Acquisition and use of mental operators: effects of type of practice

Planning interactions with the physical world requires knowledge about operations; in short, mental operators. Abstractness of content and directionality of access are two important properties to characterize the representational units of this kind of knowledge. Combining these properties allows four classes of knowledge units to be distinguished that can be found in the literature: (a) rules, (b) mental models or schemata, (c) instances, and (d) episodes or chunks. The influence of practicing alphabet-arithmetic operators in a prognostic, diagnostic, or retrognostic way (A + 2 = ?, A? = C, or ? + 2 = C, respectively) on the use of that knowledge in a subsequent test was used to assess the importance of these dimensions. At the beginning, the retrognostic use of knowledge was worse than the prognostic use, although identical operations were involved (A + 2 = ? vs. ? - 2 = A). This disadvantage was reduced with increased practice. Test performance was best if the task and the letter pairs were the same as in the acquisition phase. Overall, the findings support theories proposing multiple representational units of mental operators. The disadvantage for the retrognosis task was recovered in the test phase, and may be evidence for the importance of the order of events independent of the order of experience.