EVOLUTION OF A STUDENT'S USE OF THE "a÷b" METHOD: QUALITATIVE ANALYSIS OF DEVELOPMENT OF PROPORTIONAL REASONING THROUGH CLASSROOM INSTRUCTION

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In this paper, a student's use of a formal symbolic method for solving proportion problems is illustrated. The method was taught by teacher during the lessons in a fifth-grade classroom. The student's use of the method was idiosyncratic and evolving in nature, which was characterized by three phases : (i) incipient use, (ii) use with developing criteria, and (iii) purposeful use. It was through passing different phases that the change in her thinking strategies had occurred. She was in the process of developing consciousness regarding the unit that can be used to solve proportion problems.