EFFECT OF THE PRESENCE OF EXTERNAL REPRESENTATIONS ON ACCURACY AND REACTION TIME IN SOLVING MATHEMATICAL DOUBLE-CHOICE PROBLEMS BY STUDENTS OF DIFFERENT LEVELS OF INSTRUCTION

This study explores the effects of the presence of external representations of a mathematical object (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric figures. Performance was evaluated according to the reaction time (RT) required for solving the problem and the accuracy of the answer. Thirty high school students studying at high and regular levels of instruction in mathematics (HL and RL) were asked to solve half of the problems with ERs and half of the problems without ERs. Each task was solved by half of the students with ERs and by half of the students without ERs. We found main effects of the representation mode with particular effect on the RT and the main effects of the level of mathematical instruction and mathematical subject with particular influence on the accuracy of students’ responses. We explain our findings using the cognitive load theory and hypothesize that these findings are associated with the different cognitive processes related to geometry and algebra.     

Where Culture Takes Hold: “Overimitation” and Its Flexible Deployment in Western,Aboriginal, and Bushmen Children

Children often “overimitate,” comprehensively copying others' actions despite manifest perceptual cues to their causal ineffectuality. The inflexibility of this behavior renders its adaptive significance difficult to apprehend. This study explored the boundaries of overimitation in 3‐ to 6‐year‐old children of three distinct cultures: Westernized, urban Australians (N = 64 in Experiment 1; N = 19 in Experiment 2) and remote communities of South African Bushmen (N = 64) and Australian Aborigines (N = 19). Children overimitated at high frequency in all communities and generalized what they had learned about techniques and object affordances from one object to another. Overimitation thus provides a powerful means of acquiring and flexibly deploying cultural knowledge. The potency of such social learning was also documented compared to opportunities for exploration and practice.