Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students

Tangül Kabael; Ayça Akın

EN TR

Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students

Öz

It was aimed to investigate seventh grade students’ problem solving strategies and quantitative reasoning skils associated with solving an algebraic verbal problem. Data was gathered with clinical interviews in this qualitative research. Findings indicated that seven participants used arithmetical stratagies and the two of these participants used algebraic strategies. It was concluded that participants’ quantitative reasoning skills were effected their usage of arithmetical or algebraic strategies. This study put forth that seventh grade students’ generaly focus on using arithmetical strategies while it is expected to use algebraic strategies in this grade.

Anahtar Kelimeler

Transition from arithmetic to algebra, problem solving, quantitative reasonin, middle school students

Kaynakça

Akkan, Y., Baki, A. ve Çakıroğlu, Ü. (2011). Aritmetik ile cebir arasındaki farklılıklar: Cebir önce- sinin önemi. İlköğretim Online, 10(3), 812-823.
Akkan, Y., Baki, A. ve Çakıroğlu, Ü. (2012). 5-8. Sınıf öğrencilerinin aritmetikten cebire geçiş prob- lem çözme bağlamında incelenmesi. Hacettepe Eğitim Fakültesi Dergisi, 43, 1-13.
Bednarz, N. ve Janvier, B. (2001). Emergence and development of algebra as a problemsolving tool: Continuities and discontinuities with arithmetic. In N. Bednarz, C. Kieran and L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 115–136). Dordrecht: Klu- wer Academic Publisher.
Cai, J. ve Knuth, E. (2011). Early algebraization: A global dialogue from multiple perspectives. New York: Springer.
Cai, J., Ng, S. F. ve Moyer, J. C. (2011). Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore. In J. Cai ve E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives. (pp. 25-41). Springer Berlin Heidelberg.
Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
Day, R. ve Jones, G. A. (1997). Building bridges to algebraic thinking. Mathematics Teaching in the Middle Schools, 2(4), 208-213.
Dede, Y. (2004). Öğrencilerin cebirsel sözel problemleri denklem olarak yazarken kullandıkları çözüm stratejilerinin belirlenmesi. Eğitim Bilimleri ve Uygulama, 3, 175 -192.
Didiş, M. G. ve Erbaş, A. K. (2012). Lise öğrencilerinin cebirsel sözel problemleri çözmedeki ba- şarısı. X.Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi Bildiri Özetleri Kitabı, Nigde, Turkey, Haziran 27-30, 2012 (p. 430): Nigde Üniversitesi, Türkiye.
Ellis, A. B. (2007). The influence of reasoning with emergent quantities on students’ generalizations. Cognition and Instruction, 25(4), 439–478.

