ÖĞRETMEN ADAYLARININ ARİTMETİK ORTALAMA VE AÇIKLIK KAVRAMLARINA İLİŞKİN BİLGİLERİNİN İNCELENMESİ

Abstract

Bu çalışmada öğretmen adaylarının aritmetik ortalama ve açıklık kavramlarına ilişkin istatistiği öğretme bilgilerinin ders araştırması bağlamında incelenmesi amaçlanmıştır. Nitel araştırma yöntemi benimsenmiş ve üç son sınıf öğretmen adayı ile çalışılmıştır. Öğretmen adayları üç ders araştırması gerçekleştirmiştir. Bu süreçte veriler, görüşmeler, öğretmen adaylarının hazırladıkları ders planları, video ve ses kayıtları, gözlem ve alan notları ile yansıtıcı günlükler aracılığı ile toplanmıştır. Elde edilen verilerden hareketle öğretmen adaylarının alan, alana ilişkin öğretim ve alana ilişkin öğrenci bilgilerindeki değişimler incelenmiştir. Bulgular öğretmen adaylarının başlangıçta aritmetik ortalama ve açıklık kavramlarını işlemsel olarak ele aldıklarını, ders plan ve uygulamalarını bu doğrultuda düzenlediklerini göstermiştir. Süreç ilerledikçe bu iki kavramın anlamları üzerine yoğunlaşmışlar diğer istatistiksel kavramlarla olan ilişkisini değerlendirebilmişlerdir. Buradan hareketle hazırladıkları görevler ve gerçekleştirdikleri uygulamalarda kavramların keşfine olanak sağladıkları gözlemlenmiştir. Bunun yanında öğrencilerin zorlanabilecekleri noktalar ve nasıl düşüneceklerine yer vermişlerdir. Sonuçlardan hareketle bu tarz öğretmen eğitimi programlarının lisans programlarına entegre edilmesi önerilmiştir.

Keywords

• öğretmen adayları
• ders araştırması
• aritmetik ortalama

AN INVESTIGATION OF PRE-SERVICE TEACHERS’ KNOWLEDGE ABOUT THE CONCEPT OF ARITMETIC MEAN AND RANGE

Abstract

This study was aimed to investigate pre-service teachers’ knowledge of teaching statistics related to the concepts of arithmetic mean and range within the context of lesson study. Qualitative research method was conducted.Three senior pre-service teachers participated in the study and performed three lesson study. Data were collected by means of interviews, lesson plans prepared by the pre-service teachers, video and audio recordings, observations, field notes and reflective journals. On the basis of the collected data, the changes having occurred in the pre-service teachers’ content, teaching and student knowledge were examined. Pre-service teachers initially handled the concepts of arithmetic mean and range procedurally and arranged their lesson plans and practices accordingly. As they participated in the lesson study, they concentrated on the meanings of these two concepts and were able to evaluate their relationship with other statistical concepts. Thus, it was been observed that they enabled the discovery of the concepts through the tasks they prepared and the applications they implemented. In addition, they also focused on the points where students might have difficulties and how they would think. It can be suggested that such teacher training programs should be integrated into undergraduate programs.

