The role of prior knowledge, executive function, and perceived cognitive load on the effectiveness of faded worked examples in geometry

Abstract

Mathematics remains a subject many students fail to become competent in by the time they graduate from high school. Most students often require one on one, individualized tutoring to help them reach competence. That remains a challenge since most classrooms are understaffed and underfunded, frequently having only one teacher in a overpopulated classroom. One strategy that has been used to alleviate some of this over reliance on the teacher has been faded worked examples, or fading. Fading is the successive removal of the last steps in a series of problems until the student is solving problems completely on their own. The current study aimed to determine whether fading improves learning, and for whom. The goal was to compare fading with business as usual (control), worked examples with self-explanations, and fading with self-explanations. Specifically, I was interested in the following research questions: (1) Do the three experimental conditions differ in promoting posttest scores on surface area and volume? (2) Do the three experimental conditions differ in promoting conceptual knowledge and procedural knowledge of surface area and volume at posttest? and (3) When interaction terms are created between student profiles and conditions within regression analyses, which profiles explain significant variance in posttest scores? Repeated measures analysis of variance, principle axis factor analysis, and simple linear regressions were used to examine the differences between conditions at posttest, to create propensity scores, and to determine whether there were any interactions between propensity scores and conditions. Results indicated a significant effect of fading on posttest scores. A regression with propensity factors indicated that the fading conditions appeared to benefit low propensity students moreso than high propensity students. Findings are discussed in terms of educational implications and future research that can complement these findings to contribute to future research.