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The Relationship between 9th Grade Students' Symbol Sense Behaviors, Algebraic Thinking Skills and Academic Achievement: A Case Study

Year 2024, Volume: 11 Issue: 2, 98 - 134, 31.12.2024
https://doi.org/10.59409/ojer.1521992

Abstract

The aim of this study is to investigate the relationship between ninth grade students’ symbol sense behaviors, algebraic thinking skills and academic achievement. To achieve this aim, a qualitative research approach known as case study design was employed. A total of three students studying in a high school in Gümüşhane province constituted the study group of the research. In the study, considering the opinions of the mathematics teacher conducting the course and the academic achievement levels of the students in the mathematics course, one student from each achievement level was selected as low, medium and high academic achievement level. The data were acquired from five research inquiries in the literature and adapted in line accordance with expert perspectives. The data were analyzed using thematic coding with an analysis table prepared in line with expert opinions. Students with high achievement level showed symbol sense behaviors at the desired level by using symbols in a flexible and fluent way, while students with low and medium achievement level could not exhibit symbol sense behaviors at the desired level. Students with high academic achievement have advanced algebraic thinking skills. The algebraic thinking skill behaviors of students with low academic achievement are more in the form of rote stereotyped signs. As a result, students' algebraic thinking skills and symbol sense behaviors were found to be compatible with their academic achievement levels. In addition, it was concluded that there was a positive relationship between algebraic thinking skills and symbol sense behaviors.

