The Effectiveness of Feedback Provided by Middle School Mathematics Teachers and Preservice teachers on Student Solutions: An Evaluative Study
Yıl 2024,
Cilt: 7 Sayı: 2, 323 - 352, 29.10.2024
Fatmanur Öztürk
,
Zehra Taşpınar Şener
Öz
The aim of this study is to reveal the suggestions of middle school mathematics teachers and preservice mathematics teachers that can both correct errors in students’ incorrect solutions and contribute to the advancement of students who have provided correct solutions. The study is based on the case study method. Initially, six problems related to proportional reasoning were posed to middle school students in a public school, and the solutions obtained from the students were classified according to their proportional reasoning strategies. These solutions were then examined by the students' mathematics teachers and by preservice mathematics teachers. Two questions were asked to mathematics teachers and preservice mathematics teachers during these examinations. After the examination, interviews were conducted to discuss the suggestions made to (1) correct the errors in incorrect solutions and (2) advance the proportional reasoning skills of students who obtained correct solutions. The findings indicate that both mathematics teachers and preservice mathematics teachers were adequate in providing suggestions to correct errors in students’ incorrect solutions. However, it was also found that both groups had difficulties in making suggestions to further the advancement of students who provided correct solutions.
Kaynakça
- Arican, M. (2019). Preservice mathematics teachers’ understanding of and abilities to differentiate proportional relationships from nonproportional relationships. International Journal of Science and Mathematics Education, 17(7), 1423-1443. https://doi.org/10.1007/s10763-018-9931-x
- Artut, P. D., & Pelen, M. S. (2015). 6th grade students’ solution strategies on proportional reasoning problems. Procedia-Social and Behavioral Sciences, 197, 113-119. https://doi.org/10.1016/j.sbspro.2015.07.066
- Bahar, G. (2016). Measurıng pre-service teachers' mathematics content knowledge and mathematics pedagogical content knowledge on ratio and proportion [Master’s thesis, Bosphorus University]. YÖK Tez Merkezi.
- Bart, W., Post, T., Behr, M., Lesh, R. (1994). A diagnostic analysis of a proportional reasoning test item: An introduction to the properties of a semi-dense item. Focus on Learning Problems in Mathematics, 16(3), 1-11.
- Ben-Chaim, D., Fey, J.T., Fitzgerald, W.M., Benedetto, C., Miller, J (1998). Proportional Reasoning among 7th Grade Students with Different Curricular Experiences. Educational Studies in Mathematics 36, 247–273. https://doi.org/10.1023/A:1003235712092
- Benson, S. L. D. (2009). The influence of studying students' proportional reasoning on middle school mathematics teachers' content and pedagogical content knowledge [PhD Thesis, University of Houston]. ProQuest.
- Birinci, M., & Baki, M. (n.d.). Bir Ortaokul Matematik Öğretmeninin Mesleki Gelişiminden Yansımalar: Kesir Öğretiminde Fark Etme Becerisinin İşe Koşulması. İlköğretim Online1141-1156. https://doi.org/10.17051/ilkonline.2019.610853
- Boyacı, H. S. (2019) The proportional reasoning ability of pre-service mathematics teachers: a mixed method study. [Master’s thesis, Bosphorus University]. YÖK Tez Merkezi.
- Brown, R.E., Weiland, T. & Orrill, C.H. (2019). Mathematics Teachers’ Use of Knowledge Resources When Identifying Proportional Reasoning Situations. International Journal of Science and Mathematics Education 18, 1085–1104 https://doi.org/10.1007/s10763-019-10006-3
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., Demirel, F. (2018) Bilimsel Araştırma Yöntemleri. Pegem Akademi.
- Chick, H. (2010). Aspects of Teachers' Knowledge for Helping Students Learn about Ratio. Mathematics Education Research Group of Australasia.
- Choy, B. H. (2014). Noticing Critical Incidents in a Mathematics Classroom. Mathematics Education Research Group of Australasia.
- Cramer, K. & Post, T. (1993, May). Connecting Research To Teaching Proportional Reasoning. Mathematics Teacher, 86(5), 404-407.
- Cramer, K., Behr, M., & Bezuk, N. (1989, October). Proportional Relationships and Unit Rates. Mathematics Teacher, 82 (7), 537-544.
- Cramer, K., Post, T., & Currier, S. (1993). Learning and Teaching Ratio and Proportion: Research Implications. D. Owens (Ed.), Research Ideas For the Classroom (pp. 159-178). NY: Macmillan Publishing Company.
