Investigation of Seventh Grade Students’ Transition Skills among Representations

Yıl 2023, , 552 - 571, 27.10.2023

İhsan Balkan

https://doi.org/10.18009/jcer.1312608

Öz

This descriptive case study was aimed at revealing the level of students’ transition skills among representations (verbal, numeric, algebraic, graphic) at the completion of 7th grade. The participants included 133 students attending 7th grade at a state school located in Ankara in Turkey. Students’ skills in transitioning between representations were tested using the “Test of Skills in Transitioning between Representations (TSTBR)”, which included 12 open-ended questions and analyzed student answers through a graded rubric developed by the researcher. Descriptive statistics such as frequency and percentage were used to examine students’ skills in making transitions between representations. Thus, it was determined in the findings that a majority of students had moderate transition skills. According to the mean scores, the number of students with low representation transition skills was greater than the number of students with high representation transition skills. Also, the students were most successful at transitioning from other representations to algebraic, verbal, numeric, and graphic representations, respectively. The mean scores for each representation transition were examined and possible reasons for the difficulties that students faced were discussed.

Anahtar Kelimeler

Algebra, representation skills, multiple representations, middle school students

Etik Beyan

In this research, the principles of scientific research and publication ethics were followed. This research was conducted with the permission of Ankara University Social Sciences Sub-Ethics Committee, dated 01.02.2022 and number 4/45.

Teşekkür

I would like to thank Prof. Dr. Seniye Renan SEZER and Prof. Dr. Tuba GÖKÇEK for their contributions in the writing process of the article.