Ellis, A. B. (2011). Algebra in the middle school: Developing functional relationships through qu- antitative reasoning. In J. Cai ve E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives. (pp. 215-238). Springer Berlin Heidelberg.
Fan, L. ve Zhu,Y. (2007). Representation of problem-solving procedures: A comparative look at Chi- na, Singapore, and US mathematics textbooks. Education Studies Mathematics, 66(1), 61-75.
Harel, G. (2013). The Kaputian program and its relation to DNR-based instruction: A common com- mitment to the development of mathematics with meaning, In M. Fried ve T. Dreyfus (Eds.), The SimCalc vision and contribution (pp. 438-448). Springer.
Harel, G. ve Lim, K. H. (2004). Mathematics teachers’ knowledge base: Preliminary results. In M. Hoines ve A. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3(3), pp. 25 – 32). Bergen, Norway.
Hattikudur, S., Prather, R. W., Asquith, P., Alibali, M. W., Knuth, E. J. ve Nathan, M. (2012). Cons- tructing graphical representations: Middle schoolers’ intuitions and developing knowledge abo- ut slope and Y‐intercept. School Science and Mathematics, 112(4), 230-240.
Goldin, G. (2000). A scientific perspective on structures, task-based interviews in mathematics edu- cation research. In A. E. Kelly ve R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517–545). New Jersey: Lawrence Erlbaum.
Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Lear- ning and Instruction, 7(4), 293-307.
Guberman, R. ve Leikin, R. (2013). Interesting and difficult mathematical problems: changing teachers’ vi- ews by employing multiple-solution tasks. Journal of Mathematics Teacher Education, 16(1), 33-56.
Gürbüz, R. & Akkan, Y. (2008). Farklı öğrenim seviyesindeki öğrencilerin aritmetikten cebire geçiş düzeylerinin karşılaştırılması: Denklem örneği. Eğitim ve Bilim, 33(148), 64-76.
Kabael, T. ve Kızıltoprak, F. (2014). Sixth grade students’ ways of thinking associated with solving algebraic verbal problems. In S. Oesterle, C. Nicol, P. Liljedahl ve D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 6, p. 120). Vancouver, Canada: PME.
Kaput, J. (1995). Long term algebra reform: Democratizing access to big ideas. In C. Lacampagne, W. Blair ve J. Kaput (Eds.), The algebra initiative colloquium (pp. 33–52). Washington, DC: U.S. Department of Education.
Kılıç, Ç. (2011). İlköğretim matematik öğretmen adaylarının standart olmayan sözel problemle- re verdikleri yanıtlar ve yorumlar. Ahi Evran Üniversitesi Kırşehir Eğitim Fakültesi Dergisi, 12(3), 55-74.
Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390-419). New York: Macmillan.
Koichu, B. ve Harel, G. (2007). Triadic interaction in clinical task-based interviews with mathema- tics teachers. Educational Studies in Mathematics, 65(3), 349-365.
Küchemann, D.E. (1981). Algebra. In K.M. Hart (Ed.), Children’s understanding of mathematics (pp. 102-119). John Murray.
Mayer, R. E., Lewis, A. B. ve Hegarty, M. (1992). Mathematical misunderstandings: Qualitative reasoning about quantitative problems. Advances in Psychology, 91, 137-153.
Moore, K. C. ve Carlson, M. P. (2012). Students’ images of problem contexts when solving applied problems. The Journal of Mathematical Behavior, 31(1), 48-59.
Nathan, M. J. ve Young, E. (1990). Thinking situationally: Results with an unintelligent tutor for word algebra problems. In A. McDougell ve C. Dowling (eds.), Computers and education (pp. 187-216). New York: North-Holland.
Leikin, R. (2011). Multiple-solution tasks: From a teacher education course to teacher practice. ZDM - The International Journal on Mathematics Education, 43(6), 993-1006.
Lesh, R. ve Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The handbook of research on mathematics teaching and learning (2nd ed., pp. 763–804). Reston, VA: National Council of Teachers of Mathematics; Charlotte, NC: Information Age Publishing. (Joint Publication).
Moore, K. C. (2010). Relationships between quantitative reasoning and students’ problem solving behaviors. Proceedings of the Fourteenth Annual Conference on Research in Undergraduate Mathematics Education (pp. 298-313). Portland, OR: Portland State University.
Moore, K. C., Carlson, M. P. ve Oehrtman, M. (2009). The role of quantitative reasoning in solving applied precalculus problems. Paper presented at the Twelfth Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Educati- on (SIGMAA on RUME) Conference, Raleigh, NC: North Carolina State University.
Olive, J. ve Çağlayan, G. (2008). Learners’ difficulties with quantitative units in algebraic word problems and the teacher’s interpretation of those difficulties. International Journal of Science and Mathematics Education, 6(2), 269-292.
Palomares, J. C. A. ve Hernandez, J. G. (2002). Identification of strategies used by fifth graders to solve mathematics word problems. In D. Mewborn, P. Sztajn, D. White, H. Wiegel, R. Bryant ve K. Nooney (Eds.), Proceedings of the Twenty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 3, p.1379). Athens, Georgia State University.
Pólya, G. (1957). How to solve it. Princeton. New Jersey: Princeton University.
Reusser, K., ve Stebler, R. (1997). Every word problem has a solution – The social rationality of mathematical modeling in schools. Learning and Instruction, 7, 309-327
Schoenfeld, A.H. (1985). Mathematical problem solving. New York: Academic Press.
Smith, J. ve Thompson, P. (2007). Quantitative reasoning and the development of algebraic reaso- ning. In J. Kaput ve D. Carraher (Eds.), Algebra in the early grades (pp. 95-132). New York, NY: Lawrence Erlbaum Associates.
Stacey, K. ve MacGregor, M. (1999). Learning the algebraic method of solving problems. The Journal of Mathematical Behavior, 18(2), 149-167.
Thompson, P. (1988). Quantitative concepts as a foundation for algebraic reasoning: Sufficiency, necessity, and cognitive obstacles. In M. Behr, C. Lacampagne ve M. Wheeler (1988) (Eds.), Proceedings of the Annual Conference of the International Group for the Psychology of Mathe- matics Education (pp. 163-170). Dekalb, IL: Northern Illinois University.
Thompson, P. (1989). A cognitive model of quantity-based algebraic reasoning. Paper presented at the Annual Meeting of the American Educational Research Association, USA.
Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3), 165-208.
Van Dooren, W., Verschaffel, L ve Onghena, P. (2003). Pre-service teachers’ preferred strategies for solving arithmetic and algebraic word problems. Journal of Mathematics Teacher Education, 6, 27-52.
Yıldırım, A., ve Şimşek, H. (2005). Sosyal bilimlerde nitel araştırma yöntemleri. (genişletilmiş 5. Baskı), Ankara: Seçkin Yayıncılık.