Keywords

• pre-service teachers
• lesson study
• aritmetic mean
• range

References

1. Arı, E. (2010). İlköğretim 6-7 ve 8. sınıflarda matematik dersinin istatistik ve olasılık konusunun öğreniminde yaşanan problemler ve çözüm önerileri (Yayınlanmamış yüksek lisans tezi). Afyon Kocatepe Üniversitesi, Afyon.
2. Arı, E. (2010). İlköğretim 6-7 ve 8. sınıflarda matematik dersinin istatistik ve olasılık konusunun öğreniminde yaşanan problemler ve çözüm önerileri (Yayınlanmamış yüksek lisans tezi). Afyon Kocatepe Üniversitesi, Afyon.
3. Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389- 407.
4. Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389- 407.
5. Batanero, C.,Burrill, G., & Reading, C. (2011). Teaching statistics in school mathematics—Challenges for teaching and teacher education: A joint ICMI/IASE study: the 18th ICMI study. Dordrecht:Springer.
6. Batanero, C.,Burrill, G., & Reading, C. (2011). Teaching statistics in school mathematics—Challenges for teaching and teacher education: A joint ICMI/IASE study: the 18th ICMI study. Dordrecht:Springer.
7. Ben-Zvi, D. & Makar, K. (2016). International Perspectives on the Teaching and Learning of Statistics, D. Ben-Zvi and K. Makar (Eds.), The Teaching and Learning of StatisticsInternational Perspectives (pp. 1-10). Switzerland, Springer.
8. Ben-Zvi, D. & Makar, K. (2016). International Perspectives on the Teaching and Learning of Statistics, D. Ben-Zvi and K. Makar (Eds.), The Teaching and Learning of StatisticsInternational Perspectives (pp. 1-10). Switzerland, Springer.

