Students’ Algebra Achievement, Algebraic Thinking and Views in the Case of Using Algebra Tiles in Groups

Year 2021, , 254 - 281, 31.12.2021

Büşra Çaylan Ergene , Çiğdem Haser

https://doi.org/10.17522/balikesirnef.1019292

Cited By: 2

Abstract

The study investigated how using algebra tiles in group work affected students’ algebra achievement, algebraic thinking and views about using algebra tiles. 40 sixth grade students in the same school participated in a pretest-posttest control group design study. Students in the experimental group (EG) used algebra tiles in groups and those in the control group (CG) continued with their regular instruction. Prior Algebra Knowledge Test and Algebra Achievement Test were implemented to both groups as pretest and posttest. EG students expressed their views in the Views about Algebra Tiles Questionnaire. Although students’ performances did not differ in the statistical analysis in both tests, qualitative analysis of the responses revealed that algebra tiles had positive effect on EG students’ algebraic thinking. EG students indicated that using algebra tiles in group work supported their learning, they made them understand the concepts meaningfully, and the lessons were more enjoyable.

Keywords

algebra tiles, algebra achievement, algebraic thinking, middle school students, group work

References

• Akkaya, R. (2006). İlköğretim altıncı sınıf öğrencilerinin cebir öğrenme alanında karşılaşılan kavram yanılgılarının giderilmesinde etkinlik temelli yaklaşımın etkililiği [The Effectiveness of activity based approach in overcoming misconception in the field of learning algebra appeared among the sixth students] [Unpublished master’s thesis]. Abant İzzet Baysal University.
• Akkuş, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representation preference [Unpublished doctoral dissertation]. Middle East Technical University.
• Balt, J. (2017). Small group math instruction in the middle school classroom [Unpublished master’s thesis]. Saint Catherine University.
• Bybee, R. (1997). Achieving scientific literacy: From purposes to practices. Heinemann Publications.
• Chappell, M. F., & Strutchens, M. E. (2001). Creating connections: Promoting algebraic thinking with concrete models. Mathematics Teaching in the Middle School, 7(1), 20-25.
• Driscoll, M. (1999). Fostering algebraic thinking: A Guide for teachers, grades 6-10. Heinemann.
• Enki, K. (2014). Effects of using manipulatives on seventh grade students' achievement in transformation geometry and orthogonal views of geometric figures [Unpublished master’s thesis]. Middle East Technical University.
• Fennema, E. H. (1972). Models and mathematics. Arithmetic Teacher, 19(8), 635-640.
• Fletcher, J. A. (2008). Developing algebraic thinking through group discussion. Mathematics Connection, 7, 25-36.
• Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phillips, N. B., Karns, K., & Dutka, S. (1997). Enhancing students' helping behaviour during peer-mediated instruction with conceptual mathematical explanations. The Elementary School Journal, 97(3), 223-249.
• Goins, K. B. (2001). Comparing the effect of visual and algebra tile manipulatives methods on student skill and understanding of polynomial multiplication [Unpublished doctoral dissertation]. University of South Carolina.
• Hinton, P., McMurray, I., & Brownlow, C. (2014). SPSS explained (2nd ed.). Routledge.
• Hinzman, K. P. (1997). Use of manipulatives in mathematics at the middle school level and their effects on students’ grades and attitudes [Unpublished master’s thesis]. Salem-Teikyo University.
• Jansen, A. (2012). Developing productive dispositions during small-group work in two sixth-grade mathematics classrooms. Middle Grades Research Journal, 7(1), 37-56.
• Johnson, K. A. (1993). Manipulatives allow everyone to learn mathematics. Contemporary Education, 65(1), 10-12.
• Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2015). Improving grade 7 students’ achievement in initial algebra through a technology based intervention. Digital Experiences in Mathematics Education, 1(1), 28-58.
• Kaput, J. J. (1995). A research base supporting long term algebra reform? In D. Owens, M. Reed, & G. M. Millsaps (Eds.), Proceedings of the 17th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 71–94). The ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
