Pre-Service Elementary Teachers’ Problem Posing Skills

Abstract

It was aimed in this study, to determine the problem posing skills of pre-service elementary teachers’ over semi-structured situations. Study included 114 senior class teacher candidates from Elementary Teacher Program of a university. Problem Posing Test (PPT) consists of 2 items towards open-ended situations within semi-structured problem posing situations and it consists of 1 problem posing item towards symbolic representations. Analyzes of pre-service elementary teachers’ posed problems indicate that numbers of various problems posed towards semi-structured situations were low. The candidates had relatively higher difficulties in posing problems towards dividing with remainder, in particular. In addition to this, upon examining the interrogative roots of the posed problems, it was revealed that problem types which associated expressions provided with different mathematical concepts were limited and the problems which could be solved with rather simple calculations were by far preferred.

Keywords

• pre-service elementary teachers
• problem posing
• numbers

Sınıf Öğretmeni Adaylarının Problem Kurma Becerileri

Abstract

Çalışmada sınıf öğretmeni adaylarının yarı yapılandırılmış durumlar üzerinden problem kurma becerilerinin belirlenmesi amaçlanmıştır. Çalışma, doğudaki bir üniversitenin Sınıf Öğretmenliği Programı son sınıfında öğrenim gören 114 öğretmen adayı ile yapılmıştır. Problem Kurma Testi(PKT) yarı-yapılandırılmış problem kurma etkinlikleri içerisinde yer alan açık-uçlu durumlara yönelik iki, sembolik temsillere yönelik bir problem kurma maddesinden oluşmaktadır. Çalışma bulguları adayların, yarı-yapılandırılmış durumlara yönelik farklı problemler kurabilme sayılarının düşük olduğuna işaret etmektedir. Adaylar özellikle kalanlı bölme işlemine yönelik farklı problemler kurmada daha fazla zorlanmışlardır. Bunun yanı sıra kurulan problemlerin soru kökleri dikkate alındığında, farklı matematiksel kavramlar ile verilen ifadeleri ilişkilendiren problem çeşitlerinin sınırlı olduğu ve basit hesaplamalar ile çözülebilecek problemlerin daha fazla tercih edildiği tespit edilmiştir.

Keywords

• sınıf öğretmeni adayları
• problem kurma
• sayılar

References

1. sürecinde karşılaşılabilecek olası güçlükler belirlenerek, bu güçlüklerin giderilmesine yönelik
2. deneysel çalışmalar yapılabilir.
3. Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.) Proceedings of theInternational conference on Mathematical Education into the 21st Century: Social Challenges, Issues and Approaches, (Vol. II, pp. 1-8), Cairo Egypt.
4. Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in S.E. Asia, 25(1), 56-69.
5. Akay, H. (2006). Problem kurma yaklaşımı ile yapılan matematik öğretiminin öğrencilerin akademik başarısı, problem çözme becerisi ve yaratıcılığı üzerindeki etkisinin incelenmesi (Yayınlanmamış doktora tezi). Gazi Üniversitesi, Ankara.
6. Akay, H. ve Boz, N. (2010). The effect of problem posing oriented analyses-II course on the attitudes toward mathematics and mathematics self-efficacy of elementary prospective mathematics teachers. Australian Journal of Teacher Education, 35(1), 59-75.
7. Akkan Y., Çakıroğlu, Ü. ve Güven, B. (2009). Equation forming and problem posing abilities
8. of 6th and 7th grade primary school students. Mehmet Akif Ersoy Üniversitesi Eğitim

