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 1st 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.
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