• 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.
• Karakırık, E., & Aydın, E. (2011). Matematik öğrenme nesneleri. In E. Karakırık (Ed.), Matematik eğitiminde teknoloji kullanımı (pp. 19-33). Nobel Yayın Dağıtım.
• Kieran, C. (1996). The changing face of school algebra. In C. Alsina, J. Alvarez, B. Hodgson, C. Laborde, & A. Pérez (Eds.), 8th International Congress on Mathematical Education: Selected lectures (pp. 271-290). S.A.E.M. Thales.
• Koblitz, B., & Wilson, J. (2014). Effective group work in a mathematics classroom. http://jwilson.coe.uga.edu/EMAT7050/Papers2014/Koblitz.Effective%20Group%20 Work.pdf.
• Larbi, E., & Okyere, M. (2016). The use of manipulatives in mathematics education. Journal of Education and Practice, 7(36), 53-61.
• Lawrence, A., & Hennessy, C. (2002). Lessons for algebraic thinking: Grades 6-8. Math Solutions Publications.
• Leitze, A. R., & Kitt, N. A. (2000). Using homemade algebra tiles to develop algebra and prealgebra concepts. Mathematics Teacher, 93(6), 462-520.
• MacGregor, M. (2004). Chapter twelve: Goals and content of an algebra curriculum for the compulsory years of schooling. In The future of the teaching and learning of algebra (pp. 313-328). Kluwer.
• Magruder, R. L. (2012). Solving linear equations: A comparison of concrete and virtual manipulatives in middle school mathematics [Unpublished doctoral dissertation]. University of Kentucky.
• Milli Eğitim Bakanlığı (MEB) (2013). İlköğretim matematik dersi (5-8. Sınıflar) öğretim programı [Elementary mathematics curriculum (Grades 5-8)]. MEB.
• Milli Eğitim Bakanlığı (MEB) (2018). Matematik dersi öğretim programı (Ilkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar) [Mathematics curriculum (Primary and middle school Grades 1, 2, 3, 4, 5, 6, 7 and 8)]. MEB.
• Mulryan, C. M. (1994). Perceptions of intermediate students’ cooperative small-group work in mathematics. The Journal of Educational Research, 87(5), 280-291.
• National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. NCTM.
• Okpube, N. M. (2016). Card games and algebra tic tacmatics on achievement of junior secondary ii students in algebraic expressions. International Journal of Evaluation and Research in Education, 5(2), 93-100.
• Palabıyık, U., & Akkuş, O. (2011). Örüntü temelli cebir öğretiminin öğrencilerin cebirsel düşünme becerileri ve matematiğe karşı tutumlarına etkisi [The effects of pattern-based algebra instruction on students’ algebraic thinking and attitude towards mathematics]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 30, 111-123.
• Picciotto, H., & Wah, A. (1993). A new algebra: Tool, themes, concepts. Journal of Mathematical Behaviour, 12(1), 19-42.
• Saraswati, S., Putri, R. I. I., & Somakim (2016). Supporting students’ understanding of linear equations with one variable using algebra tiles. Journal on Mathematics Education, 7(1), 21-32.
• Schlosser, T. K. (2010). Using algebra tiles to aid students in factoring polynomials [Unpublished master’s thesis]. Central Connecticut State University.
• Sharp, J. M. (1995, October). Results of using algebra tiles as meaningful representations of algebra concepts [Paper presentation]. Annual Meeting of the Mid-Western Education Research Association, Chicago, IL.
• Thompson, W. P., & Lambdin, D. (1994). Concrete materials and teaching for mathematical understanding. Arithmetic Teacher, 41(9), 556-558.
• Thornton, G. J. (1995). Algebra tiles and learning styles [Unpublished master’s thesis]. University of Rhodesia.
• Wang, J., & Goldschmidt, P. (2003). Importance of middle school mathematics on high school students’ mathematics achievement. Journal of Educational Research, 97, 3-19.
• Webb, N. M., & Farivar, S. (1994). Promoting helping behaviour in cooperative small groups in middle school mathematics. American Educational Research Journal, 31(2), 369-395.
• Windsor, W. (2010). Algebraic thinking: A problem solving approach. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (pp. 665-672). MERGA.
• Yıldız, B. (2012). A case study of the use of manipulatives in upper elementary mathematics classes in a private school: Teachers’ and students’ views [Unpublished doctoral dissertation]. Middle East Technical University.