Ayrıntılar

Birincil Dil

İngilizce

Konular

-

Bölüm

-

Yazarlar

Tangül Kabael Bu kişi benim
Anadolu Üniversitesi, Eğitim Fakültesi, İlköğretim Bölümü, Matematik Eğitimi Anabilim Dalı, Eskişehir, Türkiye

Ayça Akın Bu kişi benim
Anadolu Üniversitesi, Eğitim Fakültesi, İlköğretim Bölümü, Matematik Eğitimi Anabilim Dalı, Eskişehir, Türkiye

Yayımlanma Tarihi

15 Temmuz 2016

Gönderilme Tarihi

15 Temmuz 2016

Kabul Tarihi

-

Yayımlandığı Sayı

Yıl 2016 Cilt: 24 Sayı: 2

IZ

https://izlik.org/JA68GK32CY

APA

Kabael, T., & Akın, A. (2016). Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students. Kastamonu Education Journal, 24(2), 875-894. https://izlik.org/JA68GK32CY

AMA

1.Kabael T, Akın A. Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students. Kastamonu Eğitim Dergisi. 2016;24(2):875-894. https://izlik.org/JA68GK32CY

Chicago

Kabael, Tangül, ve Ayça Akın. 2016. “Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students”. Kastamonu Education Journal 24 (2): 875-94. https://izlik.org/JA68GK32CY.

EndNote

Kabael T, Akın A (01 Mart 2016) Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students. Kastamonu Education Journal 24 2 875–894.

IEEE

[1]T. Kabael ve A. Akın, “Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students”, Kastamonu Eğitim Dergisi, c. 24, sy 2, ss. 875–894, Mar. 2016, [çevrimiçi]. Erişim adresi: https://izlik.org/JA68GK32CY

ISNAD

Kabael, Tangül - Akın, Ayça. “Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students”. Kastamonu Education Journal 24/2 (01 Mart 2016): 875-894. https://izlik.org/JA68GK32CY.

JAMA

1.Kabael T, Akın A. Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students. Kastamonu Eğitim Dergisi. 2016;24:875–894.

MLA

Kabael, Tangül, ve Ayça Akın. “Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students”. Kastamonu Education Journal, c. 24, sy 2, Mart 2016, ss. 875-94, https://izlik.org/JA68GK32CY.

Vancouver

1.Tangül Kabael, Ayça Akın. Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students. Kastamonu Eğitim Dergisi [Internet]. 01 Mart 2016;24(2):875-94. Erişim adresi: https://izlik.org/JA68GK32CY

Kastamonu Eğitim Dergisi, Creative Commons Atıf 4.0 Uluslararası Lisansı (CC BY) ile lisanslanmıştır.

Yedinci Sınıf Öğrencilerinin Cebirsel Sözel Problemlerini Çözerken Kullandıkları Stratejiler ve Niceliksel Muhakeme Becerileri

Problem Solving Strategies and Quantitative Reasoning Skills in Solving Algebraic Verbal Problems of Seventh Grade Students

Öz

Anahtar Kelimeler

Yedinci Sınıf Öğrencilerinin Cebirsel Sözel Problemlerini Çözerken Kullandıkları Stratejiler ve Niceliksel Muhakeme Becerileri

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

IZ

Kaynak Göster