Educational Alternatives, Volume 16, 2018

Abstract: In spatial geometry instruction, investigating study-time allocation has the potential to further guide and assist the quest of understanding visual difficulty, and to shed additional light on the issue of using prototypes. Many classroom practices are designed based on the intuitive belief that difficulty increases the time allocated for learning. However, empirical findings from studies on metacognition show this is not always so. Research on metacognition suggests two theoretical explanations: 1) the Difficulty Reduction model intended to explain findings explaining simple cognitive tasks, and 2) the Region of Proximal Learning framework, explaining complex cognitive tasks. This preliminary study attempted to empirically examine study-time allocated for perceiving 3-D geometrical situations from 2-D sketches in spatial geometry tasks. The study aimed at debating the two theories about study-time allocation by using a priori measure of visual difficulty of 2-D sketches depicting cubes with auxiliary constructions. 12 corresponding pairs of normatively and un-normatively oriented cube-related sketches of different visual difficulty levels were individually approached by 174 12th grade high-school students, studying mathematics at the highest stream level. Data consisted of self-reported study-time while attending these sketches. Findings show that transforming the sketches’ orientation from normative to un-normative, triggered a substantial change in the metacognitive mechanisms involved in decisions about study-time allocated to learning. This may indicate that a greater cognitive complexity is involved in comprehending un-normatively oriented sketches. Therefore, these preliminary findings have theoretical and practical implications for both spatial geometry instruction and metacognitive research.