### Title page for etd-0720105-140614

URN etd-0720105-140614 Sung-chieh Chuang windowxx5408@yahoo.com.tw This thesis had been viewed 5385 times. Download 2552 times. Education 2004 2 Master zh-TW.Big5 Chinese A Study on the Concept of Unknown and Problem-Solving Process Among Different Graders in Concrete Situations 2005-05-30 213 Problem-solving process Unknown Algebra Semi-structured interview The aim of this study is to explore different graders’ concept of unknown and performance in solving equations in concrete situations. In recent years of early algebra research in the United States (Carraher, Schliemann, & Schwartz, in press), it was found that through systematic teaching, low and middle graders’ algebra performance was better than the same or even higher graders without teaching. Therefore, semi-structured interview was adopted to collect data on three cases: a second-grader, a fifth-grader and a seventh-grader who were using textbooks that follow Grade one-nine Integrated Coordinate Curriculum in SY89. The interview questions included addition and subtraction CHANGE problems, as well as multiplication and division EQUAL GROUPS problems; with natural numbers below 20, and given in four types: one-step, two-steps mixed, relating two unknowns and comparing two unknowns. Data analysis was conducted by referring to three sources of data: protocols from interviews, children’s problem-solving records and interviewer’s observation records. Research findings were: all three cases that received guidance could use equations to express problems; “Undoing” was the most frequently used problem-solving strategy; both second and fifth graders could simplify expressions by number properties in concrete situations; both fifth and seventh graders could check if answers were reasonable; the meaning of equal sign developed from “finding the results of” to “equality in measures”; and, individual differences in “trial and error substitution” among three cases. Such results were consistent to that of Carraher. It is suggested that, introducing early algebra in the elementary school is helpful to children’s learning of formal algebra in the junior high school. Shian Leou - chair Tzyh-chiang Ning - co-chair Shuk-Kwan Leung - advisor indicate in-campus access immediately and off_campus access in a year 2005-07-20

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