MATHEMATICAL CONNECTION SKILL IN THE CONTEXT OF PROBLEM SOLVING: THE CASE OF PRE-SERVICE TEACHERS

Abstract

The purpose of this study is to identify pre-service mathematics teachers` mathematical connection skills and examine its relation with problem solving skill. In order to determine 28 pre-service mathematics teachers` mathematical connection skills, case study method was used. For determining connection skills, problem solving process were examined by written documents. Pre-service teachers are asked to three non routine mathematical problems. Rubric was used to examine the connection and problem solving skills. Descriptive statistical analysis, correlation and regression analyzes were used in obtained data. It is determinded that the pre-service teachers` connection level is low. In terms of connections type the skills of connections among mathematics is not desired level. Furthermore, pre-service connection skills between other disciplines and in real world is found at very low level. It is found that pre-service teachers connections skills are not adequate level and were limitations in many ways in the context of problem solving.

Keywords

• Connection, Problem Solving, Pre-service teachers, Non-Routine Problem, Real World,

PROBLEM ÇÖZME BAĞLAMINDA MATEMATİKSEL İLİŞKİLENDİRME BECERİSİ: ÖĞRETMEN ADAYLARI ÖRNEĞİ

Abstract

Bu araştırmanın amacı, matematik öğretmen adaylarının matematiksel ilişkilendirme becerilerini belirlemek ve problem çözme becerisi ile olan ilişkilerini incelemektir. 28 matematik öğretmen adayının ilişkilendirme becerilerini belirlemek amacıyla özel durum çalışması yöntemi kullanılmıştır. İlişkilendirme becerisinin belirlenmesinde, problem çözme süreci yazılı dokümanlarla incelenmiştir. Öğretmen adaylarına üç rutin olmayan matematiksel problem yöneltilmiştir. İlişkilendirme ve problem çözme becerilerini incelemek amacıyla rubrik kullanılmıştır. Elde edilen verilerin analizinde, betimsel istatistiksel analizler, korelasyon ve regresyon analizinden yararlanılmıştır. Öğretmen adaylarının ilişkilendirme becerilerinin düşük düzeyde olduğu belirlenmiştir. Kullanılan ilişkilendirme türü açısından ise matematiği kendi içinde ilişkilendirmenin istenen düzeyde olmadığı, farklı disiplinler ve günlük yaşamla ilişkilendirmenin ise çok düşük düzeylerde kaldığı görülmüştür. Öğretmen adaylarının ilişkilendirme becerilerini yeterli düzeyde olmadığı ve problem çözme becerileri kapsamında birçok yönden sınırlılıklarının olduğu belirlenmiştir.

Keywords

• İlişkilendirme, Problem Çözme, Öğretmen Adayları, Rutin Olmayan Problem, Günlük Yaşam,

References

1. Ball, D.L., Hill, H., and Bass, H., (2005). Knowing Mathematics for Teaching: Who Knows Mathematics well Enough to Teach Third (Grade, and How Can We Decide? American Educator, 29(3), 14-46. Bell, E.S., and Bell, R.N., (1985). Writing and Problem Solving: Arguments in Favour of Synthesis. School Science andMathematics, 85(3), 210-221. DOI: 10.1111/j.19498594.1985.tb09614.x
2. Bodner, B.L., (2006). Bridges 2006: Mathematical Connectins in Art, Music, and Science. Conference Report. 4-9 August 2006, London. Nexus Network Journal, 9(1), 145-149.
3. Bosse, M.J., (2003). The Beauty of “And” And “Or”: Connections within Mathematics for Students with Learning Differences. Mathematics and Computer Education, 37(1), 105-114.
4. Brutlag, D. and Maples, C., (1992). Making Connections: Beyond The Surface. The Mathematics Teacher, 85(3), 230-235.
5. Businskas, A.M., (2008). Conversations About Connections: How Secondary Mathematics Teachers Conceptualize and Contend with Mathematical Connections. Yayinlanmamiş Doktora Tezi, Simon Fraser University.
6. Chapman, O., (2012). Challenges in Mathematics Teacher Education. Journal of Mathematics Teacher Education, 15(4), 2632 DOI: 1007/s10857-012-9223-2
7. Chapman, O., (2006). Preservice Elementary Teachers’ Conceptual Understanding of Word Problems. In J. Novotna´, H. Moraova´, M. Kra´tka´, and N. Stehlı´kova´ (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 1, p. 372, Prague, Czech Republic: PME.
8. Cotti, R. and Schiro, M., (2004). Connecting Teacher Belief to the Use of Children’s Literature in the Teaching of Mathematics. Journal of Mathematics Teacher Education,7(4), 329-356. DOI: 1007/s10857-004-1787-z

