| Summary: | 碩士 === 國立台中師範學院 === 初等教育學系 === 83 === The purposes of this study were to investigate elementary-
school-students'''''''' conception and thinking strategies in
multiplication and division word problems. The theoretical
orientation of the research was based on the "implicit model"
propounded by E. Fischbein et al.(1985). This research was the
first study to join the analysis of "item relational structure"
(IRS) and "item response theory of non-parameter", developed
by Fu-shen Teng.
By interviewing, this study found the following results.
A. Children based on the expected results to choose a proper
operation.
B. Children chose a relatively smaller number in the problems
to divide the larger one.
C. Children preferred to use a whole number as a multiplier
or divisor.
D. Children used the unit associated with the anticipated
result as a hint for determining the proper multiplicand or
dividend.
According the analyzing of "IRS", the results were as
follows:
A. The number types of multipliers were the influential
factor of item difficulity.
B. The partition word problems revealed the rules of "a
larger number is divided by a smaller number"(LDS) and "the
multiplier or divisor is an integer" (MDI). These rules
influenced the difficulity of test items.
C. About quotation word problems, the rule of "LDS"
influenced the difficulity of test items.
Similarly, by using "item response theory of non-parameter"
, the results were as follows:
A. The multiplication word problems indicated five ICC types.
The number types of multipliers were the influential factor of
item difficulity.
B. The partition word problems revealed three ICC types. The
rules of "LDS" and "MDI" influenced the ICC types and difficulity
of test items.
C. The quotation word problems indicated three ICC types. The
rule of "LDS" influenced the ICC types and difficulity of test
items.
Accoring to the above results, this study prove the "implicit
model". The author also raise another advanced and different
explanation for this model.
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