenlerinin Görüşlerine Dayalı Olarak Değerlendirilmesi
Year 2022,
, 1621 - 1641, 29.12.2022
Selçuk Fırat
,
Ramazan Gürbüz
Abstract
Bu çalışmada olasılık öğretme-öğrenme sürecinin matematik öğretmenlerinin görüşlerine dayalı olarak değerlendirilmesi amaçlanmıştır. Nitel araştırma yöntemlerinden durum çalışması deseni ile gerçekleştirilmiş olan çalışmada katılımcılar amaçsal örneklem yolu ile belirlenen sekiz ortaokul, sekiz lise matematik öğretmeni ve bu öğretmenlerin 66 öğrencisinden oluşmaktadır. Araştırmanın verileri yarı yapılandırılmış görüşme formları ve olasılık problemleri kullanılarak üç aşamada toplanmıştır. Araştırmadan elde edilen veriler, açık kodlama ve eksensel kodlama yöntemleri kullanılarak analiz edilmiştir. İlk iki aşamadan elde edilen verilerin analizi sonucunda öğretmenlerin çoğunluğunun olasılık konusuna ayrılan sürenin kavramsal öğrenmeyi gerçekleştirmek için yeterli olmadığı görüşünde oldukları belirlenmiştir. Lise öğretmenleri, kazanımların dağınık olmasından memnun olmadıklarını ve bu durumun olasılık öğretiminde sorunlara neden olduğunu belirtmişlerdir. Ortaokul öğretmenleri, olasılık konusunun öğretiminin daha küçük yaşlardan başlaması gerektiğini vurgulamışlar ancak lise öğretmeleri ise genel olarak lise seviyesinden başlaması gerektiğini belirtmişlerdir. Öğretmenler olasılık öğretim sürecinde rutin problem tiplerini kullandıklarını belirtmişler ve bu görüşleriyle paralel olarak bu sorularda daha fazla doğru çözüme ulaşmışlardır. Ayrıca öğretmenler öğrencilerinin çözümleri hakkında rutin olmayan problemlere göre rutin problemlerin çözümünde daha gerçekçi tahminlerde bulunmuşlardır.
References
- Andrew, L. (2009). Experimental probability in elementary school. Teaching Statistics, 31 (2), 34–36.
- Arican, M., & Kuzu, O. (2020). Diagnosing preservice teachers’ understanding of statistics and probability: Developing a test for cognitive assessment. International Journal of Science and Mathematics Education, 18(4), 771-790.
- Bagehot, W. (1956). Probability. In J. R. Newman (Ed.), The world of mathematics (pp. 421–455). New York, NY; Simon and Schuster.
- Bakeman, R. and Gottman, J. M. (1997). Observing interaction: An introduction to sequential analysis. Cambridge university press.
- Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466.
- Batanero, C. (2020). Probability Teaching and Learning. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (Second Edi, pp. 682–686). https://doi.org/10.1007/978-94- 007-4978-8_47
- Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S. & Sánchez, E. (2016). Research on teaching and learning probability. In Research on teaching and learning probability (pp. 1-33). Springer International Publishing.
- Batanero, C. and Díaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3(1), 3-13.
- Batanero, C., Godino, J. D. & Roa, R. (2004). Training teachers to teach probability. Journal of Statistics Education, 12(1), 1-19.
- Batanero, C. & Serrano, L. (1999). The meaning of randomness for secondary school students. Journal for Research in Mathematics Education, 30(5), 558-567.
- Ben-Hur, M. (2006). Concept-rich mathematics instruction: Building a strong foundation for reasoning and problem solving. Alexandria, VA: Association for Supervision and Curriculum Development.
- Borovcnik, M. G., & Kapadia, R. (2010, April). Research and developments in probability education internationally. In Proceedings of the British Congress for Mathematics Education (Vol. 30, No. 1).
- Bryant, P. and Nunes, T. (2012). Children's understanding of probability: A literature review (full Report). Nuffield Foundation.
- Bulut, S. (1994). The effects of different teaching methods and gender on probability achievement and attitudes toward probability. Doctoral Dissertation, Middle East Technical University, Ankara, Turkey.