9. Coxford, A.F., (1995). The Case for Connections. In P. A. House and A.F. Coxford (Eds.), Connecting Mathematics across the Curriculum, pp. 3-12. Reston, VI: National Council of Teachers of Mathematics.
10. Çepni, S., (2007). Araştırma ve Proje Çalışmalarına Giriş (3. Baskı). Trabzon: Celepler Matbaacılık.
11. Delice, A. ve Sevimli, E., (2010). Matematik Öğretmeni Adaylarının Belirli İntegral Konusunda Kullanılan Temsiller İle İşlemsel ve Kavramsal Bilgi Düzeyleri. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 9(3), 581-605.
12. Eli, J.A., (2009). An Exploratory Mixed Methods Study of Prospective Middle Grades Teachers’ Mathematical Connections while Completing Investiagtive Tasks in Geometry. Yayınlanmamış Doktora Tezi, University of Kentucky.
13. Eli, J.A., Mohr-Schroeder, M.J., and Lee, C.W., (2011). Exploring Mathematical Connections of Prospective Middle-Grades Teachers through Card-Sorting Tasks. Mathematics Education Research Journal, 23(3), 297-319. DOI: 10.1007/s13394-011-0017-0 Evitts, T.A., (2004). Investigating the Mathematical Connections that Preservice Teachers Use and Develop while Solving Problems from Reform Curricula. Yayınlanmamış Doktora Tezi, Pennsylvania State University College of Education.
14. Flores, A., (1992). Mathematical Connection with a Spirograph. The Mathematics Teacher, 85(2), 129-132.
15. Gainsburg, J., (2008). Real-World Connections in Secondary Mathematics Teaching. Journal of Mathematics Teacher Education, 11(3), 199-219. DOI: 1007/s10857-007-9070-8
16. Gonzales, N.A., (1998). A Blueprint for Problem Posing. School Science and Mathematics, 98(8), 448-465. DOI: 10.1111/j.1949851998.tb17437.x
17. Guberman, R. and Leikin, R., (2013). Interesting and Difficult Mathematical Problems: Changing Teachers’ Views by Employing Multiple-Solution Tasks. Journal of Mathematics Teacher Education, 16(1), 33-56. DOI: 1007/s10857-012-9210-7
18. Hiebert, J., and Carpenter, T., (1992). Learning and Teaching with Understanding. In D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 65–97). New York: Macmillan.
19. Ishii, D.K., (2003). First-Time Teacher-Researchers Use Writing in Middle School Mathematics Instruction. The Mathematics Educator, 13(2), 38-46.
20. Kutlu, Ö., Doğan, C.D. ve Karakaya, İ., (2009). Öğrenci Başarısının Belirlenmesi Performansa ve Portfolyoya Dayalı Durum Belirleme (2. Baskı). Ankara: PegemA.
21. Lee, J.E., (2012). Prospective Elementary Teachers’ Perceptions of Real-Life Connections Reflected in Posing and Evaluating
22. Story Problems. Journal of Mathematics Teacher Education, 15(6), 429-4 DOI: 10.1007/s10857-012-9220-5
23. Leikin, R., (2011). Multiple Solution Tasks: From a Teacher Education Course to Teacher Practice. Zentralblatt für Didaktik der Mathematik, 43(6-7), 993-1006. DOI: 1007/s11858-011-03425
24. Leikin, R. and Levav-Waynberg, A., (2007). Exploring Mathematics Teacher Knowledge to Explain the Gap between Theory-Based Recommendations and School Practice in the Use of Connecting Tasks. Educational Studies in Mathematics, 66(3), 349-371. DOI: 1007/s10649-006-9071-z
25. Lockwood, E., (2011). Students Connections among Counting Problems: An Exploration Using Actor-Oriented Transfer. Educational Studies in Mathematics, 78(3), 307-322. DOI: 1007/s10649-011-9320-7.
26. MEB. (2005). Matematik Dersi Öğretim Programı ve Kılavuzu(9-12. Sınıflar). Ankara.
27. Monroe, E.E. and Mikovch, A.K., (1994). Making Mathematical Connection across the Curriculum: Activities to Help Teachers Begin. School Science and Mathematics, 94(7), 371-376. DOI: 1111/j.1949-8594.1994.tb15697.x