- Çıkla, O. A., & Duatepe, A. (2002). İlköğretim matemetik öğretmen adaylarının orantısal akıl yürütme becerileri üzerine niteliksel bir çalışma. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23(23).
- De la Cruz, J. A. (2008). A look at middle school mathematics teachers' instruction related to proportional reasoning: A cognitively guided perspective [PhD Thesis, University of Virginia]. ProQuest.
- Degrande, T., Verschaffel, L., & Van Dooren, W. (2019). To add or to multiply? An investigation of the role of preference in children's solutions of word problems. Learning and Instruction, 61, 60-71. https://doi.org/10.1016/j.learninstruc.2019.01.002Get rights and content
- Dick, L. K. (2013). Preservice student teacher professional noticing through analysis of their students' work [PhD Thesis, North Carolina State University]. ProQuest.
- Dooren, W. V., Bock, D. D., & Verschaffel, L. (2010). From addition to multiplication… and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360-381.
- Dougherty, B., Bryant, D.P., Bryant, B.R. & Shin, M. (2016) Helping Students with Mathematics Difficulties Understand Ratio and Proportion. Teaching Exceptional Children, Vol. 49, No. 2, pp. 96–105. Copyright 2017 The Author(s). https://doi.org/10.1177/0040059916674897
- Dündar, S., Temel, H., & Gündüz, N. (2015). Matematik Eğitiminde Görselleştirme ve Somutlaştırma Üzerine Bir Değerlendirme. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi(24), 339-362. https://doi.org/10.14582/DUZG
- Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional Development Focused on Children's Algebraic Reasoning in Elementary School. Journal for Research in Mathematics Education JRME, 38(3), 258-288. https://doi.org/10.2307/30034868
- Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional Noticing of Children's Mathematical Thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
- Johnson, K. (2017, October 5-8). A Study of Pre-Service Teachers Use of Representations in Their Proportional Reasoning [Conference session]. The Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education, Indianapolis, IN, United States of America.
- Kaiser, G., Blömeke, S., König, J., Busse, A., Döhrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—Cognitive versus situated approaches. Educational Studies in Mathematics, 94, 161-182. https://doi.org/10.1007/s10649-016-9713-8
- Kasemsukpipat, W. (2016). An Exploration of Thai Pre-service Mathematics Teachers' Knowledge: Cases of Subject Matter Knowledge, Knowledge of Students' Understanding, and Knowledge of Instructional Strategies in Ratio and Proportion [PhD Thesis, University of Wyoming]. ProQuest.
- Lamon, S. J. (1993). Ratio and proportion: Connecting content and children's thinking. Journal for research in mathematics education, 24(1), 41-61.
- Lamon, S. J. (2006). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.
- Langrall, C. W., & Swafford, J. (2000). Three Balloons for Two Dollars: Developing Proportional Reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261. https://doi.org/10.5951/MTMS.6.4.0254
- LaRochelle, R. M. (2018). Secondary teachers' professional noticing of students' mathematical thinking. [PhD Thesis, University of California]. ProQuest.
- Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. J. Hiebert & M. Behr (Ed.) Number Concepts and Operations in the Middle Grades(pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.
- Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of teacher education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302
- Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 51-65). Routledge.
- Milli Eğitim Bakanlığı (2018). İlkokul ve Ortaokul Matematik Dersi Öğretim Programı, https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335-368. https://doi.org/10.1016/S0732-3123(03)00025-7
- Modestou, M., & Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Thinking and Learning, 12(1), 36-53. https://doi.org/10.1080/10986060903465822
- Noelting, G. (1980). The development of proportional reasoning and the ratio concept part I-differentiation of stages. Educational Studies in Mathematics, 217-253.
- Özel, Z. (2019). Investigation into prospective middle school mathematics teachers' noticing of students' algebraic thinking within the context of pattern generalization [Master’s thesis, Middle East Technical University]. YÖK Tez Merkezi.
- Sherin M. G., Jacobs V. R., & Philipp R. A. (2011). Situating the study of teacher noticing. G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing:Seeing through teachers’ eyes (pp. 3-13). Routledge.
- Sherin, M. G., Russ, R. S., & Colestock, A. A. (2011). Accessing mathematics teachers’ in-the-moment noticing. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79-94). Routledge
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
- Singletary, L. M. (2012). Mathematical connections made in practice: An examination of teachers’ belief and practices [PhD Thesis, University of Georgia]. Google Akademik.
