Literature Index

Technology-based problem-solving models are being successfully implemented in the mathematics curriculum. This study focused on enhancing problem-solving ability by supplementing traditional instruction in statistics with metacognitively-cued, computer-coached activities. The purposes of this study were to investigate the: (1) differences in ability to solve basic, statistical word problems when comparing a metacognitively-cued, computer-tool (MCCT) group to a metacognitively-cued, computer-coached (MCCC) group; (2) differences in metacognitive ability while solving basic, statistical word problems when comparing a MCCT group to a MCCC group; (3) relationship between problem-solving ability and metacognitive ability while solving basic statistical word problems. A sample of 120 community college, elementary statistics students was divided into four sections with a MCCT and a MCCC group at one time period and a MCCT and a MCCC group at a different time period. Treatments lasted eight weeks of a summer semester. Dependent variables were ability to solve basic statistical word problems as measured by a teacher-made test and ability to think metacognitively while solving the word problems, as measured by the Assessment of Cognition Monitoring Effectiveness (ACME) procedure. The students were also measured on the quality of their responses to written metacognitive cues while solving a basic statistical word problem before each of the exams during the experiment. The dependent variables were measured at five different times throughout the semester. It was expected that the metacognitively-cued, computer-coached groups would show the most improvement and metacognitively-cued, computer-tool groups would show the least improvement on all measures. The data analysis revealed that the apparent difference in problem-solving ability between the MCCT groups and the MCCC groups grew as the study progressed, achieving statistical significance at the last testing, with the MCCC groups being significantly higher at the last testing. The MCCC groups also demonstrated significant higher metacognitive-ability. In addition, significant correlations were found between problem-solving ability and metacognitive ability, ranging from .28 to .66. The presence of some significant teacher effects suggests that the effectiveness of coaching software may be affected by instructional strategy.

Innovation and efficiency were examined for their effects on collaboration and learning in two experiments with university students. From the first experiment, the Innovation task promoted more knowledge-sharing behaviors than the Efficiency task. In the second experiment (built from the first experiment), participants learned about the Chi-square formula and their understanding of it was assessed with basic calculation questions, comprehension questions, and difficult transfer problems. As part of the transfer problems, a preparation for future learning (PFL) assessment was used to measure participants' ability to adapt their knowledge of the chi-square formula (Bransford & Schwartz, 1999). Participants in the Innovation condition scored significantly higher on the transfer problems, and Innovation dyads showed he greatest performance on the target PFL question.

A long-standing belief is that statistical rules helpful in solving practical problems do not transfer beyond the subject matter domain in which they were learned. Recent research by G. T. Fong, D. H. Krantz, and R. E. Nisbett (1986) challenges this belief. Fong et al. showed that instructing learners about abstract rules, such as the law of large numbers, improved reasoning about ill-defined problems and transferred to solving everyday statistical problems that involved probabilistic relations. Fong et al.'s research is extended in 3 experiments with 276 university, secondary, and middle school students. The law-of-large-numbers heuristic was taught in regular classroom settings and students' abilities to solve ill-structured, everyday problems were tested. Students learned a good deal about how to reason statistically, and these gains generalized over different structures of problems and topics. The results support a revival of formalist views of transfer, that teaching formal rules about inference making can improve reasoning and support transfer.

The purpose of the current research was to assess whether egocentric perceptions do occur in a variety of settings and to examine associated psychological processes.