The Four-Card Problem Resolved? Proportional Reasoning and Reasoning to a Contradiction.

This study hypothesized that subjects who display proportional responses on the Pouring Water Task have developed the ability to comprehend logical arguments of the form referred to as "reasoning to a contradiction," while subjects who display additive responses on the same task have not. To test this hypothesis, 100 additive and proportional high school subjects (mean age 16.4 years) were administered three versions of a four-card task requiring them to reason to a contradiction before, immediately after, and one month after verbal instruction in the use of the reasoning pattern. Results were generally as predicted as most of the additive subjects failed the immediate and delayed posttest problems (62 percent and 80 percent respectively) while most of the proportional subjects succeeded (80 percent and 71 percent respectively). Group differences were significant (p less than .001). Since science is an enterprise based upon the process of falsification of hypothesis, it seems clear that this fundamental property is lost on many students as indicated by the results. Clearly, if these students are to grasp this property, a far greater effort by teachers and curriculum developers will have to be made. (Author/JN)