Student’s Concepts of Subtraction in Mathematics Classroom Using Lesson Study and Open Approach

Abstract

The purpose of this research was to analyze mathematical concept of students through mathematical representation in the classroom of using Lesson Study and Open Approach. The target group of this research was 25 Grade 1 students at Bansomkob (Ratradbamrung) School, Kaset Sombun District, Chaiyaphum Province in the academic year 2016. The school has been participating in the Project of Development of student’s Mathematics Higher-Order Thinking at North East of Thailand, and also the professional development process through Lesson Study and Open Approach of Inprasitha [6]’s framework. The collected data included: 1) protocol data transcribed from voice and video recorders during classroom instruction 2) students’ writings and 3) protocol from interviews with students. The data were analyzed by using Vergnaud [15]’s conceptual framework. The results of this research indicated that student’s concepts of subtraction in mathematics classroom using Lesson Study and Open Approach consisted of 1) set of situations: students were involved to the real world situations which was meaningful to them so they could describe the situations while ‘take away’ and the number of objects in the situations decreased and ‘Take different’ they could describe situations that there was one more thing than one. 2) set of operational invariant: students’ concept of subtraction ‘take away’ students presented the problem solving by removing objects from the situations so the number was decreased, while the similar or analogous operation occurred in each situation repeatedly in relation to other situations until become operational invariant and students’ concept of subtraction ‘take different’ students presented the problem solving by operation of matching for comparison was also found before figuring out the emergent number of the concept on subtraction of taking different. and 3) set of symbolic representations: students used symbols as sentences or words through the forms of natural language such as being ‘expelled, ‘scooped out’, ‘disappeared’, ‘none’, ‘given’, in concept of ‘take away’ and ‘over’ in concept of ‘take different’ as well as the sentences or words in mathematical language and other symbols which included number sentence, mathematical sign drawing a line, circle, and arrow for representing the operation of being ‘took out’, ‘eaten’, ‘gone, and ‘took away’ whereas concept of ‘take different’ student drew line to matching one to one thing and drawing a line, circle, and arrow for representing the operation of ‘over’