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Middle School Mathematics Teachers' Professional Noticing Skills: The Case of Rectangular Prism Volume Problem

Yıl 2022, Cilt 18, Sayı 2, 154 - 174, 22.08.2022
https://doi.org/10.17860/mersinefd.1093364

Öz

This study aimed to identify the professional noticing skills of middle school mathematics teachers on student thinking about a problem related to the volume of the rectangular prism. The participants were 35 middle school mathematics teachers working in public schools in six different provinces of Turkey and having less than 15 years of professional experience. As a data collection tool, alternative student’s approach to a given problem about the volume of rectangular prism (Tekin-Sitrava, 2014) was taken as basis within the scope of the components of the “Professional Noticing of the Children’s Mathematical Thinking” (Jacobs, Lamb, and Philipp, 2010). Written data from teachers were analyzed through the coding table adapted in the light of current studies based on the theoretical framework of Jacobs et al. (2010). The findings indicated that middle school mathematics teachers generally attended to the student's mathematical strategy regarding the volume of rectangular prism with limited and robust levels. In addition, most of the teachers were at lack and limited levels of interpretation skills. Then, they usually responded to given student’s thinking at ignoring and questioning levels. The findings indicated that teachers need to develop their professional noticing skills, especially interpreting and deciding skills.

Kaynakça

  • Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270-296. doi: 10.2307/30034851
  • Alstad, E., Berre, M., & Nilsson, P. (2021). Exploring units-locating in enumerating units of 3d arrays: linking units-locating to units-representation. Mathematics Education Research Journal, 1-23. doi:10.1007/s13394-021-00405-7
  • Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371- 383. doi: 10.1080/01626620.2015.1119764
  • Baki, M. (2013). Pre-service classroom teachers' mathematical knowledge and instructional explanations associated with division. Egitim ve Bilim-Education and Science, 38(167).
  • Baki, G. Ö., & Işık, A. (2018). Investigation of the noticing levels of teachers about students’ mathematical thinking: A lesson study model. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(1), 122-146.
  • Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers’ ability to attend, analyze, and respond to student thinking. Teaching and Teacher Education, 15, 83–93.
  • Baştürk, S., & Dönmez, G. (2011). Mathematics student teachers’ misconceptions on the limit and continuity concepts. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 225-249.
  • Battista, M. T., & Clements, D. H. (1996). Students' understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258-292. doi:10.5951/jresematheduc.27.3.0258
  • Battista, M., & Clements, D. H. (1998). Research into practice: Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4(5), 258-264. doi: 10.5951/TCM.4.5.0258
  • Ben-Haim, D., Lappan, G., & Houang, R. T. (1985). Visualizing rectangular solids made of small cubes: analyzing and effecting students' performance. Educational Studies in Mathematics, 16(4), 389-409.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309-333. doi:10.1007/s10857-016-9343-1
  • Contreras, J. M., Batanero, C., Díaz, C., & Fernandes, J. A. (2011, February). Prospective teachers’ common and specialized knowledge in a probability task. Paper presented at Seventh Congress of the European Society Research in Mathematics Education: Rzeszów, Polen.
  • Esen, Y. ve Çakıroğlu, E. (2012). İlköğretim matematik öğretmen adaylarının hacim ölçmede birim kullanmaya yönelik kavrayışları. MATDER Matematik Eğitimi Dergisi, 1(1), 21-30.
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM, 44(6), 747-759. doi: 10.1007/s11858-012-0425-y
  • Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653-689.
  • Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392. doi: 10.1177/0022487109339906
  • Gökkurt, B. ve Soylu, Y. (2016). Ortaokul matematik öğretmenlerinin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi: koni örneği. İlköğretim Online, 15(3).
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.doi: 10.5951/jresematheduc.39.4.0372
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. Doi: 10.3102/00028312042002371
  • Işıksal-Bostan, M., & Yemen-Karpuzcu, S. (2017, February). The role of definitions on classification of solids including (non) prototype examples: The case of cylinder and prism. Paper presented at Tenth Congress of the European Society Research in Mathematics Education: Dublin, Ireland.
  • Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1), 185-197. doi: 10.1007/s11858-015-0717-0
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.doi: 10.5951/jresematheduc.41.2.0169
  • Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In Mathematics teacher noticing: seeing through teachers’ eyes, 97-116. Routledge.
  • Kilic, H., & Dogan, O. (2021). Preservice mathematics teachers’ noticing in action and in reflection. International Journal of Science and Mathematics Education, 20(2), 345-366. doi:10.1007/s10763-020-10141-2
  • Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.
  • Livy, S., & Vale, C. (2011). First year pre-service teachers' mathematical content knowledge: Methods of solution to a ratio question. Mathematics Teacher Education and Development, 13(2), 22-43.
  • Melhuish, K., Thanheiser, E., & Guyot, L. (2020). Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization. Journal of Mathematics Teacher Education, 23(1), 35-67. doi: 10.1007/s10857-018-9408-4
  • Nickerson, S. D., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381-398). Springer, Cham.
  • Plomp, T. (2013). Educational design research: An introduction In T. Plomp, & N. Nieveen (Eds.), Educational design research (pp. 11-50). Enschede, the Netherlands: SLO.
  • Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379-397.
  • Seidel, T., Stürmer, K., Blomberg, G., Kobarg, M., & Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27(2), 259-267.
  • Sherin, B., & Star, J. R. (2011). Reflections on the study of teacher noticing. Mathematics teacher noticing (pp. 96-108). Routledge.
  • Sherin, M., & van Es, E. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. doi:10.3102/0013189X015002004
  • Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125.
  • Taylan, R. D. (2017). Characterizing a highly accomplished teacher’s noticing of third-grade students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(3), 259-280. doi: 10.1007/s10857-015-9326-7
  • Tekin-Sitrava, R. (2014). The nature of middle school mathematics teachers’ subject matter knowledge: The case of volume of prisms. (Yayınlanmamış doktora tezi). Orta Doğu Teknik Üniversitesi Sosyal Bilimler Enstitüsü, Ankara.
  • Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3-25.
  • Ulusoy, F., & Çakıroğlu, E. (2018). Using video cases and small-scale research projects to explore prospective mathematics teachers’ noticing of student thinking. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1571. doi:10.29333
  • Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244-276.
  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523-550. doi:10.1007/s10857-014-9289-0
  • Yıldırım, A. ve Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin.
  • Yin, R.K. (2003). Case study research design and methods (3rd ed.). Thousand Oaks, CA: Sage.
  • Zawojewski, J. S., Chamberlin, M., Hjalmarson, M. A., & Lewis, C. (2008). Designing design studies for professional development in mathematics education. Handbook of design research methods in education, 219-245.