9. Fakültesi Dergisi, 9(17), 41-55.
10. Albayrak, M., İpek, A.S. ve Işık, C. (2006). Temel işlem becerilerinin öğretiminde problem kurma-çözme çalışmaları. Erzincan Eğitim Fakültesi Dergisi, 8(2), 1-11.
11. Altun, M. (2005). İlköğretim İkinci Kademe (6-7 ve 8.sınıflarda) Matematik Öğretimi. Bursa: Aktüel Yayınları.
12. Bonotto, C. (2006). Extending students’ understanding of decimal numbers via realistic mathematical modeling and problem posing. In J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics (vol. 2, pp. 193–200). Prague: Charles University.
13. Cai, J. & Cifarelli, V. (2004). Thinking mathematically by Chinese learners: A cross-national comparative perspective. In L. Fan, N.-Y. Wong, J. Cai & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders. Singapore: World Scientific.
14. Cai, J. & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. Journal of Mathematical Behavior, 21, 401–421.
15. Cankoy, O. ve Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal of Education, 38, 11-24.
16. Capraro, M. M. ve Joffrion, H. (2006). Algebraic equations: Can middle-school students meaningfully translate from words to mathematical symbols? Reading Psychology, 27, 147–164.
17. Chang, N. (2007). Responsibilities of a teacher in a harmonic cycle of problem solving and problem posing. Early Child hood Education Journal, 34(4), 265-271.
18. Chen, L., Van Dooren, W., Chen, Q. & Verschaffel, L. (2005). The relationship between posing and solving division with remainder problems among Chinese elementary school children. Mediterranean Journal for Research in Mathematics Education, 4(2), 85–109.
19. Chen, L., Van Dooren, W., Chen, Q. & Verschaffel, L. (2007). The relationship between posing and solving arithmetic word problems among Chinese elementary school children. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 11(1), 1–31.
20. Chen, L., Van Dooren, W., Chen, Q. & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919-948.
21. Christou, C., Mousoulides, N., Pittalis, M., Pitta – Pantazi, D. & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149 – 158.
22. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52, 243–270.
23. Crespo, S. & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal Mathematics Teacher Education, 11, 395–415.
24. Cunningham, R. (2004). Problem posing: an opportunity for increasing student responsibility. Mathematics and Computer Education, 38(1), 83-89.
25. Dickerson, V. M. (1999). The impact of problem-posing instruction on the mathematical problem-solving achievement of seventh graders (Unpublished doctoral dissertation). University of Emory, Atlanta.
26. English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183-217.
27. English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
28. English, L. D. (2003). Problem posing in elementary curriculum. In F. Lester, & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.
29. Fetterly, J. M. (2010). An exploratory study of the use of a problem posing approach on pre- service elementary educatıon teachers’ mathematıcal creativity, beliefs, and anxiety (Unpublished doctoral dissertation). University of Florida, USA.
30. Gonzales, N. A. (1998). A blueprint for problem posing. School Science and Mathematics, 94(2), 78- 85.
31. Greer, B. & Verschaffel, L. (2007). Modeling competencies-overview. In W. Blum, P. L. Galbraith, H. W. Henne & M. Niss (Eds.), Modelling and applications in mathematics education (ICMI Study 14) (pp. 219–224). New York: Springer.
32. Grundmeier, A. T. (2003). The effects of providing mathematical problem posing experiences for K-8 Pre-service Teachers: Investigating teacher’s beliefs and Characteristic of posed problems (Unpublished doctoral dissertation). University of News Hampshire, USA.
33. Işık, C. (2011). İlköğretim matematik öğretmeni adaylarının kesirlerde çarpma ve bölmeye yönelik kurdukları problemlerin kavramsal analizi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 41, 231-243.
34. Işık, C. ve Kar, T. (2011). İlköğretim 6, 7 ve 8. sınıf öğrencilerinin sayı algılama ve rutin olmayan problem çözme becerilerinin incelenmesi. Ahi Evran Üniversitesi Eğitim Fakültesi Dergisi, 12(1), 57-72.
35. Işık, C. ve Kar, T. (2012). Matematik dersinde problem kurmaya yönelik öğretmen görüşleri üzerine nitel bir çalışma. Milli Eğitim Dergisi, 194, 199-215.
36. Işık, C., Işık, A. ve Kar, T. (2011). Öğretmen adaylarının sözel ve görsel temsillere yönelik kurdukları problemlerin analizi. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 39- 49.
37. Işık, C., Kar, T., Yalçın, T. ve Zehir, K. (2011). Prospective teachers’ skills in problem posing with regard to different problem posing models. Procedia Social and Behavioral Sciences, 15, 485–489.
38. Jitendra, A. K., Griffin, C. C., Deatline-Buchman, A. ve Sczesniak, E. (2007). Mathematical word problem solving in third-grade classrooms. The Journal of Educational Research, 100(5), 283-302.