References

  • Altun, M. (2005). Matemetik öğretimi: İlköğretim ikinci kademede (6, 7 ve 8. sınıflarda). Bursa: Aktüel.
  • Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
  • Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 42-47.
  • Bağdat, O., & Anapa-Saban, P. (2014). İlköğretim 8. Sınıf öğrencilerinin cebirsel düşünme becerilerinin solo taksonomisi ile incelenmesi. The Journal of Academic Social Science Studies, 26(Summer II), 473-496.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi (4.Baskı). Ankara: Harf Eğitim Yayıncılığı.
  • Bokhove, C. (2010). Implementing feedback in a digital tool for symbol sense. International Journal for Technology in Mathematics Education, 17(3), 121-126.
  • Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43-49.
  • Boyatzis, R. E. (1998). Transforming qualitative information: Thematic analysis and code development. Thousand Oaks, CA : Sage Publications.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri (23. Baskı). Ankara: Pegem Akademi.
  • Chow, T-C. F. (2011). Students' difficulties, conceptions and attitudes towards learning algebra: An intervention study to improve teaching and learning [Doctoral dissertation]. Science and Mathematics Education Centre, Curtin University, Perth, Australia.
  • Christou, K. P., & Vosniadou, S. (2005). How students interpret literal symbols in algebra: A conceptual change approach. In B. G. Bara, L. Barsalou, & M. Bucciarelli (Eds.), Proceedings of the XXVII annual conference of the cognitive science society (pp.453-458). Italy.
  • Clement, J., Lochhead, J., &, Monk, G. S. (1981). Translation difficulties in learning mathematics. American Mathematical Monthly, 88(4), 286-290. doi:10.2307/2320560.
  • Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16-30. doi: 10.5951/jresematheduc.13.1.0016.
  • Creswell, J. W. (2017). Nitel araştırmacılar için 30 temel beceri (1. Baskı) (H. Özcan, Çev.). Ankara: Anı Yayıncılık.
  • Darojaturrofiah, L. (2017). Profil symbol sense dalam memecahkan masalah aljabar ditinjau dari kemampuan matematika siswa di smp negeri 1 sidoarjo [Unpublished master's thesis]. Universitas Islam Negeri Sunan Ampel Surabaya, Surabaya, Indonesia.
  • Dede, Y., & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(24), 180-185.
  • Demetgül, Z., & Baki, A. (2020). Teknoloji donanımlı bir sınıfta mutlak değer ve eşitsizlikler konusunun öğretiminden yansımalar: Bir aksiyon araştırması. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 91-127. https://doi.org/10.16949/turkbilmat.333662.
  • Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 61-94). Washington, D.C.: National Academies Press.
  • Guba, E. G. (1981). Criteria for assessing the trustworthiness of naturalistic inquiries. Educational Communication and Technology, 29(2), 75-91.
  • Guba, E. G., & Lincoln, Y. S. (1981). Effective evaluation: Improving the usefulness of evaluation results through responsive and naturalistic approaches. San Francisco, CA: Jossey-Bass.
  • Irwin, K. C., & Britt, M. S. (2007). The development of algebraic thinking: Results of a three-year study. In Ministry of Education (Ed.), Findings from the New Zealand Numeracy Development Projects 2006, 33-43.
  • Jupri, A., & Sispiyati, R. (2020). Students’ algebraic proficiency from the perspective of symbol sense. Indonesian Journal of Science and Technology, 5(1), 86-94.
  • Kamol, N. (2005). A framework in characterizing lower secondary school students’ algebraic thinking [Unpublished doctoral dissertation]. Srinakharinwirot University, Bangkok, Thailand.
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Erlbaum.
  • Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J.J. Kaput, D.W. Carraher, & M.L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Lawrence Erlbaum Associates, New York.
  • Keller, B. A. (1993). Symbol sense and it’s development in two computer algebra system environments [Unpublished doctoral dissertation]. Western Michigan University, U.S.A.
  • Kenney, R. H. (2008). The influence of symbols on pre-calculus students’ problem-solving goals and activities [Unpublished doctoral dissertation]. North Carolina State University, U.S.A.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151.
  • Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205-263. doi: 10.1007/s10758-006-0006-7.
  • Kop, P. M. G. M., Janssen, F. J. J. M., Drijvers, P. H. M., &, van Driel, J. H. (2020). The relation between graphing formulas by hand and students’ symbol sense. Educational Studies in Mathematics (Springer Netherlands), 105, 137-161. doi: 10.1007/S10649-020-09970-3.
  • Kriegler, S. (2007). Just what is algebraic thinking? Introduction to Algebra: Teacher Handbook, 1–11.
