Negation, disjunctive syllogisms, and mathematics achievement

It was hypothesized that high math achievement students would correctly assess syllogisms with positively and negatively worded premise statements more often than students of low math achievement, and that they would be more confident in their answers. The Mathematics Inventory I examination prepared by the School Mathematics Study Group and a disjunctive syllogism test authored by the investigator were administered to 550 male and female 8th/9th grade algebra students. Students with the top 150 and bottom 150 scores on the Mathematics Inventory made up the high and low groups. Findings revealed that students of high math achievement were not more competent in analyzing disjunctive syllogisms than students of low math achievement, nor did they express more confidence in their responses. Unexpectedly, low math achievement students were more competent with syllogisms of the form PVQ, ∼ P and PVQ, ∼ Q than high math achievement students. This was particularly true when at least one of the statements P or Q was negatively worded. As expected, students of high math achievement were more competent with forms of the type PVQ, P and PVQ, Q than low math achievement students. The observed differences, however, were not statistically significant.