Ortaokul Matematik Öğretmenlerinin Mesleki Fark Etme Becerileri: Dikdörtgenler Prizmasının Hacmine İlişkin Problem Durumu

Yıl 2022, Cilt 18, Sayı 2, 154 - 174, 22.08.2022
https://doi.org/10.17860/mersinefd.1093364

Öz

Bu çalışmanın amacı, ortaokul matematik öğretmenlerinin dikdörtgenler prizmasının hacmine ilişkin bir probleme dair öğrenci düşünüşüne yönelik mesleki fark etme becerilerini belirlemektir. Bu amaca bağlı olarak çalışmada, Türkiye’nin altı farklı ilinde Milli Eğitim Bakanlığı’na bağlı devlet okullarında görev yapan ve öğretmenlik deneyimi 15 yılı aşmamış 35 öğretmen ile çalışılmıştır. Jacobs, Lamb ve Philipp’in (2010) ortaya koyduğu “Öğrencilerin Matematiksel Düşünmelerine Yönelik Mesleki Fark Etme” kuramsal çerçevesinin bileşenleri kapsamında hazırlanan veri toplama aracında, Tekin-Sitrava’nın (2014) geliştirmiş olduğu dikdörtgenler prizmasının hacminin bulunmasına ilişkin bir probleme verilen farklı öğrenci yanıtları kullanılmıştır. Öğretmenlerden gelen yazılı veriler, Jacobs ve diğerlerinin (2010) kuramsal çerçevesi temel alınarak güncel çalışmalar ışığında uyarlanan kodlama tablosu aracılığı ile analiz edilmiştir. Çalışmanın bulguları, ortaokul matematik öğretmenlerinin dikdörtgenler prizmasının hacmine yönelik öğrencinin matematiksel stratejisini dikkate alma becerilerinin genellikle sınırlı ve tam düzeyde olduğunu göstermektedir. Ayrıca, öğretmenlerin büyük çoğunluğunun yetersiz ve sınırlı düzeyde yorumlama becerisine sahip olduğu gözlenirken, verilen öğrenci düşünüşüne genellikle ilgisiz ve yineleme düzeyinde karşılık verdikleri görülmektedir. Çalışmanın bulguları öğretmenlerin mesleki fark etme becerilerinin özellikle yorumlama ve karşılık verme boyutlarının geliştirilmesi gerektiğine işaret etmektedir.