9. Bilen, O. (2017). Ortaokul 7. sınıf matematik ders kitabı. Ankara: Gizem yayıncılık.
10. Bilen, O. (2017). Ortaokul 7. sınıf matematik ders kitabı. Ankara: Gizem yayıncılık.
11. Bjuland, R. & Mosvold, R. (2015). Lesson study in teacher education: learning from a challenging case. Teaching and Teacher Education, 52, 83–90.
12. Bjuland, R. & Mosvold, R. (2015). Lesson study in teacher education: learning from a challenging case. Teaching and Teacher Education, 52, 83–90.
13. Burgess, T. A. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. (Unpublished doctoral dissertation). Massey University, New Zealand.
14. Burgess, T. A. (2007). Investigating the nature of teacher knowledge needed and used in teaching statistics. (Unpublished doctoral dissertation). Massey University, New Zealand.
15. Canada, D. L. (2008). Conceptions of distribution held by middle school students and preservice teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: ICMI and IASE. Retrieved from http://www.ugr.es/~icmi/iase_study.
16. Canada, D. L. (2008). Conceptions of distribution held by middle school students and preservice teachers. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: ICMI and IASE. Retrieved from http://www.ugr.es/~icmi/iase_study.
17. Chassels, C.,& Melville, W. (2009). Collaborative, reflective, and iterative Japanese lesson study in an initial teacher education program: Benefits and challenges. Canadian Journal of Education, 32(4), 734-763.
18. Chassels, C.,& Melville, W. (2009). Collaborative, reflective, and iterative Japanese lesson study in an initial teacher education program: Benefits and challenges. Canadian Journal of Education, 32(4), 734-763.
19. Chick, H. L. & R. U. Pierce (2008), Teaching statistics at the primary school level: beliefs, affordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading, veA. Rossman (Eds.), Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18, Monterrey.
20. Chick, H. L. & R. U. Pierce (2008), Teaching statistics at the primary school level: beliefs, affordances, and pedagogical content knowledge. In C. Batanero, G. Burrill, C. Reading, veA. Rossman (Eds.), Joint ICMI/IASE Study: Teaching Statistics in School Mathematics. Challenges for Teaching and Teacher Education. Proceedings of the ICMI Study 18, Monterrey.
21. Cobb, P.,& McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375–396). Dordrecht, The Netherlands: Kluwer Academic Publishers.
22. Cobb, P.,& McClain, K. (2004). Principles of instructional design for supporting the development of students’ statistical reasoning. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 375–396). Dordrecht, The Netherlands: Kluwer Academic Publishers.
23. Darling‐Hammond, L. (2007). Building a system for powerful teaching and learning. In R. Whehling (Ed.), Building a 21st Century U.S. Education System (pp.65‐74). Washington, DC: National Commission on Teaching and America’s Future.
24. Darling‐Hammond, L. (2007). Building a system for powerful teaching and learning. In R. Whehling (Ed.), Building a 21st Century U.S. Education System (pp.65‐74). Washington, DC: National Commission on Teaching and America’s Future.
25. Fennema, E.,& Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematical teaching and learning (pp. 575-596). New York: Macmillan.
26. Fennema, E.,& Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.), Handbook of research on mathematical teaching and learning (pp. 575-596). New York: Macmillan.
27. Fernandez, M. L. (2005). Learning through microteaching lesson study in teacher preparation. Action in Teacher Education, 26(4), 37-47
28. Fernandez, M. L. (2005). Learning through microteaching lesson study in teacher preparation. Action in Teacher Education, 26(4), 37-47
29. Fernández, M. L. (2010). Investigating how and what prospective teachers learn through microteaching lesson study. Teaching and Teacher Education, 26(2), 351–562.
30. Fernández, M. L. (2010). Investigating how and what prospective teachers learn through microteaching lesson study. Teaching and Teacher Education, 26(2), 351–562.
31. Fernandez, C., & Yoshida, M. (2004). Lesson study: A case of a Japanese approach to improving instruction through school-based teacher development. Mahwah, NJ: Lawrence Erlbaum.
32. Fernandez, C., & Yoshida, M. (2004). Lesson study: A case of a Japanese approach to improving instruction through school-based teacher development. Mahwah, NJ: Lawrence Erlbaum.
33. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M. & Scheaffer, R. (2005) Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K–12 Curriculum Framework. Alexandria, VA: American Statistical Association.
34. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M. & Scheaffer, R. (2005) Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K–12 Curriculum Framework. Alexandria, VA: American Statistical Association.
35. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A Pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.
36. Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., et al. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report: A Pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.
37. Franklin, C., Kader, G., Bargagliotti, A., Scheaffer, R., Case, C., & Spangler, D. (2015). Statistical education of teachers. Alexandria, VA: American Statistical Association.
38. Franklin, C., Kader, G., Bargagliotti, A., Scheaffer, R., Case, C., & Spangler, D. (2015). Statistical education of teachers. Alexandria, VA: American Statistical Association.
39. Friel, S. N.,& Bright, G. W. (1998). Teach-Stat: A model for professional development in data analysis and statistics for teachers K-6. In S.P. Lajoie (Ed.), Reflections on St Romberg statistics (63-117). Mahwah, New Jersey: Lawrence Erlbaum.
40. Friel, S. N.,& Bright, G. W. (1998). Teach-Stat: A model for professional development in data analysis and statistics for teachers K-6. In S.P. Lajoie (Ed.), Reflections on St Romberg statistics (63-117). Mahwah, New Jersey: Lawrence Erlbaum.
41. Fullan, M. G. (1991). The New Meaning of Educational Change. London: Cassell Educational Limited Wellington House.
42. Fullan, M. G. (1991). The New Meaning of Educational Change. London: Cassell Educational Limited Wellington House.
43. Gal, I. & Garfield, J. (1997) The Assessment Challenge in Stutistics Education. Amsterdam: IOS Press
44. Gal, I. & Garfield, J. (1997) The Assessment Challenge in Stutistics Education. Amsterdam: IOS Press
45. Garfield, J. & Ben-Zvi, D. (2008). Preparing school teachers to develop students’ statistical reasoning, In C. Batanero, G. Burrill & C. Reading & A. Rossman (Ed.) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, A Joint ICMI/IASE study: The 18th ICMI study (pp.187-198). Springer.
46. Garfield, J. & Ben-Zvi, D. (2008). Preparing school teachers to develop students’ statistical reasoning, In C. Batanero, G. Burrill & C. Reading & A. Rossman (Ed.) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, A Joint ICMI/IASE study: The 18th ICMI study (pp.187-198). Springer.
47. Garfield, J. B., delMas, R., & Chance, B. (2007). Using students’ informal notions of variability to develop an understanding of formal measures of variability, In M. Lovett & P. Shah (Ed.) Thinking with data (pp. 117-147), New York, Erlbaum.
48. Garfield, J. B., delMas, R., & Chance, B. (2007). Using students’ informal notions of variability to develop an understanding of formal measures of variability, In M. Lovett & P. Shah (Ed.) Thinking with data (pp. 117-147), New York, Erlbaum.
49. Gonzalez, O. (2014). Examining Venezuelan Secondary School Mathematics Teachers’ Professıonal Competencıes To Teach Statistics: Focusıng On The Instruction Of Descriptive Statistics, Nineth International Conference on Teaching Statistics.
50. Gonzalez, O. (2014). Examining Venezuelan Secondary School Mathematics Teachers’ Professıonal Competencıes To Teach Statistics: Focusıng On The Instruction Of Descriptive Statistics, Nineth International Conference on Teaching Statistics.
51. Gonzalez, M. T.; Espinel, M. C. & Ainley, J. (2011). Teachers’ graphical competence, In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, A Joint ICMI/IASE study: The 18th ICMI study, (pp.187-198). Springer.
52. Gonzalez, M. T.; Espinel, M. C. & Ainley, J. (2011). Teachers’ graphical competence, In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.) Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education, A Joint ICMI/IASE study: The 18th ICMI study, (pp.187-198). Springer.
53. Groth, R.E. & Bergner, J.A. (2006). Preservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, 37-63.
54. Groth, R.E. & Bergner, J.A. (2006). Preservice elementary teachers' conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8, 37-63.
55. Groth, R.E. (2009). Characteristics of teachers' conversations about teaching mean, median, and mode. Teaching and Teacher Education, 25, 707-716.
56. Groth, R.E. (2009). Characteristics of teachers' conversations about teaching mean, median, and mode. Teaching and Teacher Education, 25, 707-716.
57. Harle, J. (2009). Lesson study: Mathematics teachers become the professionals in their professional development. (Unpublished master dissertation). University of Alberta, Alberta.
58. Harle, J. (2009). Lesson study: Mathematics teachers become the professionals in their professional development. (Unpublished master dissertation). University of Alberta, Alberta.
59. Hiebert, J., Morris, A. K. & Glass, B. (2003). Learning to learn to teach: An “experiment” model for teaching and teaching preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222.
60. Hiebert, J., Morris, A. K. & Glass, B. (2003). Learning to learn to teach: An “experiment” model for teaching and teaching preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201-222.
61. Ijeh, S. B. (2012). How competent mathematics teachers develop pedagogical content knowledge in statistics teaching. (Unpublised doctoral dissertation). University of Pretoria, South Africa.