Kaynakça

• Akkuş-Çıkla, O. (2004). The effects of multiple representations-based instruction on seventh grade students' algebra performance, attitude towards mathematics, and representation preference. (PhD Thesis). Orta Doğu Teknik Üniversitesi, Ankara.
• Ayyıldız H. & Cansız Aktaş, M. (2022). Türkiye’deki matematik eğitimi alanındaki temsil araştırmalarının eğilimleri: Tematik içerik analizi çalışması [Tendencies of representation studies in mathematics education in Turkey: A thematic content analysis]. Cumhuriyet Uluslararası Eğitim Dergisi, 11(1), 127-144. https://doi.org/10.30703/cije.969821
• Brenner, M. E., Brar, T., Durán, R., Mayer, R. E., Moseley, B., Reed, B. S., & Webb, D. (1995, October). The role of multiple representations in learning algebra. Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus.
• Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R., Reed, B. S., & Webb, D. (1997). Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal, 34(4), 663-689. https://doi.org/10.2307/1163353
• Bruner, J. S. (1966). Toward a theory of instruction. Cambridge: Belknap Press of Harvard University. Choike, J. (2000). Teaching strategies for algebra for all. Journal of Mathematics Teacher Education, 93(7), 556-560. https://doi.org/10.5951/MT.93.7.0556
• Davis, J. (2005). Connecting procedural and conceptual knowledge of functions. Mathematics Teacher, 99(1), 36-39. https://doi.org/10.5951/MT.99.1.0036
• Demir, U. Ö. & Cansız-Aktaş, M. (2019, Eylül). 8. sınıf öğrencilerinin çoklu temsiller arasındaki geçiş becerileri: Doğrusal ilişki içeren durumlar örneği [Eighth grade students’ performances in translating among multiple representations: Including cases of linear relationship]. 4. Uluslararası Türk Bilgisayar ve Matematik Eğitimi Sempozyumu, İzmir.
• Even, R. (1998). Factors involved in linking representations of functions. The Journal of Mathematical Behavior, 17(1), 105-121. https://doi.org/10.1016/S0732-3123(99)80063-7
• Friedlander, A. & Tabach, M. (2001). Promoting multiple representations in algebra. In A.A. Cuoco & F.R. Curcio (Eds.), The roles of representation in school mathematics (pp. 173-185). National Council of Teachers of Mathematics.
• Goldin, G. A. (2003). Representations in school mathematics: a unifying research perspectives. In J. Kilpatrick, W. G. Martin., & D. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 275-285). National Council of Teachers of Mathematics.
• Gök, M. & Cansız-Aktaş, M. (2019, Eylül). 7 ve 8. sınıf öğrencilerinin cebir öğrenme alanında çoklu temsilleri kullanma becerilerinin incelenmesi [Examination of the seventh and eighth grade students’ ability to use multiple representations in learning algebra]. 4. Uluslararası Türk Bilgisayar ve Matematik Eğitimi Sempozyumu, İzmir.
• Gürbüz, R. & Şahin, S. (2015). 8. sınıf öğrencilerinin çoklu temsiller arasındaki geçiş becerileri [Eighth grade students’ skills in translating among multiple representations]. Kastamonu Eğitim Dergisi, 23(4), 1869-1888.
• Hotmanoğlu, Ç. (2014). Sekizinci sınıf öğrencilerinin grafik çizme, yorumlama ve grafikleri diğer gösterimlerle ilişkilendirme becerilerinin incelenmesi [Examining of 8th grade students' skills on drawing, interpreting of graphs and connecting graphs to other representations]. (Master’s Thesis). Karadeniz Teknik Üniversitesi, Trabzon.
• İncikabi, S. (2017). Çoklu temsiller ve matematik öğretimi: Ders kitapları üzerine bir inceleme [Multiple representations and teaching mathematics: An analysis of the mathematics textbooks]. Cumhuriyet Uluslararası Eğitim Dergisi, 6(1), 66-81. https://doi.org/10.30703/cije.321438
• Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Research on mathematics teaching and learning (pp. 515-556). Macmillan.
• Kaya, D. (2015). Çoklu temsil temelli öğretimin öğrencilerin cebirsel muhakeme becerilerine, cebirsel düşünme düzeylerine ve matematiğe yönelik tutumlarına etkisi üzerine bir inceleme [A study on the effects of multiple representations-based instruction on students' algebraic reasoning skills, algebraic thinking levels and attitudes towards mathematics]. (PhD Thesis). Dokuz Eylül Üniversitesi, İzmir.
• Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 390-419). Macmillan Publishing Company.
• Lesh, R. (1979, November). Mathematical learning disabilities: Considerations for identification, diagnosis and remediaton. ERIC Information Analysis Center for Science, Mathematics, and Environmental Education, Columbus, Ohio.
• Merriam, S. B. (2013). Nitel araştırma desen ve uygulama için bir rehber [Qualitative research a guide to design and implementation] (Çeviren: S. Turan) Ankara: Nobel Akademik Yay.
• Mertler, C. A. (2000). Designing scoring rubrics for your classroom. Practical Assessment, Research and Evaluation, 7(1). https://doi.org/10.7275/gcy8-0w24
• Miles, M. B. & Huberman A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Thousand Oaks: Sage Publications.
• Ministry of National Education (MoNE) (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar) [Mathematics lesson curriculum (primary and middle school 1, 2, 3, 4, 5, 6, 7 and 8th grades)]. Ankara: Ministry of National Education.
• Moseley, B. & Brenner, M. A. (1997). Using multiple representations for conceptual change in pre-algebra: A comparison of variable usage with graphic and text based problems. Washington DC: Office of Educational Research and Improvement.
• National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Author, Reston, Virgina: NCTM.
• Panasuk, R. M. & Beyranevand, M. L. (2010). Algebra students' ability to recognize multiple representations and achievement. International Journal for Mathematics Teaching and Learning. Retrieved from https://www.cimt.org.uk/journal/panasuk.pdf
• Panasuk, R. M. & Beyranevand, M. L. (2011). Preferred representations of middle school algebra students when solving problems. The Mathematics Educator, 13(1), 32–52.
• Patton, M. Q. (2014). Qualitative research and evaluation methods: Integrating theory and practice (4th ed.). Thousand Oaks: Sage Publications.
• Schultz, J. E. & Waters, M. (2000). Discuss with your colleagues: Why representations?. Mathematics Teachers, 93(6), 448-453. https://doi.org/10.5951/MT.93.6.0448
• Sert, Ö. (2007). Eighth grade students’ skills in translating among different representations of algebraic concepts. (Master’s Thesis). Orta Doğu Teknik Üniversitesi, Ankara.
• Tabach, M. & Friedlander, A. (2003, February). The role of context in learning beginning algebra. Proceedings of the Third Conference of the European Society for Research in Mathematics Education, Italia.
• Thompson, D. R. & Chappell, M. F. (2007). Communication and representation as elements in mathematical literacy. Reading and Writing Quarterly, 23(2), 179-196. https://doi.org/10.1080/10573560601158495 Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim [Elementary and middle school mathematics teaching developmentally] (Çeviren: S. Durmuş). Ankara: Nobel Yayıncılık.
• Williams, S. E. & Molina, D. (1997, May). Algebra: What all students can learn. The Nature and Role of Algebra in the K-14 Curriculum: Proceedings of a National Symposium, Washington.
• Yıldırım, Z. & Albayrak, M. (2016). Ortaokul öğrencilerinin farklı temsil biçimlerine göre doğrusal ilişki konusunu anlama düzeylerinin incelenmesi [Investigation of the middle school students’ levels of understanding on linear relationship according to representation forms]. Adnan Menderes Üniversitesi Eğitim Fakültesi Eğitim Bilimleri Dergisi, 7(2), 11-26.