- Steinthorsdottir, O. B. (2006, July 16-21). Proportional reasoning: Variable influencing the problems difficulty level and one’s use of problem solving strategies [Conference session]. 30th Conference of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic.
- Stylianides, A. J., & Stylianides, G. J. (2008). Studying the implementation of tasks in classroom settings: High-level mathematics tasks embedded in “real-life” contexts. Teaching and Teacher Education, 24, 859-875. https://doi.org/10.1016/j.tate.2007.11.015
- Şen, C., & Güler, G. (2017). Effect of strategy teaching for the solution of ratio problems on students' proportional reasoning skills. Malaysian Online Journal of Educational Sciences, 5(2), 1-15.
- Şermetoğlu, H., & Baki, M. (2019). Oran ve Orantı Konusu Öğretim Sürecinin Bir Matematik Öğretmeninin Fark Etme Becerisi Bağlamında İncelenmesi. Turkish Journal of Computer and Mathematics Education, 10(2), 394-425. https://doi.org/10.16949/turkbilmat.461124
- Taylan, R. D. (2018). The relationship between pre-service mathematics teachers’ focus on student thinking in lesson analysis and lesson planning tasks. International Journal of Science and Mathematics Education, 16(2), 337-356. https://doi.org/10.1007/s10763-016-9778-y
- Tunç-Pekkan, Z., & Kılıç, H. (2015, February 4-8). Mathematical opportunities: Noticing and acting [Conference session]. 9th Congress of the European Society for Research in Mathematics Education, Prague, Czech Republic. https://hal.science/CERME9/public/CERME9_Proceedings_2015.pdf
- Ünsal, A. (2009). İlköğretim 7.sınıf öğrencilerinin orantısal akıl yürütme becerilerinin başarı, tutum ve değişkenleri açısından incelenmesi: Bolu ili örneği. [Master’s thesis, Abant İzzet Baysal University]. YÖK Tez Merkezi.
- Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). İlkokul ve Ortaokul Matematiği (S. Durmuş, Tr.), Ankara: Nobel Akademik Yayıncılık
- Van Es, E. A. (2011). A framework for learning to notice student thinking. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134-151). Routledge
- Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of technology and teacher education, 10(4), 571-596.
The Effectiveness of Feedback Provided by Middle School Mathematics Teachers and Preservice teachers on Student Solutions: An Evaluative Study
Yıl 2024,
Cilt: 7 Sayı: 2, 323 - 352, 29.10.2024
Fatmanur Öztürk
,
Zehra Taşpınar Şener
Kaynakça
- Arican, M. (2019). Preservice mathematics teachers’ understanding of and abilities to differentiate proportional relationships from nonproportional relationships. International Journal of Science and Mathematics Education, 17(7), 1423-1443. https://doi.org/10.1007/s10763-018-9931-x
- Artut, P. D., & Pelen, M. S. (2015). 6th grade students’ solution strategies on proportional reasoning problems. Procedia-Social and Behavioral Sciences, 197, 113-119. https://doi.org/10.1016/j.sbspro.2015.07.066
- Bahar, G. (2016). Measurıng pre-service teachers' mathematics content knowledge and mathematics pedagogical content knowledge on ratio and proportion [Master’s thesis, Bosphorus University]. YÖK Tez Merkezi.
- Bart, W., Post, T., Behr, M., Lesh, R. (1994). A diagnostic analysis of a proportional reasoning test item: An introduction to the properties of a semi-dense item. Focus on Learning Problems in Mathematics, 16(3), 1-11.
- Ben-Chaim, D., Fey, J.T., Fitzgerald, W.M., Benedetto, C., Miller, J (1998). Proportional Reasoning among 7th Grade Students with Different Curricular Experiences. Educational Studies in Mathematics 36, 247–273. https://doi.org/10.1023/A:1003235712092
- Benson, S. L. D. (2009). The influence of studying students' proportional reasoning on middle school mathematics teachers' content and pedagogical content knowledge [PhD Thesis, University of Houston]. ProQuest.
- Birinci, M., & Baki, M. (n.d.). Bir Ortaokul Matematik Öğretmeninin Mesleki Gelişiminden Yansımalar: Kesir Öğretiminde Fark Etme Becerisinin İşe Koşulması. İlköğretim Online1141-1156. https://doi.org/10.17051/ilkonline.2019.610853
- Boyacı, H. S. (2019) The proportional reasoning ability of pre-service mathematics teachers: a mixed method study. [Master’s thesis, Bosphorus University]. YÖK Tez Merkezi.