Kaynakça

  • Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270-296. doi: 10.2307/30034851
  • Alstad, E., Berre, M., & Nilsson, P. (2021). Exploring units-locating in enumerating units of 3d arrays: linking units-locating to units-representation. Mathematics Education Research Journal, 1-23. doi:10.1007/s13394-021-00405-7
  • Amador, J. M., Carter, I., & Hudson, R. A. (2016). Analyzing preservice mathematics teachers’ professional noticing. Action in Teacher Education, 38(4), 371- 383. doi: 10.1080/01626620.2015.1119764
  • Baki, M. (2013). Pre-service classroom teachers' mathematical knowledge and instructional explanations associated with division. Egitim ve Bilim-Education and Science, 38(167).
  • Baki, G. Ö., & Işık, A. (2018). Investigation of the noticing levels of teachers about students’ mathematical thinking: A lesson study model. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(1), 122-146.
  • Barnhart, T., & van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers’ ability to attend, analyze, and respond to student thinking. Teaching and Teacher Education, 15, 83–93.
  • Baştürk, S., & Dönmez, G. (2011). Mathematics student teachers’ misconceptions on the limit and continuity concepts. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 225-249.
  • Battista, M. T., & Clements, D. H. (1996). Students' understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258-292. doi:10.5951/jresematheduc.27.3.0258
  • Battista, M., & Clements, D. H. (1998). Research into practice: Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4(5), 258-264. doi: 10.5951/TCM.4.5.0258
  • Ben-Haim, D., Lappan, G., & Houang, R. T. (1985). Visualizing rectangular solids made of small cubes: analyzing and effecting students' performance. Educational Studies in Mathematics, 16(4), 389-409.
  • Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309-333. doi:10.1007/s10857-016-9343-1
  • Contreras, J. M., Batanero, C., Díaz, C., & Fernandes, J. A. (2011, February). Prospective teachers’ common and specialized knowledge in a probability task. Paper presented at Seventh Congress of the European Society Research in Mathematics Education: Rzeszów, Polen.
  • Esen, Y. ve Çakıroğlu, E. (2012). İlköğretim matematik öğretmen adaylarının hacim ölçmede birim kullanmaya yönelik kavrayışları. MATDER Matematik Eğitimi Dergisi, 1(1), 21-30.
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM, 44(6), 747-759. doi: 10.1007/s11858-012-0425-y
  • Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38(3), 653-689.
  • Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392. doi: 10.1177/0022487109339906
  • Gökkurt, B. ve Soylu, Y. (2016). Ortaokul matematik öğretmenlerinin pedagojik alan bilgilerinin bazı bileşenler açısından incelenmesi: koni örneği. İlköğretim Online, 15(3).
  • Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.doi: 10.5951/jresematheduc.39.4.0372
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. Doi: 10.3102/00028312042002371
  • Işıksal-Bostan, M., & Yemen-Karpuzcu, S. (2017, February). The role of definitions on classification of solids including (non) prototype examples: The case of cylinder and prism. Paper presented at Tenth Congress of the European Society Research in Mathematics Education: Dublin, Ireland.
  • Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: An emerging framework of teaching moves. ZDM, 48(1), 185-197. doi: 10.1007/s11858-015-0717-0
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.doi: 10.5951/jresematheduc.41.2.0169
  • Jacobs, V. R., Lamb, L. L., Philipp, R. A., & Schappelle, B. P. (2011). Deciding how to respond on the basis of children’s understandings. In Mathematics teacher noticing: seeing through teachers’ eyes, 97-116. Routledge.
  • Kilic, H., & Dogan, O. (2021). Preservice mathematics teachers’ noticing in action and in reflection. International Journal of Science and Mathematics Education, 20(2), 345-366. doi:10.1007/s10763-020-10141-2
  • Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University Press.
  • Livy, S., & Vale, C. (2011). First year pre-service teachers' mathematical content knowledge: Methods of solution to a ratio question. Mathematics Teacher Education and Development, 13(2), 22-43.
  • Melhuish, K., Thanheiser, E., & Guyot, L. (2020). Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization. Journal of Mathematics Teacher Education, 23(1), 35-67. doi: 10.1007/s10857-018-9408-4
  • Nickerson, S. D., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381-398). Springer, Cham.
  • Plomp, T. (2013). Educational design research: An introduction In T. Plomp, & N. Nieveen (Eds.), Educational design research (pp. 11-50). Enschede, the Netherlands: SLO.
  • Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379-397.
  • Seidel, T., Stürmer, K., Blomberg, G., Kobarg, M., & Schwindt, K. (2011). Teacher learning from analysis of videotaped classroom situations: Does it make a difference whether teachers observe their own teaching or that of others? Teaching and Teacher Education, 27(2), 259-267.
  • Sherin, B., & Star, J. R. (2011). Reflections on the study of teacher noticing. Mathematics teacher noticing (pp. 96-108). Routledge.
  • Sherin, M., & van Es, E. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475-491.
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. doi:10.3102/0013189X015002004
  • Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125.
  • Taylan, R. D. (2017). Characterizing a highly accomplished teacher’s noticing of third-grade students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(3), 259-280. doi: 10.1007/s10857-015-9326-7
  • Tekin-Sitrava, R. (2014). The nature of middle school mathematics teachers’ subject matter knowledge: The case of volume of prisms. (Yayınlanmamış doktora tezi). Orta Doğu Teknik Üniversitesi Sosyal Bilimler Enstitüsü, Ankara.
  • Thomas, J., Jong, C., Fisher, M. H., & Schack, E. O. (2017). Noticing and knowledge: Exploring theoretical connections between professional noticing and mathematical knowledge for teaching. The Mathematics Educator, 26(2), 3-25.
  • Ulusoy, F., & Çakıroğlu, E. (2018). Using video cases and small-scale research projects to explore prospective mathematics teachers’ noticing of student thinking. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1571. doi:10.29333
  • Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244-276.
  • Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523-550. doi:10.1007/s10857-014-9289-0
  • Yıldırım, A. ve Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin.
  • Yin, R.K. (2003). Case study research design and methods (3rd ed.). Thousand Oaks, CA: Sage.
  • Zawojewski, J. S., Chamberlin, M., Hjalmarson, M. A., & Lewis, C. (2008). Designing design studies for professional development in mathematics education. Handbook of design research methods in education, 219-245.

