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|Title: ||Taiwanese Junior High School Students’ Understanding About the Validity of Conditional Statements|
|Authors: ||Wu Yu, Jya-Yi;Chin, Erh-Tsung;Lin, Chia-Jung|
|Keywords: ||Assertion;Conditional statement;Correctness;Junior high school;Mathematical reasoning;Proof;Truth;Validity|
|Issue Date: ||2012-07-03T02:37:52Z
|Abstract: ||This research was designed to study Taiwanese junior high school students’|
understanding about the validity of conditional statements. Distinguishing between validity
and truth is a crucial topic in mathematical reasoning and argumentation but has been
always neglected in the mathematics curriculum at junior high school level of schooling.
The aims of the survey were (1) to find out the methods Taiwanese junior high school
students used when conducting mathematical justification on conditional statements; (2) to
examine whether the students could distinguish between a statement and its converse
statement; (3) to analyse whether the correctness of a conditional statement influenced
the students to conduct mathematical reasoning and argumentation. Approaching the three
aims of the survey is expected to give some insights into the issue of whether the students
could distinguish between the validity of conditional statements and the truth of
assertions. Several thousand students from different schools which were randomly sampled
from within six geographically diverse (regions of Taiwan) were administered a test
on either algebra/number-pattern or geometry corresponding to their respective grades.
The main results were (1) the methods the students used when conducting mathematical
justifications on conditional statements were called producing (supporting- or counter-)
example(s), analytical narrative, and analytical formal; (2) over a third of those students,
who considered the given conditional statement to be valid or invalid, proposed supportingor
counter-example(s), respectively; (3) over half the students considered the statement and
its converse to be the same; (4) students’ reasoning performance was influenced by their
opinions of the correctness of the conditional statements. These results seem to lead to
the conclusion that most of these students could not distinguish between the validity of
conditional statements and the truth of assertions.
|Relation: ||International Journal of Science and Mathematics Education, 2(2): 257-285|
|Appears in Collections:||[科學教育研究所] 期刊論文|
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