engleski

Metacognitive feelings and the illusion of linearity

The illusion of linearity is the tendency to comprehend certain sizes as linearly related, even when such understanding is not justified. This illusion is manifested in providing linear answers in non-linear tasks. It occurs due to linearity heuristic, that is, intuitive and automatic, but sometimes erroneous and biased type of information processing. It is assumed that mathematical education that is focused on procedural knowledge and routine expertise is important in appearance and maintenance of the illusion of linearity. In order to override linearity heuristic, people need to scrutinize information. The trigger for engaging this analytical and rational type of information processing are metacognitive feelings, which represent experiential experiences that inform person about cognitive processing, and serve as the interface between some task and the person. For instance, when people have lower metacognitive feeling of rightness (FOR), they are more inclined to deeply analyse their responses. The role of metacognitive feeling, as well as conceptual and procedural knowledge, in the occurrence of the illusion of linearity has not been thoroughly explored. Therefore, the aim of our research was to examine whether interventions focused on students’ conceptual and procedural knowledge would effect on their FOR and consequently the illusion of linearity. The participants were high-school students (N=908), who solved five linear and five non- linear tasks randomly presented on the computer and had different instructions about task solving. While some students had conceptual instruction, the other had procedural instruction, and both instructions were grounded in productive failure method. There was also the control group. In our study students answered in accordance with the illusion of linearity. The results showed that conceptual and procedural instructions decreased the illusion of linearity. Students who had lower FOR were more inclined to analyse their answers and spent more time on thinking about tasks. It can be concluded that metacognitive feelings have an important role in understanding and decreasing of the illusion of linearity.

the illusion of linearity ; metacognitive feelings ; conceptual knowledge ; procedural knowledge

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