Ayrıntılar

Birincil Dil Türkçe
Konular Eğitim, Eğitim Araştırmaları
Bölüm Makaleler
Yazarlar

Özge DIŞBUDAK KURU> (Sorumlu Yazar)
İSTANBUL MEDENİYET ÜNİVERSİTESİ
0000-0003-2565-4812
Türkiye


Ayşe Nur UCUZOĞLU>
PAMUKKALE ÜNİVERSİTESİ
0000-0001-7364-2571
Türkiye


Mine IŞIKSAL>
ORTA DOĞU TEKNİK ÜNİVERSİTESİ
0000-0001-7619-1390
Türkiye


Seçil YEMEN KARPUZCU>
KÜTAHYA DUMLUPINAR ÜNİVERSİTESİ
0000-0002-2150-000X
Türkiye


Reyhan TEKİN SİTRAVA>
KIRIKKALE ÜNİVERSİTESİ
0000-0002-1285-2791
Türkiye

Destekleyen Kurum Tübitak
Proje Numarası 218K508
Teşekkür Bu çalışma 218K508 numaralı Türkiye Bilimsel ve Teknolojik Araştırma Kurumu (TÜBİTAK) projesinden üretilmiştir.
Yayımlanma Tarihi 22 Ağustos 2022
Yayınlandığı Sayı Yıl 2022, Cilt 18, Sayı 2

Kaynak Göster

APA Dışbudak Kuru, Ö. , Ucuzoğlu, A. N. , Işıksal, M. , Yemen Karpuzcu, S. & Tekin Sitrava, R. (2022). Ortaokul Matematik Öğretmenlerinin Mesleki Fark Etme Becerileri: Dikdörtgenler Prizmasının Hacmine İlişkin Problem Durumu . Mersin Üniversitesi Eğitim Fakültesi Dergisi , 18 (2) , 154-174 . DOI: 10.17860/mersinefd.1093364

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