- Brown, R.E., Weiland, T. & Orrill, C.H. (2019). Mathematics Teachers’ Use of Knowledge Resources When Identifying Proportional Reasoning Situations. International Journal of Science and Mathematics Education 18, 1085–1104 https://doi.org/10.1007/s10763-019-10006-3
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., Demirel, F. (2018) Bilimsel Araştırma Yöntemleri. Pegem Akademi.
- Chick, H. (2010). Aspects of Teachers' Knowledge for Helping Students Learn about Ratio. Mathematics Education Research Group of Australasia.
- Choy, B. H. (2014). Noticing Critical Incidents in a Mathematics Classroom. Mathematics Education Research Group of Australasia.
- Cramer, K. & Post, T. (1993, May). Connecting Research To Teaching Proportional Reasoning. Mathematics Teacher, 86(5), 404-407.
- Cramer, K., Behr, M., & Bezuk, N. (1989, October). Proportional Relationships and Unit Rates. Mathematics Teacher, 82 (7), 537-544.
- Cramer, K., Post, T., & Currier, S. (1993). Learning and Teaching Ratio and Proportion: Research Implications. D. Owens (Ed.), Research Ideas For the Classroom (pp. 159-178). NY: Macmillan Publishing Company.
- Çıkla, O. A., & Duatepe, A. (2002). İlköğretim matemetik öğretmen adaylarının orantısal akıl yürütme becerileri üzerine niteliksel bir çalışma. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23(23).
- De la Cruz, J. A. (2008). A look at middle school mathematics teachers' instruction related to proportional reasoning: A cognitively guided perspective [PhD Thesis, University of Virginia]. ProQuest.
- Degrande, T., Verschaffel, L., & Van Dooren, W. (2019). To add or to multiply? An investigation of the role of preference in children's solutions of word problems. Learning and Instruction, 61, 60-71. https://doi.org/10.1016/j.learninstruc.2019.01.002Get rights and content
- Dick, L. K. (2013). Preservice student teacher professional noticing through analysis of their students' work [PhD Thesis, North Carolina State University]. ProQuest.
- Dooren, W. V., Bock, D. D., & Verschaffel, L. (2010). From addition to multiplication… and back: The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), 360-381.
- Dougherty, B., Bryant, D.P., Bryant, B.R. & Shin, M. (2016) Helping Students with Mathematics Difficulties Understand Ratio and Proportion. Teaching Exceptional Children, Vol. 49, No. 2, pp. 96–105. Copyright 2017 The Author(s). https://doi.org/10.1177/0040059916674897
- Dündar, S., Temel, H., & Gündüz, N. (2015). Matematik Eğitiminde Görselleştirme ve Somutlaştırma Üzerine Bir Değerlendirme. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi(24), 339-362. https://doi.org/10.14582/DUZG
- Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional Development Focused on Children's Algebraic Reasoning in Elementary School. Journal for Research in Mathematics Education JRME, 38(3), 258-288. https://doi.org/10.2307/30034868
- Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional Noticing of Children's Mathematical Thinking. Journal for Research in Mathematics Education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
- Johnson, K. (2017, October 5-8). A Study of Pre-Service Teachers Use of Representations in Their Proportional Reasoning [Conference session]. The Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education, Indianapolis, IN, United States of America.
- Kaiser, G., Blömeke, S., König, J., Busse, A., Döhrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—Cognitive versus situated approaches. Educational Studies in Mathematics, 94, 161-182. https://doi.org/10.1007/s10649-016-9713-8
- Kasemsukpipat, W. (2016). An Exploration of Thai Pre-service Mathematics Teachers' Knowledge: Cases of Subject Matter Knowledge, Knowledge of Students' Understanding, and Knowledge of Instructional Strategies in Ratio and Proportion [PhD Thesis, University of Wyoming]. ProQuest.
- Lamon, S. J. (1993). Ratio and proportion: Connecting content and children's thinking. Journal for research in mathematics education, 24(1), 41-61.
- Lamon, S. J. (2006). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers. Routledge.