  • Kusaeri, K. (2012). Menggunakan model dina dalam pengembangan tes diagnostik un-tuk mendeteksi salah konsepsi. Jurnal Penelitian dan Evaluasi Pendidikan, 16(1), 281-306. doi:10.21831/pep.v16i1.1118.
  • Lacampagne, C. B. (1995). The algebra initiative colloquium. Volume 2: Working group papers. US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
  • Mason, J. (2008). Making use of children’s power to produce algebraic thinking. In J.J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 57-94). Taylor and Francis Group. https://doi.org/10.4324/9781315097435-4.
  • Merriam, S. B. & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4td ed). San Francisco, CA: Jossey-Bass.
  • Mutammam, M. B., & Wulandari, E. N. (2023). Profile of junior high school students’ symbol sense thinking. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(2), 509-521. doi: 10.31764/jtam.v7i2.12622.
  • Naidoo, K. S. K. (2009). An investigation of learners' symbol sense and interpretation of letters in early algebraic learning [Research report in partial fulfillment of the requirements for the degree of master of sciences]. University of Witwatersrand, Johannesborg, South Africa.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. In Reston, (pp. 78-88). VA: The National Council of Teachers of Mathematics.
  • National Research Council (NRC). (1989). Everybody counts: A report to the nation on the futura of mathematics education. Washington, DC.: National Academy Press.
  • Neuman, D. (2014). Qualitative research in educational communications and technology: A brief introduction to principles and procedures. Journal of Computing in Higher Education, 26(1), 69-86. doi:10.1007/s12528-014-9078-x.
  • Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
  • Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42(3), 237-268.
  • Rini, A. D. P., Hussen, S., Hidayati, H., & Muttaqien, A. (2021). Symbol sense of mathematics students in solving algebra problems. Journal of Physics: Conference Series, 1764(1), 1-13. doi:10.1088/1742-6596/1764/1/012114.
  • Rosnick, P., & Clement, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. The Journal of Mathematical Behavior, 3(1), 3–27.
  • Rycroft-Smith, L., & Macey, D. (2022, October). Development of symbol sense. https://www.cambridgemaths.org sitesinden 4 Haziran 2024 tarihinde erişilmiştir.
  • Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2006). Bringing out the algebraic character of arithmetic: From children's ideas to classroom practice. New York: Routledge.
  • Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A Systematic review on algebraic thinking in education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), Article em2065.
  • Somasundram, P., Akmar S. N., & Eu, L. K. (2019). Year five pupils' number sense and algebraic thinking: The mediating role of symbol and pattern sense. The New Educational Review, 55(1), 100-111. doi: 10.15804/tner.2019.55.1.08.
  • Stephens, A. C., Blanton, M., Knuth, E., Isler-Baykal, I., & Gardiner, A. (2015). Just say yes to early algebra!. Teaching Children Mathematics, 22(2), 92-101. doi: https://doi.org/ 10.5951/teacchilmath.22.2.0092.
  • Sugilar, H., Kariadinata, R., & Sobarningsih, N. (2019). Spektrum symbol dan structure sense matematika siswa madrasah tsanawiyah. Kalamatika: Jurnal Pendidikan Matematika, 4(1), 37-48.
  • Şandır, H., Ubuz, B. ve Argün, Z. (2002, 16-18 Eylül). Ortaöğretim 9.sınıf öğrencilerinin mutlak değer kavramındaki öğrenme hataları ve kavram yanılgıları. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, ODTÜ, Ankara.
  • Toluk-Uçar, Z. (2018). Öğretim programları açısından cebirsel düşünmeye yaklaşımlar. Mehmet Fatih Özmantar, Hatice Akkoç, Bilge Kuşdemir Kayıran Melike Özyurt (Eds.), Ortaokul matematik öğretim programları tarihsel bir inceleme içinde (pp. 209-246). Ankara: Pegem Akademi.
  • Turşucu, S., Spandaw, J., & de Vries, M. J. (2018). Search for symbol sense behavior: Students in upper secondary education solving algebraic physics problems. Research in Science Education, 48(5), 1-27. doi: 10.1007/s11165-018-9766-z.
  • Usiskin, Z. (1999). Conception of school algebra and uses of variables. In B. Moses (Ed.), Algebraic thinking, grades K-12: Readings from NCTM’s school-based journals and other publications (pp. 7-13). Reston, VA: National Council of Teachers of Mathematics.
  • Wardah, S., Utomo., D. P., & Putri, O. R. U. (2021). An analysis of errors on mathematical symbol as a metaphor in linear programming. Jurnal Didaktik Matematika, 8(1), 45-58. doi: 10.24815/JDM.V8I1.18304.
  • Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (1994). Discovering the future of the case study. Method in evaluation research. Evaluation Practice, 15(3), 283-290.
Year 2024, Volume: 11 Issue: 2, 98 - 134, 31.12.2024
https://doi.org/10.59409/ojer.1521992