39. Kar, T., Özdemir, E., İpek, A. S. ve Albayrak, M. (2010). The relation between the problem posing and problem solving skills of prospective elementary mathematics teachers. Social and Behavioral Sciences, 2, 1577–1583.
40. Keesy, M. A. (2011). Word Problems: The effects of learner generated drawıngs on problem solving (Unpublished doctoral dissertation). Capella University.
41. Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 64-74.
42. Lavy, I. & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Paper presented at the meeting of 31st Conference of the International Group for the Psychology of Mathematics Education, Seoul.
43. Leung, S. S. (1993). The relation of mathematical knowledge and creative thinking to the mathematical problem posing of prospective elementary school teachers on tasks differing in numerical information content (Unpublished doctoral dissertation). Pittsburg.
44. Leung, S. S. & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1),5-24.
45. Lin, K. M. & Leng, L. W. (2008). Using problem-posing as an assessment tool. Paper presented at the 10th Asia-Pacific Conference on Giftedness, Singapore.
46. Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Norway: Bergen University.
47. Lowrie, T. (2002). Young children posing problems: the influence of teacher intervention on the type of problems children pose. Mathematics Education Research Journal,14(2), 87-98.
48. Mcmillan, H. J. & Schumacher, S. (2010). Research in education. Boston, USA: Pearson Education.
49. MEB (2009). İlköğretim Matematik Dersi 1-5. Sınıflar Öğretim Programı. Ankara: MEB Basımevi.
50. Nakano, A., Murakami, N., Hirashima, T. & Takeuchi, A. (2000). A learning environment for problem posing in simple arithmetical word problem. International Conference on Computers in Education: ICCE, 14, 91-98.
51. National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
52. Nicolaou, A.A. & Philippou, N. G. (2007). Efficacy beliefs, problem posing, and mathematics achievements. In D. Pitta-Pantazi, & G. Phillippou (Eds.), Proceedings of the V Congress of the European Society for Research in Mathematics Education (pp. 308-317). Larnaca, Cyprus: Department of Education, University of Cyprus.
53. Rizvi, N. F. (2004). Prospective teachers’ ability to pose word problems. http://www.cimt.plymouth.ac.uk/Journal/rizvi.pdf adresinden 17.10.2011 tarihinde alınmıştır.
54. Rudnitsky, A., Etheredge, S., Freeman, S. J. M. & Gilbert, T. (1995). Learning to solve addition and substraction word problems through a structure-plus-writing approach. Journal for Research in Mathematics Education, 26(5), 467-486.
55. Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23, 139–159.
56. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
57. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 3, 75-80.
58. Silver, E. A. & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
59. Silver, E. A. & Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135.
60. Silver, E. A., Mamona-Downs, J. & Leung, S. S. (1996). Posing mathematical problems: An exploratory study. Journal for Research in Mathematics Education, 27, 293–309.
61. Smith, M. (2000). Redefining success in mathematics teaching and learning. Mathematics Teaching in the Middle School, 5(6), 378-386.
62. Soylu, Y. ve Soylu, C. (2006). Matematik derslerinde başarıya giden yolda problem çözmenin rolü. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 7(11), 97-111.
63. Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing (Unpublished doctoral dissertation). University of Indiana, Bloomington.
64. Stoyanova, E. (1998). Problem posing in mathematics classrooms. In A. McIntosh, & N. Ellerton (Eds.), Research in mathematics education: A contemporary perspective (pp.164-185). Perth: MASTEC Publication.
65. Stoyanova, E. (2003). Extending students’ understanding of mathematics via problem- posing. Australian Mathematics Teacher, 59(2), 32-40.
66. Stoyanova, E. & Ellerton, N. F. (1996). A framework for research into students’ problem posing. In P. Clarkson (Ed.), Technology in Mathematics Education (pp.518–525). Melbourne: Mathematics Education Research Group of Australasia.
67. Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25, 166–175.
68. Usiskin, Z. (2007 ) . The arithmetic operations as mathematical models. In W. Blum, P. L. Galbraith, H.W. Henne & M. Niss (Eds.), applications and modelling in mathematics education. The 14th ICMI Study 14 (pp . 257 – 264). New York: Springer.
69. Xin, P. Y. (2007). Word problem solving tasks in textbooks and their relation to student performance. The Journal of Educational Research, 100(6), 347-359.
70. Xin, Z. (2009). Realistic problem solving in China. In L. Verschaffel, B. Greer, W. Van Dooren & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 161–176). Rotterdam, The Netherlands: Sense.
71. Yuan, X. & Sriraman, B. (2010). An exploratory study of relationshıps between students’ creativity and mathematical problem-posing abilities. In B.Sriraman, K. Lee (eds.), The Elements of Creativity and Giftedness in Mathematics, xx–xy.