62. Ijeh, S. B. (2012). How competent mathematics teachers develop pedagogical content knowledge in statistics teaching. (Unpublised doctoral dissertation). University of Pretoria, South Africa.
63. Jacobbe, T. (2007). Elementary school teachers’ understanding of essentıal topics in statistics and the influence of assessment instruments and a reform curriculum upon their understanding. (Unpublished Doctoral Dissertation). Clemson University, Clemson.
64. Jacobbe, T. (2007). Elementary school teachers’ understanding of essentıal topics in statistics and the influence of assessment instruments and a reform curriculum upon their understanding. (Unpublished Doctoral Dissertation). Clemson University, Clemson.
65. Keskin-Oğan, A., & Öztürk, S. (2019). Ortaokul ve imam hatip ortaokulu matematik 7 ders kitabı. MEB Yayınları.
66. Keskin-Oğan, A., & Öztürk, S. (2019). Ortaokul ve imam hatip ortaokulu matematik 7 ders kitabı. MEB Yayınları.
67. Kuntze, S. (2014). Teachers’ views related to goals of the statistics classroom – from global to content-specific. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the 9th International Conference on Teaching Statistics (ICOTS 9, July, 2014), Flagstaff, AZ, USA. Voorburg, The Netherlands: International Statistical Institute.
68. Kuntze, S. (2014). Teachers’ views related to goals of the statistics classroom – from global to content-specific. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the 9th International Conference on Teaching Statistics (ICOTS 9, July, 2014), Flagstaff, AZ, USA. Voorburg, The Netherlands: International Statistical Institute.
69. Korthagen, F. A. J. (2001). Linking practice and theory: The pedagogy of realistic teacher education. New Jersey: Lawrence Erlbaum Associates, Inc.
70. Korthagen, F. A. J. (2001). Linking practice and theory: The pedagogy of realistic teacher education. New Jersey: Lawrence Erlbaum Associates, Inc.
71. Leavy A .M. (2004) Indexing distributions of data: Preservice teachers’ notions of representativeness, School Science and Mathematics, 104(3), 119–133
72. Leavy A .M. (2004) Indexing distributions of data: Preservice teachers’ notions of representativeness, School Science and Mathematics, 104(3), 119–133
73. Leavy, A. M. (2006) Using data comparison to support a focus on distribution: Examining preservice teachers’ understanding of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89-114.
74. Leavy, A. M. (2006) Using data comparison to support a focus on distribution: Examining preservice teachers’ understanding of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89-114.
75. Leavy, A. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46-67.
76. Leavy, A. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46-67.
77. Leavy, A. (2015). Looking at practice: Revealing the knowledge demands of teaching data handling in the primary classroom. Mathematics Education Research Journal, 27, 283-309.
78. Leavy, A. (2015). Looking at practice: Revealing the knowledge demands of teaching data handling in the primary classroom. Mathematics Education Research Journal, 27, 283-309.
79. Lee, J. (2008). A Hong Kong case of Lesson study-benefits and concerns. Teaching and Teacher Education, 24, 1115-1124.
80. Lee, J. (2008). A Hong Kong case of Lesson study-benefits and concerns. Teaching and Teacher Education, 24, 1115-1124.
81. Lee, H. S.,& Lee, J. T. (2011). Enhancing prospective teachers’ coordination of center and spread: A window into teacher education material development. The Mathematics Educator, 21(1), 33–47.
82. Lee, H. S.,& Lee, J. T. (2011). Enhancing prospective teachers’ coordination of center and spread: A window into teacher education material development. The Mathematics Educator, 21(1), 33–47.
83. Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for Better Schools.
84. Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Philadelphia: Research for Better Schools.
85. Miles, M, B.,& Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. Thousand Oaks, CA: Sage
86. Miles, M, B.,& Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. Thousand Oaks, CA: Sage
87. Milli Eğitim Bakanlığı (MEB). (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar. Ankara, Türkiye.
88. Milli Eğitim Bakanlığı (MEB). (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar. Ankara, Türkiye.
89. Mitchener, C. P., ve Anderson, R. D. (1989). Teachers' perspectives: Developing and Implementing an STS curriculum. Journal of Research in Science Teaching, 26(4), 351-369.
90. Mitchener, C. P., ve Anderson, R. D. (1989). Teachers' perspectives: Developing and Implementing an STS curriculum. Journal of Research in Science Teaching, 26(4), 351-369.
91. Monteiro, C.,& Ainley, J. (2007). Investigating the interpretation of media graphs among student teachers. International Electronic Journal of Mathematics Education, 2(3), 188–207.
92. Monteiro, C.,& Ainley, J. (2007). Investigating the interpretation of media graphs among student teachers. International Electronic Journal of Mathematics Education, 2(3), 188–207.
93. Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.
94. Moore, D. S. (1990). Uncertainty. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.
95. Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can pre-service teachers learn? Journal for Research in Mathematics Education, 40(5), 491-529.
96. Morris, A. K., Hiebert, J., & Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can pre-service teachers learn? Journal for Research in Mathematics Education, 40(5), 491-529.
97. Murata, A. (2010). Teacher Learning with Lesson study, In P. Peterson, E. Baker & B. McGaw (Ed.), International Encyclopedia of Education,7, (pp. 575-581), Oxford: Elsevier.
98. Murata, A. (2010). Teacher Learning with Lesson study, In P. Peterson, E. Baker & B. McGaw (Ed.), International Encyclopedia of Education,7, (pp. 575-581), Oxford: Elsevier.
99. Murata, A. (2011). Introduction: Conceptual overview of lesson study. In Lesson study research and practice in mathematics education (pp. 1-12). Springer Netherlands.
100. Murata, A. (2011). Introduction: Conceptual overview of lesson study. In Lesson study research and practice in mathematics education (pp. 1-12). Springer Netherlands.
101. Pfannkuch, M.,& Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 323–333). New York: Springer.
102. Pfannkuch, M.,& Ben-Zvi, D. (2011). Developing teachers’ statistical thinking. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education: A joint ICMI/IASE study (pp. 323–333). New York: Springer.
103. Quintas, S., Tomás Ferreira, R., & Oliveira, H. (2014). Attending to students’ thinking on bivariate statistical data at secondary level: Two teachers’ pedagogical content knowledge. In K. Makar, B de Sousa, & R. Gould (Ed.), Sustainability in statistics education. Proceedings of the 9th International Conference on Teaching Statistics (ICOTS9). Flagstaff, Arizona, USA: Voorbung, The Netherlands: International Statistics Institute
104. Quintas, S., Tomás Ferreira, R., & Oliveira, H. (2014). Attending to students’ thinking on bivariate statistical data at secondary level: Two teachers’ pedagogical content knowledge. In K. Makar, B de Sousa, & R. Gould (Ed.), Sustainability in statistics education. Proceedings of the 9th International Conference on Teaching Statistics (ICOTS9). Flagstaff, Arizona, USA: Voorbung, The Netherlands: International Statistics Institute
105. Roback, P., Chance, B., Legler, J., & Moore, T. (2006). Applying Japanese lesson study principles to an upper-level undergraduate statistics course. Journal of Statistics Education, 14(2).
106. Roback, P., Chance, B., Legler, J., & Moore, T. (2006). Applying Japanese lesson study principles to an upper-level undergraduate statistics course. Journal of Statistics Education, 14(2).
107. Russell, S.J., Goldsmith, L.L., Weinberg, A. S., & Mokros, J.R. (1990, April). What’s typical? Teachers’ descriptions of data. Paper presented at the annual meeting of the Americal Educational Research Association. Boston, MA
108. Russell, S.J., Goldsmith, L.L., Weinberg, A. S., & Mokros, J.R. (1990, April). What’s typical? Teachers’ descriptions of data. Paper presented at the annual meeting of the Americal Educational Research Association. Boston, MA
109. Scheaffer, R. L. (2006). Statistics and mathematics: On making a happy marriage. In G. Burrill (Ed.) MCTM 2006 Yearbook: Thinking and reasoning with data and chance. Reston, VA: NCTM
110. Scheaffer, R. L. (2006). Statistics and mathematics: On making a happy marriage. In G. Burrill (Ed.) MCTM 2006 Yearbook: Thinking and reasoning with data and chance. Reston, VA: NCTM
111. Shaughnessy, J.M. (2007). Research on statistics learning and reasoning. In J. F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 957–1010).Charlotte, NC: Information Age Publishing.
112. Shaughnessy, J.M. (2007). Research on statistics learning and reasoning. In J. F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 957–1010).Charlotte, NC: Information Age Publishing.
113. Sorto, M. A. (2004). Prospective middle school teachers’ knowledge about data analysis and its application to teaching. (Unpublished doctoral dissertation), Michigan State University, Michigan.
114. Sorto, M. A. (2004). Prospective middle school teachers’ knowledge about data analysis and its application to teaching. (Unpublished doctoral dissertation), Michigan State University, Michigan.
115. Watson, J. M., Callingham, R., & Donne, J. (2008). Establishing pedagogical content knowledge for teaching statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: ICMI and IASE.
116. Watson, J. M., Callingham, R., & Donne, J. (2008). Establishing pedagogical content knowledge for teaching statistics. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference. Monterrey: ICMI and IASE.
117. Zhang, S & Cheng, Q. (2011) Learning to Teach Through a Practicum-Based Microteaching Model. Action in Teacher Education, 33(4), 343-358.
118. Zhang, S & Cheng, Q. (2011) Learning to Teach Through a Practicum-Based Microteaching Model. Action in Teacher Education, 33(4), 343-358.