Abstract

References

  • Altun, M. (2005). Matemetik öğretimi: İlköğretim ikinci kademede (6, 7 ve 8. sınıflarda). Bursa: Aktüel.
  • Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24-35.
  • Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the Learning of Mathematics, 25(2), 42-47.
  • Bağdat, O., & Anapa-Saban, P. (2014). İlköğretim 8. Sınıf öğrencilerinin cebirsel düşünme becerilerinin solo taksonomisi ile incelenmesi. The Journal of Academic Social Science Studies, 26(Summer II), 473-496.
  • Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi (4.Baskı). Ankara: Harf Eğitim Yayıncılığı.
  • Bokhove, C. (2010). Implementing feedback in a digital tool for symbol sense. International Journal for Technology in Mathematics Education, 17(3), 121-126.
  • Bokhove, C., & Drijvers, P. (2010). Symbol sense behavior in digital activities. For the Learning of Mathematics, 30(3), 43-49.
  • Boyatzis, R. E. (1998). Transforming qualitative information: Thematic analysis and code development. Thousand Oaks, CA : Sage Publications.
  • Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri (23. Baskı). Ankara: Pegem Akademi.
  • Chow, T-C. F. (2011). Students' difficulties, conceptions and attitudes towards learning algebra: An intervention study to improve teaching and learning [Doctoral dissertation]. Science and Mathematics Education Centre, Curtin University, Perth, Australia.
  • Christou, K. P., & Vosniadou, S. (2005). How students interpret literal symbols in algebra: A conceptual change approach. In B. G. Bara, L. Barsalou, & M. Bucciarelli (Eds.), Proceedings of the XXVII annual conference of the cognitive science society (pp.453-458). Italy.
  • Clement, J., Lochhead, J., &, Monk, G. S. (1981). Translation difficulties in learning mathematics. American Mathematical Monthly, 88(4), 286-290. doi:10.2307/2320560.
  • Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16-30. doi: 10.5951/jresematheduc.13.1.0016.
  • Creswell, J. W. (2017). Nitel araştırmacılar için 30 temel beceri (1. Baskı) (H. Özcan, Çev.). Ankara: Anı Yayıncılık.
  • Darojaturrofiah, L. (2017). Profil symbol sense dalam memecahkan masalah aljabar ditinjau dari kemampuan matematika siswa di smp negeri 1 sidoarjo [Unpublished master's thesis]. Universitas Islam Negeri Sunan Ampel Surabaya, Surabaya, Indonesia.
  • Dede, Y., & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(24), 180-185.
  • Demetgül, Z., & Baki, A. (2020). Teknoloji donanımlı bir sınıfta mutlak değer ve eşitsizlikler konusunun öğretiminden yansımalar: Bir aksiyon araştırması. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 91-127. https://doi.org/10.16949/turkbilmat.333662.
  • Fey, J. T. (1990). Quantity. In L. A. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 61-94). Washington, D.C.: National Academies Press.
  • Guba, E. G. (1981). Criteria for assessing the trustworthiness of naturalistic inquiries. Educational Communication and Technology, 29(2), 75-91.
  • Guba, E. G., & Lincoln, Y. S. (1981). Effective evaluation: Improving the usefulness of evaluation results through responsive and naturalistic approaches. San Francisco, CA: Jossey-Bass.
  • Irwin, K. C., & Britt, M. S. (2007). The development of algebraic thinking: Results of a three-year study. In Ministry of Education (Ed.), Findings from the New Zealand Numeracy Development Projects 2006, 33-43.
  • Jupri, A., & Sispiyati, R. (2020). Students’ algebraic proficiency from the perspective of symbol sense. Indonesian Journal of Science and Technology, 5(1), 86-94.
  • Kamol, N. (2005). A framework in characterizing lower secondary school students’ algebraic thinking [Unpublished doctoral dissertation]. Srinakharinwirot University, Bangkok, Thailand.
  • Kaput, J. J. (1999). Teaching and learning a new algebra. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Erlbaum.
  • Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J.J. Kaput, D.W. Carraher, & M.L. Blanton (Eds.), Algebra in the early grades (pp. 5-17). Lawrence Erlbaum Associates, New York.
  • Keller, B. A. (1993). Symbol sense and it’s development in two computer algebra system environments [Unpublished doctoral dissertation]. Western Michigan University, U.S.A.
  • Kenney, R. H. (2008). The influence of symbols on pre-calculus students’ problem-solving goals and activities [Unpublished doctoral dissertation]. North Carolina State University, U.S.A.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151.
  • Kieran, C., & Drijvers, P. (2006). The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra. International Journal of Computers for Mathematical Learning, 11(2), 205-263. doi: 10.1007/s10758-006-0006-7.
  • Kop, P. M. G. M., Janssen, F. J. J. M., Drijvers, P. H. M., &, van Driel, J. H. (2020). The relation between graphing formulas by hand and students’ symbol sense. Educational Studies in Mathematics (Springer Netherlands), 105, 137-161. doi: 10.1007/S10649-020-09970-3.
  • Kriegler, S. (2007). Just what is algebraic thinking? Introduction to Algebra: Teacher Handbook, 1–11.
  • Kusaeri, K. (2012). Menggunakan model dina dalam pengembangan tes diagnostik un-tuk mendeteksi salah konsepsi. Jurnal Penelitian dan Evaluasi Pendidikan, 16(1), 281-306. doi:10.21831/pep.v16i1.1118.