- Bulut, S. (2001). Investigation of performances of prospective mathematics teachers on probability. Hacettepe University Journal of Education, 20, 33-39.
- Chong, J. S. Y., Chong, M. S. F., Shahrill, M. and Abdullah, N. A. (2017). Implementıng Inquıry-Based Learning and Examining the Effects In Junior College Probability Lessons. Journal on Mathematics Education, 8(2), 157-164.
- Corbin, J. and Strauss, A. (1990). Grounded theory research: Procedures, canons and evaluative criteria. Zeitschrift für Soziologie, 19(6), 418-427.
- Creswell, J. W. (2002). Educational research: Planning, conducting, and evaluating qualitative and qualitative research. Upper Saddle River, N.J.: Merrill.
- Creswell, J. (2009). Research design: Qualitative, quantitative, and mixed methods approaches. SAGE Publications Inc.
- Çakmak, Z. T. & Durmuş, S. (2015). Determining the concepts and subjects in the area of learning statistics and probability that 6-8th grade math students have difficulties. Abant İzzet Baysal University Journal of Faculty of Education, 15(2), 27-58. Doi: 10.17240/aibuefd.2015.15.2-5000161312
- Fırat, S. (2018). Olasılık öğretme-öğrenme sürecinin matematik öğretmenlerinin görüşlerine dayalı olarak değerlendirilmesi [Doktora Tezi]. İnönü Üniversitesi, Malatya.
- Fischbein, H. (1975). The intuitive sources of probabilistic thinking in children (Vol. 85). Springer Science & Business Media.
- Fischbein, E. & Gazit, A. (1984). Does the teaching of probability improve probabilistic intuitions? . Educational Studies in Mathematics, 15(1), 1-24.
- Fischbein, E. & Schnarch, D. (1997). The evolution with age of probabilistic, intuitively based misconceptions. Journal of Research in Science Teaching, 28, 96-105.
- Garfield, J. (2001). Evaluating the impact of educational reform in statistics: A survey of introductory statistics courses. Final report for NSF Grant REC-9732404, 9, 13.
- Garfield, J. & Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics: Implications for research. Journal for research in Mathematics Education, 44-63.
- Gürbüz, R. (2006). Olasılık kavramlarıyla ilgili geliştirilen öğretim materyallerinin öğrencilerin kavramsal gelişimine etkisi. Buca Eğitim Fakültesi Dergisi, 20(1), 59-68.
- Gürbüz, R. (2007). The effects of computer aided instruction on students’ conceptual development: A case of probability subject. Eurasion Journal of Educational Research, 28, 75-87
- Gürbüz, R. & Birgin, O. (2012). The effect of computer-assisted teaching on remedying misconceptions: The case of the subject “probability”. Computers & Education, 58(3), 931-941.
- Haller, S. K. (1997). Adopting probability curricula: The content and pedagogical content knowledge of middle grades teachers [Doctoral dissertation]. University of Minnesota.
- Hawkins, A. S. and Kapadia, R. (1984). Children's conceptions of probability—a psychological and pedagogical review. Educational Studies in Mathematics, 15(4), 349-377.
- HodnikČadež, T. & Škrbec, M. (2011). Understanding the concepts in probability of pre-school and early school children. Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 263-279.
- Ingram, J. (2022). Randomness and probability: Exploring student teachers’ conceptions. Mathematical Thinking and Learning, 1-19. https://doi.org/10.1080/10986065.2021.2016029
- Jacobbe, T. & Horton, R. M. (2010). Elementary school teachers' comprehension of data displays. Statistics Education Research Journal, 9(1), 27-45.
- Jendraszek, P. A. (2008). Misconceptions of probability among future teachers of mathematics. Columbia University.
- Jones, G. A. (1974). The performances of first, second, and third grade children on five concepts of probability and the effects of grade, I.Q., and embodiments on their performance [Doctoral dissertation]. Indiana University, Bloomington.
- Jones, G. A. (2005). Exploring probability in school. Challenges for teaching and learning. Springer. https://doi.org/10.1007/b105829
- Jones, G. A., Langrall, C., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909–955). Information Age Publishing, Inc. & National Council of Teachers of Mathematics.