- Langrall, C. W., & Swafford, J. (2000). Three Balloons for Two Dollars: Developing Proportional Reasoning. Mathematics Teaching in the Middle School, 6(4), 254-261. https://doi.org/10.5951/MTMS.6.4.0254
- LaRochelle, R. M. (2018). Secondary teachers' professional noticing of students' mathematical thinking. [PhD Thesis, University of California]. ProQuest.
- Lesh, R., Post, T., & Behr, M. (1988). Proportional Reasoning. J. Hiebert & M. Behr (Ed.) Number Concepts and Operations in the Middle Grades(pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.
- Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of teacher education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302
- Miller, K. F. (2011). Situation awareness in teaching: What educators can learn from video-based research in other fields. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 51-65). Routledge.
- Milli Eğitim Bakanlığı (2018). İlkokul ve Ortaokul Matematik Dersi Öğretim Programı, https://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMAT%C4%B0K%20%C3%96%C4%9ERET%C4%B0M%20PROGRAMI%202018v.pdf
- Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children’s proportional reasoning. The Journal of Mathematical Behavior, 22(3), 335-368. https://doi.org/10.1016/S0732-3123(03)00025-7
- Modestou, M., & Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Thinking and Learning, 12(1), 36-53. https://doi.org/10.1080/10986060903465822
- Noelting, G. (1980). The development of proportional reasoning and the ratio concept part I-differentiation of stages. Educational Studies in Mathematics, 217-253.
- Özel, Z. (2019). Investigation into prospective middle school mathematics teachers' noticing of students' algebraic thinking within the context of pattern generalization [Master’s thesis, Middle East Technical University]. YÖK Tez Merkezi.
- Sherin M. G., Jacobs V. R., & Philipp R. A. (2011). Situating the study of teacher noticing. G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing:Seeing through teachers’ eyes (pp. 3-13). Routledge.
- Sherin, M. G., Russ, R. S., & Colestock, A. A. (2011). Accessing mathematics teachers’ in-the-moment noticing. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 79-94). Routledge
- Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
- Singletary, L. M. (2012). Mathematical connections made in practice: An examination of teachers’ belief and practices [PhD Thesis, University of Georgia]. Google Akademik.
- Steinthorsdottir, O. B. (2006, July 16-21). Proportional reasoning: Variable influencing the problems difficulty level and one’s use of problem solving strategies [Conference session]. 30th Conference of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic.
- Stylianides, A. J., & Stylianides, G. J. (2008). Studying the implementation of tasks in classroom settings: High-level mathematics tasks embedded in “real-life” contexts. Teaching and Teacher Education, 24, 859-875. https://doi.org/10.1016/j.tate.2007.11.015
- Şen, C., & Güler, G. (2017). Effect of strategy teaching for the solution of ratio problems on students' proportional reasoning skills. Malaysian Online Journal of Educational Sciences, 5(2), 1-15.
- Şermetoğlu, H., & Baki, M. (2019). Oran ve Orantı Konusu Öğretim Sürecinin Bir Matematik Öğretmeninin Fark Etme Becerisi Bağlamında İncelenmesi. Turkish Journal of Computer and Mathematics Education, 10(2), 394-425. https://doi.org/10.16949/turkbilmat.461124
- Taylan, R. D. (2018). The relationship between pre-service mathematics teachers’ focus on student thinking in lesson analysis and lesson planning tasks. International Journal of Science and Mathematics Education, 16(2), 337-356. https://doi.org/10.1007/s10763-016-9778-y
- Tunç-Pekkan, Z., & Kılıç, H. (2015, February 4-8). Mathematical opportunities: Noticing and acting [Conference session]. 9th Congress of the European Society for Research in Mathematics Education, Prague, Czech Republic. https://hal.science/CERME9/public/CERME9_Proceedings_2015.pdf
- Ünsal, A. (2009). İlköğretim 7.sınıf öğrencilerinin orantısal akıl yürütme becerilerinin başarı, tutum ve değişkenleri açısından incelenmesi: Bolu ili örneği. [Master’s thesis, Abant İzzet Baysal University]. YÖK Tez Merkezi.
- Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). İlkokul ve Ortaokul Matematiği (S. Durmuş, Tr.), Ankara: Nobel Akademik Yayıncılık
- Van Es, E. A. (2011). A framework for learning to notice student thinking. M.G. Sherin, V. R. Jacobs ve R. A. Randolph (Ed.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134-151). Routledge
- Van Es, E. A., & Sherin, M. G. (2002). Learning to notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of technology and teacher education, 10(4), 571-596.