  • Lacampagne, C. B. (1995). The algebra initiative colloquium. Volume 2: Working group papers. US Government Printing Office, Superintendent of Documents, Mail Stop: SSOP, Washington, DC 20402-9328.
  • Mason, J. (2008). Making use of children’s power to produce algebraic thinking. In J.J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 57-94). Taylor and Francis Group. https://doi.org/10.4324/9781315097435-4.
  • Merriam, S. B. & Tisdell, E. J. (2016). Qualitative research: A guide to design and implementation (4td ed). San Francisco, CA: Jossey-Bass.
  • Mutammam, M. B., & Wulandari, E. N. (2023). Profile of junior high school students’ symbol sense thinking. JTAM (Jurnal Teori dan Aplikasi Matematika), 7(2), 509-521. doi: 10.31764/jtam.v7i2.12622.
  • Naidoo, K. S. K. (2009). An investigation of learners' symbol sense and interpretation of letters in early algebraic learning [Research report in partial fulfillment of the requirements for the degree of master of sciences]. University of Witwatersrand, Johannesborg, South Africa.
  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. In Reston, (pp. 78-88). VA: The National Council of Teachers of Mathematics.
  • National Research Council (NRC). (1989). Everybody counts: A report to the nation on the futura of mathematics education. Washington, DC.: National Academy Press.
  • Neuman, D. (2014). Qualitative research in educational communications and technology: A brief introduction to principles and procedures. Journal of Computing in Higher Education, 26(1), 69-86. doi:10.1007/s12528-014-9078-x.
  • Polya, G. (1945). How to solve it. Princeton, NJ: Princeton University Press.
  • Radford, L. (2000). Signs and meanings in students' emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42(3), 237-268.
  • Rini, A. D. P., Hussen, S., Hidayati, H., & Muttaqien, A. (2021). Symbol sense of mathematics students in solving algebra problems. Journal of Physics: Conference Series, 1764(1), 1-13. doi:10.1088/1742-6596/1764/1/012114.
  • Rosnick, P., & Clement, J. (1980). Learning without understanding: The effect of tutoring strategies on algebra misconceptions. The Journal of Mathematical Behavior, 3(1), 3–27.
  • Rycroft-Smith, L., & Macey, D. (2022, October). Development of symbol sense. https://www.cambridgemaths.org sitesinden 4 Haziran 2024 tarihinde erişilmiştir.
  • Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2006). Bringing out the algebraic character of arithmetic: From children's ideas to classroom practice. New York: Routledge.
  • Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A Systematic review on algebraic thinking in education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), Article em2065.
  • Somasundram, P., Akmar S. N., & Eu, L. K. (2019). Year five pupils' number sense and algebraic thinking: The mediating role of symbol and pattern sense. The New Educational Review, 55(1), 100-111. doi: 10.15804/tner.2019.55.1.08.
  • Stephens, A. C., Blanton, M., Knuth, E., Isler-Baykal, I., & Gardiner, A. (2015). Just say yes to early algebra!. Teaching Children Mathematics, 22(2), 92-101. doi: https://doi.org/ 10.5951/teacchilmath.22.2.0092.
  • Sugilar, H., Kariadinata, R., & Sobarningsih, N. (2019). Spektrum symbol dan structure sense matematika siswa madrasah tsanawiyah. Kalamatika: Jurnal Pendidikan Matematika, 4(1), 37-48.
  • Şandır, H., Ubuz, B. ve Argün, Z. (2002, 16-18 Eylül). Ortaöğretim 9.sınıf öğrencilerinin mutlak değer kavramındaki öğrenme hataları ve kavram yanılgıları. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, ODTÜ, Ankara.
  • Toluk-Uçar, Z. (2018). Öğretim programları açısından cebirsel düşünmeye yaklaşımlar. Mehmet Fatih Özmantar, Hatice Akkoç, Bilge Kuşdemir Kayıran Melike Özyurt (Eds.), Ortaokul matematik öğretim programları tarihsel bir inceleme içinde (pp. 209-246). Ankara: Pegem Akademi.
  • Turşucu, S., Spandaw, J., & de Vries, M. J. (2018). Search for symbol sense behavior: Students in upper secondary education solving algebraic physics problems. Research in Science Education, 48(5), 1-27. doi: 10.1007/s11165-018-9766-z.
  • Usiskin, Z. (1999). Conception of school algebra and uses of variables. In B. Moses (Ed.), Algebraic thinking, grades K-12: Readings from NCTM’s school-based journals and other publications (pp. 7-13). Reston, VA: National Council of Teachers of Mathematics.
  • Wardah, S., Utomo., D. P., & Putri, O. R. U. (2021). An analysis of errors on mathematical symbol as a metaphor in linear programming. Jurnal Didaktik Matematika, 8(1), 45-58. doi: 10.24815/JDM.V8I1.18304.
  • Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yin, R. K. (1994). Discovering the future of the case study. Method in evaluation research. Evaluation Practice, 15(3), 283-290.
There are 57 citations in total.

Details

Primary Language English
Subjects Mathematics Education
Journal Section Articles
Authors

Tuğba Tat

Pınar Anapa Saban

Publication Date December 31, 2024
Submission Date July 24, 2024
Acceptance Date December 30, 2024
Published in Issue Year 2024 Volume: 11 Issue: 2

Cite

APA Tat, T., & Anapa Saban, P. (2024). The Relationship between 9th Grade Students’ Symbol Sense Behaviors, Algebraic Thinking Skills and Academic Achievement: A Case Study. Osmangazi Journal of Educational Research, 11(2), 98-134. https://doi.org/10.59409/ojer.1521992