Algebraic Reasoning in Early Grade: Promoting through Lesson Study and Open Approach
- 1 Doctoral Program in Mathematics Education, Khon Kaen University, Khon Kaen, Thailand
- 2 Mathematics Education Program, Faculty of Education, Khon Kaen University, Khon Kaen, Thailand
- 3 Mathematics Education Program, Faculty of Education, Khon Kaen University, Khon Kaen, Thailand
Abstract
The objective of this study is to analyze what characteristics are of early grade students’ algebraic reasoning in context of open approach and lesson study. Ethnographic study was employed to conduct in this qualitative study. The study was carried out in one mathematics classroom which is a case study of this study and it is the case of classroom which has been using open approach and lesson study since 2006. The 3 teachers are as a member of school lesson study team participated the study as informant and so were 10 students from the class. The data were collected through 9 consecutive lessons by observation with audio-video tape recording, interview, students’ written works and daily field notes. The lessons were designed by carrying into 4 steps of open approach: posing problem, students’ self-learning, whole class discussion and comparison, and summing-up by connecting students’ emergent mathematical ideas. All activities were guided by Thai version of 1 st grade Japan mathematics textbook. The results showed that characteristics of first grade students’ algebraic reasoning are as follows: 1) using algebraic expressions to represent addition situation and posing situation to represent given expressions, 2) constructing and using a tool to find problem results more easily, 3) extending solutions to another domain of number, 4) using various representations to justify their ways of thinking, and 5) reasoning about relations among numbers. The algebraic reasoning occurred under the condition that teachers and students had connected among 3 worlds oriented to Inprasitha’s approach: real world, semi-concrete world, and mathematics world.
- Bassey, M. (1999). Case Study Research in Educational Settings. Buckingham, Philadelphia: Open University Press.
- Blanton, M., & Kaput, J. (2005). Characterizing a Classroom Practice that Promotes Algebraic Reasoning. Journal for Research in Mathematics Education, 36, 412-446.
- Blanton, M., & Kaput, J. (2011). Functional Thinking as a Route into Algebra in the Elementary Grades. In J. Cai, & E. Knuth (Eds.), Early Algebraization, Advances in Mathematics Education. Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/978-3-642-17735-4_2
- Cai, et al. (2005). The Development of Students’ Algebraic Thinking in Earlier Grades: A Cross-Cultural Comparative Perspective. Zentralblattfuer Didaktik der, 37, 5-15.
- 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, 87-115.
- Carraher, D., Brizuela, B., & Schliemann, A.D. (2000). Early Algebra, Early Arithmetic: Treating Operations as Functions. Plenary Address. XXII Meeting of the Psychology of Mathematics Education, North American Chapter, Tucson, AZ: (Available in CD-Rom).
- Howden, H. (1990). Prior Experiences. In L. Edwards Edgar, Jr. (Ed.), Algebra for Everyone (Session 1) (pp. 7-23). Reproduced with Permission from Algebra for Everyone by the National Council of Teachers of Mathematics.
- Inprasitha, M. (2011). One Feature of Adaptive Lesson Study in Thailand: Designing a Learning Unit. Journal of Science and Mathematics Education in Southeast Asia, 34, 47-66.
- Inprasitha, M. (2013). Paper presented at “Workshop for Teachers in the Project School ofMathematics Teachers Professional Development using Lesson Study and Open Approachfor conducting Lesson Study and Open Approach, KhonKaen University”.
- Inprasitha, M. (2014). Paper Presented at “Workshop on Lesson Study and Open Approach for Demonstration School’s Teachers, Khon Kaen University”. Khon Kaen: Khon Kaen University.
- Inprasitha, M. (2016a). Personal Communication. Khon Kaen: Khon Kaen University. 19 March 2016
- Inprasitha, M. (2016b). Personal Communication. Khon Kaen: Khon Kaen University. 9 August 2016
- Isoda, M. (2010). Lesson Study: Problem Solving Approaches in Mathematics Education as a Japanese Experience. Procedia Social and Behavioral Sciences, 8, 17-27. https://doi.org/10.1016/j.sbspro.2010.12.003