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.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0720105-140614 |
| Date | 20 July 2005 |
| Creators | Chuang, Sung-chieh |
| Contributors | Shian Leou, Shuk-Kwan Leung, Tzyh-chiang Ning |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0720105-140614 |
| Rights | off_campus_withheld, Copyright information available at source archive |
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