28. Mosvold, R., (2008). Real-Life Connections in Japan and the Netherlands: National teaching patterns and cultural beliefs. International Journal for Mathematics Teaching and Learning. Plymouth University, UK: Centre for Innovation in Mathematics Teaching, 1-18. [Online]: http://www.cimt.plymouth.ac.uk/journal/mosvold.pdf adresinden 13 Haziran 2011 tarihinde indirilmiştir.
29. Mousley, J., (2004). An Aspect of Mathematical Understanding: The Notion of “Connected Knowing”. Proceedings of the 28 th Conference of the International Group for the Psychology of Mathematics Education, 3-25, 377-384.
30. National Council of Teachers of Mathematics [NCTM]. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.
31. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.
32. Noss, R. and Hoyles, C., (1996). Windows on Mathematical Meaning: Learning Cultures and Computers (Vol. 17). Dordrecht, the Netherlands: Kluwer Academic Publishers.
33. Özgen, K., and Alkan, H., (2012). The Relationship between Secondary School Pre-service Mathematics Teachers’ Skills in Problem Solvig Dimensions and Their Learning Style Characteristics. Educational Sciences: Theory & Practice, 12(2), 1159-1182.
34. Passmore, T., (2007). Polya’s Legacy: Fully Forgotten or Getting a New Perspective in Theory and Practice? Australian Senior Mathetmatics Journal, 21(2), 44-53.
35. Pesen, C., (2003). Eğitim Fakülteleri ve Sınıf Öğretmenleri İçin Matematik Öğretimi(1. Baskı). Ankara: Nobel.
36. Polya, G., (1973). How to Solve It – A New Aspect of Mathematical Method. New Jersey: Princeton University Press.
37. Pugalee, D.K., (2001). Writing, Mathematics, and Metacognition: Looking for Connections thorugh Students’ Work in Mathematical Problem Solving. School Science and Mathematics, 101(5), 2362 DOI: 10.1111/j.1949-8594.2001.tb18026.x
38. Schoenfeld, A.H., (1991). On Mathematics as Sense-Making: An Informal Attack on the Unfortunate Divorce of Formal and Informal Mathematics. In J. Voss, D. N. Perkins, and J. Segal (Eds.), Informal Reasoning and Education, pp. 311–343. Hillsdale, NJ: Erlbaum.
39. Schwalbach, E.M., and Dosemagen, D.M., (2000). Developing Student Understanding: Contextualizing Calculus Concepts. School Science and Mathematics, 100(2), 90-98. DOI: 10.1111/j.1949852000.tb17241.x
40. Taylor, J.A., and McDonald, C., (2007). Writing in Groups as a Tool for Non-Routine Problem Solving in First Year University Mathematices. International Journal of Mathematics Education in Science and Technology, 38(5), 639-655. DOI:1080/00207390701359396
41. Tekin, H., (2007). Eğitimde Ölçme ve Değerlendirme (18. Baskı). Ankara: Yargı.
42. Toluk-Uçar, Z., (2011). Öğretmen Adaylarının Pedagojik İçerik Bilgisi: Öğretimsel Açıklamalar. Turkish Journal of Computer and Mathematics Education, 2(2), 87-102.
43. Umay, A., (2007).Eski Arkadaşımız Okul Matematiğinin Yeni Yüzü. Ankara: Aydan Web Tesisleri.
44. Vale, C., McAndrew, A., and Krishnan, S., (2011). Connecting with the Horizon: Developing Teachers’ Appreciation of Mathematical Structure. Journal of Mathematics Teacher Education, 14(3), 193-212.DOI: 10.1007/s10857-010-9162-8
45. Verschaffel, L., DeCorte, E., Lasure, S., Van Vaerengbergh, G., Bogaerts, H. and Ratinckx, E., (1999). Learning to Solve Mathematical Application Problems: A Design Experiment with Fifth Graders. Mathematical Thinking and Learning, 1(3), 1952 DOI:10.1207/s15327833mtl0103_2
46. Yıldırım, A., ve Şimşek, H., (2005). Sosyal Bilimlerde Nitel Araştırma Yöntemleri (5. Baskı). Ankara: Seçkin.
47. URL-1. (2000). Mathematics K-12 Connections Rubric.[Online]: media.bethelsd.org/website/resources/static/performanceLearning/ math/ma06.html adresinden 02.04.2012 tarihinde indirilmiştir.