Taiwanese Junior High School Students’ Understanding about the Validity of Conditional Statements

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 supporting- or 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.