Algebraic Thinking of Grade 2 Students in a Mathematics Classroom Using the Open Approach -
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Abstract
This research article aimed to investigate the characteristics of algebraic thinking demonstrated by Grade 2 students in a mathematics classroom using the Open Approach. A qualitative research design based on classroom ethnography was employed. The key informants consisted of six Grade 2 students, purposively selected to represent three levels of mathematical ability — two high-ability, two medium-ability, and two low-ability students — from a classroom in a school participating in the Thailand Lesson Study Incorporated with Open Approach (TLSOA) project. Data were collected across four instructional periods from multiple sources, including students' written work, classroom protocols, blackboard photographs, classroom observations, and think-aloud protocols. Data analysis was conducted using Kieran's (2004) three-part model of algebraic activity, referred to in this study as the GTG Model, in conjunction with evidence situated within the Open Approach process. The quality of the research instruments was verified by three experts using the Index of Item-Objective Congruence (IOC), which yielded values ranging from 0.67 to 1.00. Inter-observer reliability was established using Cohen's Kappa coefficient (κ = 0.78). Data trustworthiness was ensured through triangulation, member checking, and peer debriefing. The findings revealed that students demonstrated algebraic thinking across all three axes of the GTG Model, comprising 11 sub-patterns: four patterns of Generational Activity, four patterns of Transformational Activity, and three patterns of Global Meta-level Activity. The key finding was that the symbol □ evolved from a blank space at the end of an equation for recording a known result to a symbol representing an unknown quantity at various positions within an equation. Bar Models and whole-class mathematical discussions served as critical mechanisms enabling students to connect problem situations, symbolic sentences, and structural reasoning. These findings suggest that early elementary students are capable of engaging with Early Algebra concepts through regular arithmetic content when open-ended problems, representational tools, and mathematical discussions are systematically and intentionally designed.
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หากผู้เสนอบทความมีความจำเป็นเร่งด่วนในการตีพิมพ์โปรดส่งลงตีพิมพ์ในวารสารฉบับอื่นแทน โดยกองบรรณาธิการจะไม่รับบทความหากผู้เสนอบทความไม่ปฏิบัติตามเงื่อนไขและขั้นตอนที่กำหนดอย่างเคร่งครัด ข้อมูลของเนื้อหาในบทความถือเป็นลิขสิทธิ์ของ Journal of Inclusive and Innovative Education คณะศึกษาศาสตร์ มหาวิทยาลัยเชียงใหม่
References
Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers’ algebra eyes and ears. Teaching Children Mathematics, 10(2), 70-77.
Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., Isler-Baykal, I., & Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3 to 5. American Educational Research Journal, 56(5), 1930-1972.
Bunlang, S., Inprasitha, M., & Changsri, N. (2024). Students’ mathematization in mathematics classrooms using the Thailand Lesson Study Incorporated Open Approach model. International Journal for Lesson and Learning Studies, 13(1), 14-27.
Cai, J., Ng, S. F., & Moyer, J. C. (2011). Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 25-41). Springer.
Cai, J., & Rott, B. (2024). On understanding mathematical problem-posing processes. ZDM - Mathematics Education, 56(1), 61-71.
Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87-115.
Ellis, A. B., & Özgür, Z. (2024). Trends, insights, and developments in research on the teaching and learning of algebra. ZDM - Mathematics Education, 56(2), 199-210.
Inprasitha, M. (2022). Lesson study and open approach development in Thailand: A longitudinal study. International Journal for Lesson and Learning Studies, 11(5), 1-15.
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. 5-18). Lawrence Erlbaum Associates.
Kieran, C. (2004). Algebraic thinking in the early grades: What is it?. The Mathematics Educator, 8(1), 139-151.
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159-174.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. SAGE Publications.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE Publications.
Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice (pp. 3-25). Springer
Sun, S., Sun, D., & Xu, T. (2023). The developmental progression of early algebraic thinking of elementary school students. Journal of Intelligence, 11(12), Article 222.
Thinwiangthong, S., Ya-amphan, D., Sythong, P., & Ishizaka, H. (2024). The investigation of best practices on symbolic mathematical communication: A comparative study in Japan, Lao PDR, and Thailand. Malaysian Journal of Learning and Instruction, 21(1), 67-101.
Torres, M. D., Moreno, A., Vergel, R., & Cañadas, M. C. (2024). The evolution from “I think it plus three” towards “I think it is always plus three.” Transition from arithmetic generalization to algebraic generalization. International Journal of Science and Mathematics Education, 22, 971-991.
Wilkie, K. J., & Hopkins, S. (2024). Generalizing actions with the subtraction-compensation property: Primary students’ algebraic thinking with tasks involving vertical towers of blocks. Educational Studies in Mathematics, 115(3), 433-458.
