Overcoming intuitive interference in mathematics: insights from behavioral, brain imaging and intervention studies

Abstract

It is well known that many students encounter difficulties when solving problems in mathematics. Research indicates that some of these difficulties may stem from intuitive interference with formal/logical reasoning. Our research aims at deepening the understanding of these difficulties and their underlying reasoning mechanisms to help students overcome them. For this purpose we carried out behavioral, brain imaging and intervention studies focusing on a previously demonstrated obstacle in mathematics education. The literature reports that many students believe that shapes with a larger area must have a larger perimeter. We measured the accuracy of responses, reaction time, and neural correlates (by fMRI) while participants compared the perimeters of geometrical shapes in two conditions: (1) congruent, in which correct response was in line with intuitive reasoning (larger area-larger perimeter) and (2) incongruent, in which the correct answer was counterintuitive. In the incongruent condition, accuracy dropped and reaction time for correct responses was longer than in the congruent condition. The congruent condition activated bilateral parietal brain areas, known to be involved in the comparison of quantities, while correctly answering the incongruent condition activated bilateral prefrontal areas known for their executive control over other brain regions. The intervention, during which students' attention was drawn to the relevant variable, increased accuracy in the incongruent condition, while reaction times increased in both congruent and incongruent conditions. The findings of the three studies point to the importance of control mechanisms in overcoming intuitive interference in mathematics. Overall, it appears that adding a cognitive neuroscience perspective to mathematics education research can contribute to a better understanding of students' difficulties and reasoning processes. Such information is important for educational research and practice.

Investigating a case of hidden misinterpretations of an additive word problem: structural substitution

“…These observations confirm that the presence or absence of particular mathematical knowledge does not directly produce structure substitution. Our data supports the idea of the main role that control mechanisms play in the reasoning and interpretation process (Giroux and Ste-Marie 2001;Masson et al 2012;Stavy and Babai 2010).…”

“…Stavy and Babai (2010) used the method of brain imaging to analyse the process of solving certain geometric problems. Their results showed that while the mathematical concepts at play were the same in all problems, there was a tendency for a different part of the brain to be more activated than the rest depending on the geometric condition.…”

“…According to some research in neuro-education (Masson et al 2012;Stavy and Babai 2010), the prefrontal region of the brain, known for its inhibitory control over other regions, actively participates when a non-trivial situation occurs: a straightforward intuitive solution is overlooked and replaced by another one. It is possible that in the structure substitution model described above, the lack of critical control over the whole process plays an important role.…”

The neuroscience of conceptual learning in science and mathematics

“…A key element of learning any new concepts is the need to overcome strongly held prior beliefs about a domain before new knowledge can be effectively assimilated 14,15 . Thus, a major challenge in mathematics and science education is the need for children to inhibit pre-existing beliefs or superficial perception in order to engage in acquiring and applying new and counterintuitive knowledge 13,16,17,18 . Because of the importance of this process in scientific reasoning, many researchers have focused on investigating the naïve concepts that children and adults hold about phenomena in various scientific domains.…”

Fundamental Concepts Bridging Education and the Brain

“…However, the same team of researchers (Houdé et al, 2000) also found that adults who were trained to overcome a perceptual bias leading to wrong answers in a deductive logic task showed more activation after rather than before training in frontal lobe areas involved in inhibition. Other researchers (Stavy & Babai, 2010) found that the activation of brain areas related to inhibition is also correlated to the capacity to correctly answer counter-intuitive questions about the perimeter of figures.…”