- Kurt Birel, G. (2017). The investigation of pre-service elementary mathematics teachers' subject matter knowledge about probability. Mersin University Journal of the Faculty of Education, 13 (1), 348-362. Doi: 10.17860/mersinefd.306023
- Lee, P. Y. (Ed.). (2006). Teaching secondary school mathematics: A resource book. Singapore: McGraw-Hill.
Liu, Y. and Thompson, P. (2007). Teachers' understandings of probability. Cognition and Instruction, 25(2-3), 113-160.
- Ministry of National MoNE (1990). Primary school mathematics curriculum. Ankara: MoNE
- Ministry of National MoNE (2009). Elementary school mathematics curriculum (Grades 6-8). Ministry of National Education, Ankara.
- Ministry of National Education (MoNE) (2013a). Middle school mathematics curriculum (Grades 5–8). Ministry of National Education, Ankara.
- Ministry of National Education (MoNE) (2013b). High school mathematics curriculum (Grades 9-12). Ministry of National Education, Ankara.
- Memnun, D. S. (2008). Olasılık kavramlarının öğrenilmesinde karşılaşılan zorluklar, bu kavramların öğrenilememe nedenleri ve çözüm önerileri. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15), 89-101.
- Njenga, D. N. (2010). Seventh-grade curriculum in probability (a guide for teachers). [Master’s thesis]. Louisiana State University.
- Noddings, N., Gilbert-MacMillan, K. and Lutz, S. (1980). What does an individual gain in small group mathematical problem solving. In Meeting of the American Educational Research Association, Montreal.
- Patton, M. Q. (2002) Qualitative Research and Evaluation Methods. Thousand Oaks, CA: Sage Publications, Inc.
- Paul, M. & Hlanganipai, N. (2014). The nature of misconceptions and cognitive obstacles faced by secondary school mathematics students in understanding probability: A case study of selected Polokwane secondary schools. Mediterranean Journal of Social Sciences, 5(8), 446.
- Piaget, J. & Inhelder, B. (1975). The origin of the idea of chance in children. New York: Norton.
- Pijls, M., Dekker, R. & Van Hout-Wolters, B. (2007). Reconstruction of a collaborative mathematical learning process. Educational Studies in Mathematics, 65, 309-329.
- Richardson, V. (1996). The role of attitudes and beliefs in learning to teach. In J. Sikula, T. J. Buttery, & E. Guyton (Eds.), Handbook of research on teacher education (pp. 102–119). Macmillan
- Richardson, V., Anders, P., Tidwell, D. & Lloyd, C. (1991). The relationship between teachers’ beliefs and practices in reading comprehension instruction. American Educational Research Journal, 28(3), 559-586.
- Shaughnessy, J. M. (1992). Research on probability and statistics: Reflections and directions. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 465–494). Macmillan Publishing Company.
- Staub, F. C. and Stern, E. (2002). The nature of teachers' pedagogical content beliefs matters for students' achievement gains: Quasi-experimental evidence from elementary mathematics. Journal of Educational Psychology, 94(2), 344.
- Stohl, H. (2005). Probability in teacher education and development. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345–366). Springer.
- Strauss, A. L. & Corbin, J. M. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Newbury Park: Sage.
- Strauss, A. & Corbin, J. (1998). Basics of qualitative research techniques. Sage publications.
- Swenson, K. A. (1997). Middle school mathematics teachers' subject matter knowledge and pedagogical content knowledge of probability: Its relationship to probability instruction [Doctoral dissertation]. Oregon State University.
- Talawat, P. (2015). Thai secondary school students’ probability misconceptions: The impact of formal instruction [Doctoral Dissertation]. University of California.
- Taylor, F. M. (2011). Why teach probability in the elementary classroom. Louisiana Association of Teachers Mathematics Journal, 2(1).
- 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). MacMillan.
- Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education 4(4), 305 – 337.
- Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. Baskı). Ankara: Seçkin Yayıncılık.
- Yin, R.K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.