Electronic Thesis and Dissertation Repository

Thesis Format



Master of Science




Ansari, Daniel


Knowledge of fraction magnitudes are an important, but notoriously difficult mathematical concept to master. Behavioural work has begun to explore and compare the instructional tools used for fraction learning. However, how fraction instructional tools are processed in the brain remains an underexplored question. Therefore, in the present thesis, we used functional brain MRI methodology to examine the neural activity of adult participants while completing a fraction verification task using the number line and area model, two common methods of fraction learning. We found that both models commonly recruited fronto-parietal activity, the neural regions typically implicated in number processing. However, we also found specific clusters of activation in frontal and parietal regions that displayed a greater response to area models. Given that participants indicated a greater familiarity with the area model, we suggest this could arise due to differences in strategy employed when using the number line and area model formats.

Summary for Lay Audience

As the classic joke goes, “6 out of 5 people struggle to understand fractions”. Unfortunately, this joke holds some truth, as many studies have documented that both children and educated adults struggle considerably to understand fraction magnitude. As a result, this raises the question of whether methods used for teaching fractions are not effective instructional approaches. In the past, mathematics curriculums have predominantly relied on use of the area/pie model for teaching fraction magnitudes. However, recently, there has been a growing push to emphasize number line use in early fraction learning instead. Indeed, behavioural work has supported the notion that the number line is an effective model for fraction magnitude learning. However, it currently remains unknown how the brain processes magnitude in number line and area model formats. The inclusion of neuroimaging can complement our knowledge from the behavioural literature and can provide valuable insight towards best practices for fraction learning. Therefore, in this thesis, we used functional brain MRI methodology to explore commonalities and differences in how the brain processes fraction magnitude in number line and area model formats. Through this, we found that while the two models were processed in the brain highly similarly (both recruiting regions of the brain typically involved in magnitude processing), there were also regions within this network that were activated to a greater extent by the area model. We suggest that it is possible that these differences arose because the participants in our sample had a greater familiarity with the area model. Therefore, it is possible that there were different approaches taken when completing trials in number line and area model format. However, we encourage future work to explore this question more directly to obtain better insight towards the mechanisms that may be causing these differences between the models at the level of the brain. Given that our study is the first to directly explore how the brain processes fraction instructional models, we believe this can serve as a strong framework for future neuroimaging studies exploring fraction learning. Ultimately, we hope this will improve our knowledge regarding best practices for fraction learning.