Investigation of within- and cross-notation neural activation for fractions, percentages, and whole numbers

Lauren Schiller

Co-Presenters: Luis Rodriguez, Juan Gavilanes, Noah Mea, Anastasia Grubyak, Piper Rennerfeldt, Roberto Abreu-Mendoza, Jennifer Chen, Karen Woodruff, Miriam Rosenberg-Lee, Clarissa Thompson

College: College of Education

Department: Elementary and PE/Health Educ

Abstract:

Poor rational number knowledge has many consequences. Past research has mainly focused on assessing within-notation knowledge (e.g., which is larger: 5/6 vs. 7/9?), highlighting whole number bias as a critical challenge. Whole number bias involves a tendency to inappropriately apply whole number thinking to rational numbers (e.g., incorrectly stating 7/9 > 5/6, because the numerator/denominators are greater (i.e., 7 > 5 and 9 > 6)). Recently, my work has identified the importance of cross-notation knowledge (e.g., which is larger: 78% vs. 5/6?). Specifically, we uncovered a percentages-are-larger bias, where people are more likely to select a percentage as larger in cross-notation comparisons (e.g., incorrectly stating 78% > 5/6, but correctly identifying 83% > 7/9). Individuals with this percentages-are-larger bias have worse math outcomes, including reporting lower SAT/ACT scores. Thus, integrated number sense, the ability to flexibly estimate and compare rational numbers of different notations, is critical for mathematical success. The intraparietal sulcus (IPS), a key region for magnitude processing, has been implicated in rational number processing, and more recently the role of cognitive control regions such as the middle frontal gyrus (MFG), anterior cingulate cortex (ACC) and the insula has been explored in this context. However, prior studies have not considered percentages or cross-notation comparisons. Therefore, in our current study, we use functional MRI to investigate the neural processing of rational numbers within and across notations. We are recruiting right-handed young adults (N=20). Region of interest analyses will focus on IPS and cognitive control regions. Data collection is in progress, and we anticipate completion in the next few months. Planned comparisons involve examining brain activation during within-notation versus cross-notation tasks to determine which involves more cognitive control. Additional planned comparisons allow us to tease apart whether the neural processing involved in overcoming percentages-are-larger bias during fractions-to-percentage comparisons (e.g., 78% vs. 5/6) differs from that of whole number bias in fraction-to-fraction comparisons (e.g., 7/9 vs. 5/6). Understanding the brain responses involved in cross-notation versus within-notation processing in skilled adults can inform instructional practices to develop proficiency.